tidal modeling of an ancient tide dominated seaway part 1 model validation and application to global early cretaceous aptian tides abstract the utility of deep time global paleotidal modeling is evaluated with a series of modeling experiments focused on the early cretaceous aptian the results from a series of paleobathymetry sensitivity experiments indicate that despite paleogeographic and paleobathymetric uncertainty appropriate use of global paleotidal models complements and enhances stratigraphic and sedimentological methods before being applied to global paleotidal modeling the imperial college ocean model icom is validated for the computation of modern global tides the icom results only deviate slightly from a state of the art published model and were achieved with considerably less computational expense and without data assimilation the results from global paleotidal modeling of the early cretaceous aptian were assessed by comparison with the published geological record icom predicts high mesotidal to macrotidal ranges on the arabian platform around india especially to the north and west along the pacific coast between north and south america northeast of australia and around southeast asia the model predicts low microtidal ranges in the proto south atlantic ocean and weddell sea a further validation test assessed the ability of the model to predict the dominant tidal constituents diurnal or semidiurnal in the aptian lower greensand seaway of southeastern england and northern france during the aptian this region was connected to the boreal proto atlantic and neotethys oceans and now preserves superbly documented tidal deposits the model predicts low microtidal ranges in the proto central atlantic ocean and boreal ocean suggesting that they had little impact on tides in the lower greensand seaway higher tidal amplitudes especially of diurnal once daily tides are predicted in the northwestern neotethys ocean suggesting that this ocean was an important source of tidal energy to the lower greensand seaway sensitivity tests to paleogeographic and paleobathymetric uncertainty indicate that the model predictions are robust the prediction of predominantly diurnal tides is supported by published analyses of large dune scale deposits in the lower greensand of southeast england

observations of the internal tide in monterey canyon abstract data from two shipboard experiments in 1994 designed to observe the semidiurnal internal tide in monterey canyon reveal semidiurnal currents of about 20 cm s 1 which is an order of magnitude larger than the estimated barotropic tidal currents the kinetic and potential energy evidenced by isopycnal displacements of about 50 m was greatest along paths following the characteristics calculated from linear theory these energy ray paths are oriented nearly parallel to the canyon floor and may originate from large bathymetric features beyond the mouth of monterey bay energy propagated shoreward during the april experiment itex1 whereas a standing wave that is an internal seiche was observed in october itex2 the difference is attributed to changes in stratification between the two experiments higher energy levels were present during itex1 which took place near the spring phase of the fortnightly 14 8 days cycle in sea level while itex2 occurred close to the neap phase further evide

internal waves across the pacific 1 the long range propagation of the semidiurnal internal tide northward from the hawaiian ridge and its susceptibility to parametric subharmonic instability psi at the critical latitude c 28 8 n were examined in spring 2006 with intensive shipboard and moored observations spanning 25 37 n along a tidal beam velocity and shear at c were dominated by intense vertically standing inertially rotating bands of several hundred meters vertical wavelength these occurred in bursts following spring tide contrasting sharply with the downward propagating wind generated features seen at other latitudes these marginally stable layers which have inverse 16 meter richardson number ri16 1 0 7 are interpreted as the inertial waves resulting from psi of the internal tide elevated near inertial energy and parameterized diapycnal diffusivity and reduced asymmetry in upgoing downgoing energy were also observed at and equatorward of c yet simultaneous moored measurements of semidiurnal energy flux and 1 km deep velocity sections measured from the ship indicate that the internal tide propagates at least to 37 n with no detectable energy loss or phase discontinuity at c our observations indicate that psi occurs in the ocean with sufficient intensity to substantially alter the inertial shear field at and equatorward of c but that it does not appreciably disrupt the propagation of the tide at our location

energetics of the m2 barotropic ocean tides an estimate of bottom friction dissipation from a hydrodynamic model abstract the aim of this paper is to present a detailed energy budget of the m2 ocean tides over the world ocean based on the hydrodynamic tidal solution fes94 1 which includes not only the characteristics of the sea surface tidal elevations but also of the tidal currents global and regional budgets are given the global energy input by astronomical forcing deduced from the 2 2 spherical harmonic development of the m2 sea surface elevation solution is 2 35 tw lower by 0 1 tw than for the new altimetric solutions produced recently directly from satellite observations one major feature emerging from the present analysis is that a quarter of this energy input takes place over the south atlantic ocean on the other hand ocean tides work against astronomical forcing over three areas eastern indian ocean southwest of the south american continent and around new zealand this energy is dissipated in fes94 1 by bottom friction over the main continental shelves but the outstanding feature is that 40 of the tidal energy is dissipated over the north atlantic ocean energy is thus redistributed from the areas of energy input to feed the areas of dissipation the pacific ocean the indian ocean and the south atlantic ocean receive more energy in total than they dissipate in contrast with the atlantic ocean and the arctic ocean where a large deficit must be compensated by a net influx of energy from the other basins one third of the total m2 energy input by astronomical forcing over the world ocean flows northwards through the equatorial atlantic detailed energy dissipation estimates are computed over the different areas of energy dissipation and compared to the previous estimates published in the literature

once again once again tidal friction topex poseidon t p altimetry has reopened the problem of how tidal dissipation is to be allocated there is now general agreement of a m2 dissipation by 2 5 terawatts 1 tw 1012 w based on four quite separate astronomic observational programs allowing for the bodily tide dissipation of 0 1 tw leaves 2 4 tw for ocean dissipation the traditional disposal sites since jeffreys 1920 have been in the turbulent bottom boundary layer bbl of marginal seas and the modern estimate of about 2 1 tw is in this tradition but the distribution among the shallow seas has changed radically from time to time independent estimates of energy flux into the marginal seas are not in good agreement with the bbl estimates t p altimetry has contributed to the tidal problem in two important ways the assimilation of global altimetry into laplace tidal solutions has led to accurate representations of the global tides as evidenced by the very close agreement between the astronomic measurements and the computed 2 4 tw working of the moon on the global ocean second the detection by ray and mitchum 1996 of small surface manifestation of internal tides radiating away from the hawaiian chain has led to global estimates of 0 2 to 0 4 tw of conversion of surface tides to internal tides measurements of ocean microstructure yields 0 2 tw of global dissipation by pelagic turbulence away from topography we propose that pelagic turbulence is maintained by topographic scattering of barotropic into baroclinic tidal energy via internal tides and internal waves previous estimates by baines 1974 baines 1982 of this conversion along 150 000 km of continental coastlines gave a negligible 0 02 tw evidently the important conversion takes place along mid ocean ridges the maintenance of the abyssal global stratification requires a much larger expenditure of power 2 tw versus 0 2 tw this is usually attributed to wind forcing if tidal power is to play a significant role here then the bbl estimates need to be reduced the challenge is to estimate dissipation from the energy flux divergence in the t p adjusted tidal models without prior assumptions concerning the dissipation processes

new estimates of oceanic tidal energy dissipation from satellite altimetry as a novel approach to computing the flux of tidal power into shelf areas tidal maps of an oceanic area near the patagonian shelf are derived from 11 months of altimetry records from the geosat satellite power fluxes are computed from the maps through laplace s tidal equations flux vectors for m sub 2 clearly show a convergence on to the southern portion of the shelf sea and their total is nearly twice the loss computed by miller for that area a decrease of quality factor with frequency from m sub 2 to s sub 2 is in keeping with webb s hypothesis of shelf resonances at frequencies a little higher than the tidal band

accuracy assessment of recent ocean tide models over 20 global ocean tide models have been developed since 1994 primarily as a consequence of analysis of the precise altimetric measurements from topex poseidon and as a result of parallel developments in numerical tidal modeling and data assimilation this paper provides an accuracy assessment of 10 such tide models and discusses their benefits in many fields including geodesy oceanography and geophysics a variety of tests indicate that all these tide models agree within 2 3 cm in the deep ocean and they represent a significant improvement over the classical schwiderski 1980 model by approximately 5 cm rms as a result two tide models were selected for the reprocessing of topex poseidon geophysical data records in late 1995 current ocean tide models allow an improved observation of deep ocean surface dynamic topography using satellite altimetry other significant contributions include theft applications in an improved orbit computation for topex poseidon and other geodetic satellites to yield accurate predictions of earth rotation excitations and improved estimates of ocean loading corrections for geodetic observatories and to allow better separation of astronomical tides from phenomena with meteorological and geophysical origins the largest differences between these tide models occur in shallow waters indicating that the current models are still problematic in these areas future improvement of global tide models is anticipated with additional high quality altimeter data and with advances in numerical techniques to assimilate data into high resolution hydrodynamic models

simulation of barotropic and baroclinic tides off northern british columbia abstract the tidal response of northern british columbia coastal waters is studied through simulations with a three dimensional prognostic primitive equation model the model is forced at the boundaries with the leading semidiurnal and diurnal constituents and experiments with stratified and homogeneous fluid are compared the barotropic response shows good agreement with previously published studies of tides in the region a comparison with tide gauge measurements indicates that average relative rms differences between observations and the model surface elevation field are less than 5 for the largest constituents an internal tide is generated in cases where the model is initialized with a vertical stratification diagnostic calculations of the baroclinic energy flux are used to identify regions of generation and propagation of internal tidal energy with a representative summer stratification the integrated offshore flux is about 0 5 gigawatts higher than previously estimated from theoretical model

large scale circulation with locally enhanced vertical mixing abstract the influence of localized regions of intensified vertical mixing on the stratification and circulation in a large scale ocean model is investigated with idealized numerical experiments numerical solutions are obtained of a closed basin single hemisphere ocean model based on the planetary geostrophic equations mesoscale eddy effects are minimized and vertical mixing at the turbulent microscale is represented by a vertical diffusivity solutions with uniform are contrasted with a localized mixing solution in which increases by two orders of magnitude from its interior value 0 2 10 4 m2 s 1 in a region 500 km wide adjacent to the vertical eastern boundary when is uniform the stratification beneath the ventilated thermocline is characterized by a single vertical scale in contrast the localized vertical mixing supports a deep diffusive thermocline with two distinct vertical scales an internal boundary layer centered at the base of the ventilated thermocline roughly 1000 m

storms modify baroclinic energy fluxes in a seasonally stratified shelf sea inertial tidal interaction observations made near the celtic sea shelf edge are used to investigate the interaction between wind generated near inertial oscillations and the semidiurnal internal tide linear baroclinic energy fluxes within the near inertial f and semidiurnal m2 wave bands are calculated from measurements of velocity and density structure at two moorings located 40 km from the internal tidal generation zone over the 2 week deployment period the semidiurnal tide drove 28 48 w m 1 of energy directly on shelf little spring neap variability could be detected horizontal near inertial energy fluxes were an order of magnitude weaker but nonlinear interaction between the vertical shear of inertial oscillations and the vertical velocity associated with the semidiurnal internal tide led to a 25 43 increase in positive on shelf energy flux the phase relationship between f and m2 determines whether this nonlinear interaction enhances or dampens the linear tidal component of the flux and introduces a 2 day counter clockwise beating to the energy transport two very clear contrasting regimes of a tidally and b inertially driven shear and energy flux are captured in the observations

surface manifestation of internal tides in the deep ocean observations from altimetry and island gauges the sea surface height signatures of internal tides in the deep ocean amounting to a few centimeters or less are studied using two complementary measurement types satellite altimetry and island tide gauges altimetry can detect internal tides that maintain coherence with the astronomical forcing island gauges can monitor temporal variability which in some circumstances is due to internal tides varying in response to changes in the oceanic medium this latter mechanism is at work at hilo and other stations on the northern coasts of the hawaiian islands by detecting spatially coherent low frequency internal tide modulations the tide gauges along with inverted echo sounders at sea suggest that the mean internal tide is also spatially coherent satellite altimetry confirms this at hawaii and in many other places topex poseidon altimetry detects mean surface waves spatially coherent and propagating great distances 1000 km before decaying below background noise when temporal variability is small the altimetry plus information on ocean density sets useful constraints on energy fluxes into internal tides at the hawaiian ridge 15 gw of tidal power is being converted from barotropic to first mode baroclinic motion examples elsewhere warn that a simplistic interpretation of the altimetry without regard to variability noise or in situ information may be highly misleading with such uncertainties extension of the hawaiian results into a usefully realistic estimate of the global internal tide energy balance appears premature at this time

turbidity currents and submarine channel formation in rupert inlet british columbia 1 surge observations acoustic backscatter images obtained at 107 and 200 khz of surge type turbidity currents resulting from mine tailing discharge are presented excess densities in the head of the order of 100 kg m 3 are estimated from differences in acoustic backscatter intensity and in the amplitude of the bottom reflected signal these excess densities are comparable to estimates based on surge height and speed the speed being determined by assuming a universal head shape unlike gravity current surges from an impulsively started steady source the surge type turbidity flows consist of a high concentration slug of short duration followed by a longer lived wake in which sediment concentrations are lower by 2 3 orders of magnitude the profile of the high concentration slug resembles those for density slugs on small bottom slopes obtained in laboratory experiments discrete scatterers probably fish are observed to avoid the surges

the patagonian shelf tides the patagonian shelf tides constitute one of the strongest regimes among the biggest in the world where a significant amount of global tidal energy is dissipated by the effect of bottom friction in this paper the tidal response of the patagonian shelf is described by means of information generated by a numerical model and computations of energy fluxes and dissipation rates are presented since measurements of tidal elevations and currents on the patagonian shelf are scarce and mostly limited to coastal locations the information obtained from the model offers valuable insight in a region where a detailed description was not available particularly in the context of global tidal modelling the tidal regime on the patagonian shelf is dominated by the principal lunar semidiurnal tide m2 with contributions from other semidiurnal diurnal and fourth diurnal constituents this regional study shows that dissipation is highly localized and that the integrated value of the dissipation rate over the model domain constitutes a significant fraction of the estimated global dissipation

spatial variability of turbulent mixing in the abyssal ocean ocean microstructure data show that turbulent mixing in the deep brazil basin of the south atlantic ocean is weak at all depths above smooth abyssal plains and the south american continental rise the diapycnal diffusivity there was estimated to be less than or approximately equal to 0 1 x 10 4 meters squared per second in contrast mixing rates are large throughout the water column above the rough mid atlantic ridge and the diffusivity deduced for the bottom most 150 meters exceeds 5 x 10 4 meters squared per second such patterns in vertical mixing imply that abyssal circulations have complex spatial structures that are linked to the underlying bathymetry

numerical modeling of internal tide generation along the hawaiian ridge internal m2 tides near hawaii are investigated with a two dimensional two layer numerical model it is seen that along the hawaiian ridge barotropic tidal energy is transformed into baroclinic internal tides that propagate in both northeast and southwest directions as previously hypothesized the internal tide for a certain beam is seen to propagate well over 1000 km with an approximate decay scale of 1000 km an asymmetric pattern in the baroclinic energy flux is observed to the north and south of the hawaiian ridge due to the spatially inhomogeneous baroclinic energy sources the surface manifestation of the m2 internal tide in the model is compared with analysis results from topex poseidon satellite altimetry the baroclinic short wave variation of a few centimeters amplitude superposed on the barotropic surface amplitude agrees well with the altimeter analyses this together with snapshots of the interfacial disturbance allows the authors to sketch the propagation pattern of internal waves emanating northward and southward from the hawaiian ridge tidal current ellipses in the upper layer are dominated by the baroclinic internal tide with large spatial variability in their magnitude compared to the barotropic tidal ellipses the m2 baroclinic energy flux is over 10 kw m 21 for the strongest energy beam propagating toward the northeast along the western hawaiian ridge about 3 8 gw of tidal power is converted from barotropic to baroclinic motion the average northward or southward flux density for the first baroclinic mode is about 1 35 kw m21 in the western hawaiian ridge also if 2 7 kw m21 1 35 kw m21 to each direction is assumed for the whole 2000 km long hawaiian ridge a total of 5 4 gw is obtained this value indicates that there is still a large uncertainty in the rate of barotropic to radiating baroclinic energy conversion along the hawaiian ridge

tidal conversion at a submarine ridge the radiative flux of internal wave energy the tidal conversion powered by the oscillating flow of a uniformly stratified fluid over a two dimensional submarine ridge is computed using an integral equation method the problem is characterized by two nondimensional parameters a and b the first parameter a is the ridge half width scaled by h where h is the uniform depth of the ocean far from the ridge and is the inverse slope of internal tidal rays horizontal run over vertical rise the second parameter b i s the ridge height scaled by h two topographic profiles are considered a triangular or tent shaped ridge and a polynomial ridge with continuous topographic slope for both profiles complete coverage of the a b parameter space is obtained by reducing the problem to an integral equation which is then discretized and solved numerically it is shown that in the supercritical regime ray slopes steeper than topographic slopes the radiated power increases monotonically with b and decreases monotonically with a in the subcritical regime the radiated power has a complicated and nonmonotonic dependence on these parameters as a 0 recent results are recovered for the tidal conversion produced by a knife edge barrier it is shown analytically that the a 0 limit is regular if a 1 the reduction in tidal conversion below that at a 0 is proportional to a 2 further the knife edge model is shown to be indicative of both conversion rates and the structure of the radiated wave field over a broad region of the supercritical parameter space as a increases the topographic slopes become gentler and at a certain value of a the ridge becomes critical that is there is a single point on the flanks at which the topographic slope is equal to the slope of an internal tidal beam the conversion decreases continuously as a increases through this transition visualization of the disturbed buoyancy field shows prominent singular lines tidal beams in the case of a triangular ridge these beams originate at the crest of the triangle in the case of a supercritical polynomial ridge the beams originate at the shallowest point on the flank at which the topographic slope equals the ray slope

structure of the baroclinic tide generated at kaena ridge hawaii repeat transects of full depth density and velocity are used to quantify generation and radiation of the semidiurnal internal tide from kaena ridge hawaii a 20 km long transect was sampled every 3 h using expendable current profilers and the absolute velocity profiler phase and amplitude of the baroclinic velocity pressure and vertical displacement were computed as was the energy flux large barotropically induced isopycnal heaving and strong baroclinic energy flux divergence are observed on the steep flanks of the ridge where upward and downward beams radiate off ridge directly above kaena ridge strong kinetic energy density and weak net energy flux are argued to be a horizontally standing wave the phasing of velocity and vertical displacements is consistent with this interpretation results compare favorably with the merrifield and holloway model

dynamics of the long period tides abstract the long period tides are a tool for understanding oceanic motions at low frequencies and large scales here we review observations and theory of the fortnightly monthly and pole tide constitutents observations have been plagued by low signal to noise ratios and theory by the complex lateral geometry and great sensitivity to bottom slopes a new spectral element model is used to compute the oceanic response to tidal forcing at 2 week and monthly periods the general response is that of a heavily damped q 5 system with both the energy input from the moon and the dissipation strongly localized in space the high dissipation result is probably generally applicable to all low frequency barotropic oceanic motions over much of the ocean the response has both the character of a large scale and a superposed rossby wave like character thus vindicating two apparently conflicting earlier interpretations to the extent that free waves are excited they are consistent with their being dominated by rossby and topographic rossby wave components although gravity modes are also necessarily excited to some degree in general a modal representation is not very helpful the most active regions are the southern ocean and the western and northern north atlantic these results are stable to changes in geometry topography and tide period on a global average basis the dynamical response of mm is closer to equilibrium than is mf

energetics of barotropic and baroclinic tides in the monterey bay area abstracta detailed energy analysis of the barotropic and baroclinic m2 tides in the monterey bay area is performed the authors first derive a theoretical framework for analyzing internal tide energetics based on the complete form of the barotropic and baroclinic energy equations which include the full nonlinear and nonhydrostatic energy flux contributions as well as an improved evaluation of the available potential energy this approach is implemented in the stanford unstructured nonhydrostatic terrain following adaptive navier stokes simulator suntans results from three dimensional high resolution suntans simulations are analyzed to estimate the tidal energy partitioning among generation radiation and dissipation a 200 km 230 km domain including all typical topographic features in this region is used to represent the monterey bay area of the 152 mw energy lost from the barotropic tide approximately 133 mw 88 is converted into baroclinic energy through internal tide generation and 42 56

role of tides on the formation of the antarctic slope front at the weddell scotia confluence the structure of the antarctic slope front asf and the associated antarctic slope current asc on the scotia sea side of the weddell scotia confluence wsc is described using data from a hydrographic survey and three 1 year long moorings across the continental slope the asc in this region flows westward along isobaths with an annual mean speed of 0 2 m s 1 with time variability dominated by the k1 and o1 tidal diurnal constituents a narrowband oscillation with 2 week period attributable to the spring neap tidal cycle and seasonal variability realistic and idealized high resolution numerical simulations are used to determine the contribution of tides to the structure of the asf and the speed of the asc two simulations forced by realistic atmospheric forcing and boundary conditions integrated with and without tidal forcing show that tidal forcing is essential to reproduce the measured asf asc cross slope structure the time variability at our moorings and the reduced stratification within the wsc two idealized simulations run with tide only forcing one with a homogeneous ocean and the other with initial vertical stratification that is laterally homogeneous show that tides can generate the asc and asf through volume flux convergence along the slope initiated by effects including the lagrangian component of tidal rectification and mixing at the seabed and in the stratified ocean interior climate models that exclude the effects of tides will not correctly represent the asf and asc or their influence on the injection of intermediate and dense waters from the wsc to the deep ocean

tides and the climate some speculations abstract the important role of tides in the mixing of the pelagic oceans has been established by recent experiments and analyses the tide potential is modulated by long period orbital modulations previously loder and garrett found evidence for the 18 6 yr lunar nodal cycle in the sea surface temperatures of shallow seas in this paper the possible role of the 41 000 yr variation of the obliquity of the ecliptic is considered the obliquity modulation of tidal mixing by a few percent and the associated modulation in the meridional overturning circulation moc may play a role comparable to the obliquity modulation of the incoming solar radiation insolation a cornerstone of the milankovic theory of ice ages this speculation involves even more than the usual number of uncertainties found in climate speculations

surface manifestation of internal tides generated near hawaii analysis of topex poseidon satellite altimetry reveals short wavelength fluctuations in the ocean surface tide that are attributable to internal tides a significant fraction of the semidiurnal internal tide generated at the hawaiian ridge is evidently phase locked to the astronomical potential and can modulate the amplitude of the surface tide by 5 cm the internal tide is thus easily mapped along satellite groundtracks and it is found to be spatially coherent over great distances with waves propagating well over 1000 km from the hawaiian ridge before decaying below noise level both first and second baroclinic modes are observed in both the m 2 lunar and s 2 solar tides the high space time coherence is in sharp contrast to what is often inferred from current meter observations but it confirms recent speculations from an acoustic experiment north of hawaii

insar monitoring of progressive land subsidence in neyshabour northeast iran summary the area of neyshabour a small historical city located in northeast iran is subject to land subsidence to monitor the temporal evolution of the subsidence the small baseline subset sbas algorithm is used for interferometric synthetic aperture radar sar time series analysis to limit the spatial and temporal decorrelation phenomena the interferograms produced from the raw envisat asar data are characterized by small spatial and temporal baselines accordingly four independent sar acquisition data sets separated by large spatial and temporal baselines are used in the time series analysis to link the separate data sets a smoothing constraint that minimizes the curvature of the subsidence temporal evolution is added to the least squares method the optimum smoothing factor estimated in the smoothed time series analysis reduces the atmospheric noise unwrapping and orbital errors whereas it preserves the non linear seasonal deformation features the time series results show an incremental lowering of the ground surface accompanied by small seasonal effects the mean los deformation velocity map computed from the time series analysis demonstrates a considerable subsidence rate of up to 19 cm yr 1 comparison between the insar time series and continuous gps measurements verifies the accuracy of the obtained results moreover the quantitative integration of the insar derived displacement measurements with observations of the hydraulic head fluctuations causing these displacements yields information about the compressibility and storage properties of the aquifer system

global tectonics under g having a minute westward tilt the convection seen to affect moon s mantle takes place under gravity having a component of asymmetry in the form of a minute westward slope or tilt constituting the external part of the field its effect is explored employing the equivalent potential denominated its nature is to bias convection of internal origin inducing east west polarization of a type prominent in global tectonics separately research at harvard has shown that by causing advection of non hydrostatic masses within the heterogeneous mantle deep seated convection inevitably displaces the axis of maximum moment compelling polar wander a reconstruction based on observed dissipation suggests that the combined effect of these factors is to contribute a not inconsiderable low latitude surface west component to the structure of the convection cumulative alteration in the direction west must eventually require global rearrangement of its cell structure offering explanation of the abrupt mesozoic tertiary transition and progressive net lithosphere rotation

semi diurnal and diurnal tidal dissipation from topex poseidon altimetry 1 tidal energy dissipation is estimated for eight semi diurnal and diurnal constituents using a global inverse solution constrained by topex poseidon altimeter data very similar spatial patterns are obtained for all semi diurnal constituents with about one third of the total dissipation occurring in the deep ocean over rough topography maps for diurnal constituents are also similar amongst themselves but quite different from the semi diurnal results for diurnals a smaller fraction of dissipation roughly 10 occurs in the deep ocean much of the difference can be explained by the very different spatial pattern of diurnal and semi diurnal tidal currents the lack of free internal waves at frequencies poleward of 30 at diurnal frequencies also probably plays a role limiting the effectiveness of baroclinic conversion as an energy sink for barotropic diurnal tides

estimates of m2 tidal energy dissipation from topex poseidon altimeter data most of the tidal energy dissipation in the ocean occurs in shallow seas as has long been recognized however recent work has suggested that a significant fraction of the dissipation perhaps 1 tw or more occurs in the deep ocean this paper builds further evidence for that conclusion more than 6 years of data from the topex poseidon satellite altimeter are used to map the tidal dissipation rate throughout the world ocean the dissipation rate is estimated as a balance between the rate of working by tidal forces and the energy flux divergence computed using currents derived by least squares fitting of the altimeter data and the shallow water equations such calculations require dynamical assumptions in particular about the nature of dissipation to assess sensitivity of dissipation estimates to input assumptions a large suite of tidal inversions based on a wide range of drag parameterizations and employing both real and synthetic altimeter data are compared these experiments and monte carlo error fields from a generalized inverse model are used to establish error uncertainties for the dissipation estimates owing to the tight constraints on tidal elevation fields provided by the altimeter area integrals of the energy balance are remarkably insensitive to required dynamical assumptions tidal energy dissipation is estimated for all major shallow seas excluding individual polar seas and compared with previous model and data based estimates dissipation in the open ocean is significantly enhanced around major bathymetric features in a manner consistent with simple theories for the generation of baroclinic tides

internal tidal currents and solitons in the southern bay of bengal abstract tidal currents and higher frequency internal solitons are observed from current and hydrographic fields that were recently measured at six deep water moorings in the southern bay of bengal by the naval research laboratory current temperature and salinity were measured in the upper 500 m of the water column between december 2013 and august 2015 harmonically fitted coherent tidal currents in the upper 500 m showed maximum amplitudes for the m2 constituent with velocities of the order of 3 cm s 1 m2 tidal ellipses were generally oriented towards the north northeast incoherent internal tides accounted for at least 60 of the total semidiurnal tide energy solitons were generated at multiple source regions along the andaman islands and contribute significantly to the high frequency energy greater than 1 cph solitons were present throughout the measurement period but their activity was reduced during the 2014 2015 winter monsoon soliton and internal tide amplitudes show a fortnightly modulation consistent with the spring neap cycle of the semidiurnal tide the interaction of tides and the associated high frequency waves 20 40 min periods with mesoscale eddies produced regions of enhanced shear and strain in the thermocline high strain regions were found within cyclonic eddies and high shear regions were found within anticyclonic eddies shear strain based dissipation models indicate that mixing rates can be enhanced by a factor of 3 5 by tidal and higher frequencies during interactions with eddies this study further suggests that tidal harmonics and internal tides have an important impact on the near surface currents away from coastal boundaries in the interior of the bay of bengal while the effects of the depth averaged tides are more important deeper in the water column

global abyssal mixing inferred from lowered adcp shear and ctd strain profiles abstract internal wave wave interaction theories and observations support a parameterization for the turbulent dissipation rate e and eddy diffusivity k that depends on internal wave shear vz2 and strain z2 variances its latest incarnation is applied to about 3500 lowered adcp ctd profiles from the indian pacific north atlantic and southern oceans inferred diffusivities k are functions of latitude and depth ranging from 0 03 10 4 m2 s 1 within 2 of the equator to 0 4 0 5 10 4 m2 s 1 at 50 70 diffusivities k also increase with depth in tropical and subtropical waters diffusivities below 4500 m depth exhibit a peak of 0 7 10 4 m2 s 1 between 20 and 30 latitudes where semidiurnal parametric subharmonic instability is expected to be active turbulence is highly heterogeneous though the bulk of the vertically integrated dissipation e is contributed from the main pycnocline hotspots in e show some correlation with small scale bottom roughness and near bottom flow at sites where st

topographically induced mixing around a shallow seamount measurements of the rate of dissipation of kinetic energy around a shallow seamount in the eastern north pacific show that mixing there is 100 to 10 000 times as large as that far away from the seamount if such values are typical of other seamounts mixing across density surfaces in the ocean occurs mainly at their boundaries and topographically induced mixing may help to explain the discrepancy between the observed intensity of mixing in the interior of the oceans and that required to satisfy models of ocean circulation

a preliminary tidal analysis of topex poseidon altimetry approximately 12 months of data from the topex poseidon satellite altimeter mission are analyzed for the major short period oceanic tides a harmonic analysis is performed on data captured within bins defined on a deep ocean grid which owing to tidal aliasing considerations must have a relatively coarse spatial resolution our analysis is in terms of corrections to the schwiderski and cartwright ray models and it confirms many of the schwiderski differences previously reported by cartwright and ray our differences with respect to the geosat based cartwright and ray model form a sectorial pattern in m2 with high low differences separated roughly 180 in longitude we suggest that these sectorial errors were most likely induced by geosat s relatively large orbit error comparisons to independent data validate the improved topex poseidon solutions in situ ground truth shows m2 rms differences of 4 10cm schwiderski 3 86cm cartwright and ray 2 63cm this paper global rates of energy dissipation confirm earlier estimates for m2 and show improved agreement with satellite tracking studies for k1 and s2 these preliminary exercises confirm that topex poseidon should result in a new generation of improved global tidal models

secular effects of oceanic tidal dissipation on the moon s orbit and the earth s rotation the earth and moon are considered as a two body system in gravitational isolation from the sun and other planets the lunar orbit is taken as circular and the solid earth is assumed to be a rigid sphere with no tidal deformation so that there are no precessional torques other than those arising from the tidally deformed ocean numerical solutions to laplace s tidal equations with dissipation by linear bottom friction are used to obtain ocean wide distributions of tidal amplitude for two idealized continentalities a single circular continent spherical cap centered at the north pole and a single spherical cap centered on the equator calculations are made for two different values of the frictional resistance coefficient thus giving rise to four sets of solutions the computed tidal amplitudes are used to calculate the oceanic tidal torque which in turn is used to integrate the orbital equations backward in time for solution of the two body problem the coriolis parameter and the tidal frequencies change with time thus requiring that the tidal equations be solved several times during the course of each orbital integration in this manner the earth s rotational and the moon s orbital histories are determined on a geologic time scale for each of the four models the calculated position of the lunar orbit at 4 5 billion years ago is found to range from 38 to 53 earth radii in the four models and corresponds to a sidereal month of 330 to 550 hours the sidereal day would have been 12 to 18 hours with a relative inclination of 3 to 22 between the terrestrial and lunar poles these results are in sharp contrast to those from previous studies of the earth moon system most of which indicated a roche limit approach of the two bodies roughly 1 to 2 billion years ago and presented therefore a time scale difficulty in theories of lunar origin this contrast arises mainly from the fact that previous modelers avoided solution of laplace s tidal equations by prescribing a constant frictional phase lag angle between the angular position of the moon and the major axis of the second degree harmonic of the tidally deformed surface of the earth the amount of phase lag was established from the present astronomically deduced rate of tidal dissipation but this precluded dynamic variations in tidal torque over geologic time which are critical for determination of the orbital time scale the present rate of oceanic tidal dissipation is evidently anomalously high because of the near resonance of the oceanic response in both frequency and shape to the tidal forcing for the earth and moon to have evolved to their present separation from a distance of less than about 35 earth radii solely on the basis of oceanic tidal dissipation would have required the m2 response to have been near resonance for a significant portion of geologic history a rather implausible scenario the calculations reported here show that on the contrary frictional coupling between the earth and moon was much weaker than at present throughout most of the orbital history and consequently the moon s closest approach could not have been as small as 35 earth radii although idealized continentalities were used in these calculations the general conclusion of a weaker frictional coupling in the past is believed to be relatively insensitive to the continental configuration this is because at faster paleorotation the semidiurnal tidal frequencies would be resonant only with smaller scale normal modes of the ocean rather than with global scale modes as at present the time scale difficulty heretofore present in models of orbital evolution is thereby eliminated it should be noted that the orbital history developed here supports the theory of binary planetary accretion for lunar origin as opposed to fission or tidal capture

evidence for enhanced mixing over rough topography in the abyssal ocean the overturning circulation of the ocean plays an important role in modulating the earth s climate but whereas the mechanisms for the vertical transport of water into the deep ocean deep water formation at high latitudes and horizontal transport in ocean currents have been largely identified it is not clear how the compensating vertical transport of water from the depths to the surface is accomplished turbulent mixing across surfaces of constant density is the only viable mechanism for reducing the density of the water and enabling it to rise however measurements of the internal wave field the main source of energy for mixing and of turbulent dissipation rates have typically implied diffusivities across surfaces of equal density of only approximately 0 1 cm2 s 1 too small to account for the return flow here we report measurements of tracer dispersion and turbulent energy dissipation in the brazil basin that reveal diffusivities of 2 4 cm2 s 1 at a depth of 500 m above abyssal hills on the flank of the mid atlantic ridge and approximately 10 cm2 s 1 nearer the bottom this amount of mixing probably driven by breaking internal waves that are generated by tidal currents flowing over the rough bathymetry may be large enough to close the buoyancy budget for the brazil basin and suggests a mechanism for closing the global overturning circulation

a mechanism for local dissipation of internal tides generated at rough topography abstract fine and micro structure observations indicate that turbulent mixing is enhanced within o 1 km above rough topography enhanced mixing is associated with internal wave breaking and in many regions of the ocean has been linked to the breaking and dissipation of internal tides the generation and dissipation of internal tides are explored in this study using a high resolution two dimensional nonhydrostatic numerical model which explicitly resolves the instabilities leading to wave breaking configured in an idealized domain with a realistic multiscale topography and flow characteristics the control simulation chosen to represent the brazil basin region produces a vertical profile of energy dissipation and temporal characteristics of finescale motions that are consistent with observations results suggest that a significant fraction of mixing in the bottom o 1 km of the ocean is sustained by the transfer of energy from the large scale internal tides to smaller scale internal waves by nonlin

focusing of internal tides by near inertial waves the refraction of internal waves by lower frequency near inertial waves has been predicted theoretically but never observed before here we report observations of semi diurnal internal tides generated by the rough topography of the central indian ridge in the presence of a strong lower frequency near inertial wave field generated by a tropical storm the semi diurnal internal tide energy is trapped within upward propagating bands with a periodicity close to the inertial period a ray tracing model suggests that this trapping results from the internal tide refraction by the shear associated with near inertial waves this yields a strong increase of the internal tide energy and shear in space time regions where the background flow focuses the rays leading to the formation of caustics this mechanism may increase vertical mixing generated by baroclinic tides in the vicinity of mid ocean ridges in tropical regions

tidal data inversion interpolation and inference initial efforts in applying inverse methods to studies of ocean tides have focused on making the best use of a small number of observations to map tidal fields in a large area as such inversion can be viewed as an objective analysis scheme which uses a dynamically appropriate spatial covariance derived from the shallow water equations to interpolate and smooth a sparse data set data from recent altimetry missions are not sparsely distributed relative to tidal wavelengths in the open ocean apparently reducing the need for complicated dynamically based interpolation schemes altimetric data sets are also quite large making application of rigorous inversion methods to global tidal modeling a challenging computational problem we describe here a new iterative solution scheme which allows us for the first time to fit the full set of topex poseidon cross over differences the resulting solution tpxo 3 fits validation tide gauges significantly better than previous inverse solutions tpxo 3 also reduces residual cross over variances relative to other recent inverse and empirical solutions particularly in shallow water where improvements are dramatic with the new solution approach very significant improvements in global tidal models should be possible in shallow areas and in the vicinity of complex bathymetry where high accuracy tidal modeling remains a challenging problem with the recent improvements in the definition of tidal elevations in the open ocean it should now also be possible to resolve some long unanswered questions about tidal energetics and dynamics inverse methods provide a natural framework for addressing these issues and making inferences about tidal dynamics in particular by bringing data and dynamics together in a single solution we can rigorously test the consistency of the two we present results of global and local inversions which suggest that over elongated bathymetric features oriented perpendicular to tidal flows energy dissipation in the open ocean is significantly enhanced presumably due to conversion of barotropic tidal motions into baroclinic modes for the m2 tide our preliminary results suggest that perhaps as much as 0 5 tw of energy is dissipated in this manner however due to the simplified linear dynamics and limited spatial resolution used for our inversion there are significant uncertainties associated with these results a more careful application of inverse methods to make more rigorous inferences about tidal energetics including use of more reasonable prior dynamics and the highest possible spatial resolution should allow for closure of the tidal energy budget within the next few years

internal tide generation along the south scotia ridge abstract the generation of semidiurnal internal tides along the south scotia ridge ssr the boundary between the northern weddell sea and the scotia sea is investigated using a fully three dimensional primitive equation numerical model the sensitivity of the model to changes in horizontal and vertical grid spacing stratification and choice of bathymetric data set is discussed the highest resolution model 1 16 1 25 41 levels with realistic stratification produces an average along ridge lateral baroclinic m2 energy flux magnitude j m2 160 w m 1 for the section of the ssr between the tip of the antarctic peninsula and the south orkney plateau this value is 10 to time averaged open water fraction thus baroclinic tides may play a significant role in setting mean heat and freshwater exchange and ice formation in the northern weddell sea

indirect evidence for substantial damping of low mode internal tides in the open ocean a global high resolution ocean circulation model forced by atmospheric fields and the m2 tidal constituent is used to explore plausible scenarios for the damping of low mode internal tides the plausibility of different damping scenarios is tested by comparing the modeled barotropic tides with tpxo8 a highly accurate satellite altimetry constrained tide model and by comparing the modeled coherent baroclinic tide amplitudes against along track altimetry five scenarios are tested 1 a topographic internal wave drag argued here to represent the breaking of unresolved high vertical modes applied to the bottom flow default configuration 2 a wave drag applied to the barotropic flow 3 absence of wave drag 4 a substantial increase in quadratic bottom friction along the continental shelves with wave drag turned off and 5 application of wave drag to the barotropic flow at the same time that quadratic bottom friction is substantially increased along the shelves of the scenarios tested here the default configuration 1 yields the most accurate tides in all other scenarios 2 5 the lack of damping on open ocean baroclinic motions yields baroclinic tides that are too energetic and travel too far from their sources despite the presence of a vigorous mesoscale eddy field which can scatter and decohere internal tides in the model the barotropic tides are also less accurate in the absence of an open ocean damping on barotropic motions that is in scenarios 3 and 4 the results presented here suggest that low mode internal tides experience substantial damping in the open ocean

an introduction to the physical oceanography of six seamounts in the southwest indian ocean exploratory surveys of six seamounts in the southwest indian ocean provide a description of physical processes induced by seamounts along the southwest indian ridge mean currents 15 25 cm s 1 in the vicinity of each seamount were dominated by mesoscale eddies the dominant seamount driven process was the generation of internal tides by the barotropic tide interacting with the seamount crests this led to enhanced shear in the vicinity of the crests resulting in mixing where stratification was weak for example in the core of an anticyclonic mesoscale eddy or where there had been a winter mixed layer tidally driven up and downwelling was observed at the seabed with associated variability in bottom temperature of up to 3 c over a tidal cycle vertical displacement of isopycnals by internal tidal waves reached 200 m peak to trough fluorescence in the surface eutrophic layer could thus extend down to the seamount crest on each tidal cycle apparently spatial variations in short conductivity temperature depth sections across each seamount were probably aliased temporal variations from the strong tidal signal evidence for taylor caps or other potential trapped circulations at the seamount crest was weak most likely because currents associated with mesoscale eddies were too strong to allow their formation

latitudinal distribution of mixing rate caused by the m2 internal tide abstract ten years of ocean topography experiment topex poseidon tidal data and an energy balance relation are used to estimate the mixing rate caused by m2 internal tides in the upper ocean the results indicate that latitudinal distribution of the mixing rate has a generally symmetrical structure with respect to the equator the maxima are distributed around 28 9 n and 28 9 s and can be as high as 3 8 10 5 m2 s 1 in the pacific 5 10 5 m2 s 1 in the atlantic and 3 7 10 5 m2 s 1 in the indian oceans the minimum which is only 10 of those at 28 9 is located near the equator the data imply that midlatitudes are the key regions for internal tide mixing

significant dissipation of tidal energy in the deep ocean inferred from satellite altimeter data how and where the ocean tides dissipate their energy are long standing questions1 that have consequences ranging from the history of the moon2 to the mixing of the oceans3 historically the principal sink of tidal energy has been thought to be bottom friction in shallow seas4 5 there has long been suggestive evidence6 7 however that tidal dissipation also occurs in the open ocean through the scattering by ocean bottom topography of surface tides into internal waves but estimates of the magnitude of this possible sink have varied widely3 8 9 10 11 here we use satellite altimeter data from topex poseidon to map empirically the tidal energy dissipation we show that approximately 1012 watts that is 1 tw representing 25 30 of the total dissipation occurs in the deep ocean generally near areas of rough topography of the estimated 2 tw of mixing energy required to maintain the large scale thermohaline circulation of the ocean12 one half could therefore be provided by the tides with the other half coming from action13 on the surface of the ocean

empirical ocean tide models estimated from topex poseidon altimetry three empirical ocean tide models are determined from repeat cycles 10 to 78 of the topex poseidon t p altimeter mission the three models investigate the effects of the satellite orbit ephemeris on the ocean tides determined from t p altimetry and the effect of extracting the free core nutation resonance in the definition of the diurnal ocean tide admittance the altimetric data series use the joint gravity model jgm 2 geopotential orbit ephemeris and the preliminary jgm 3 orbit ephemeris computed at the university of texas center for space research the altimetric data from the t p mission are shown to have the precision necessary to estimate the monthly and fortnightly ocean tides in each bin inclusion of existing models of the ocean tides in the polar latitudes not sampled by the altimeter demonstrates the importance of these latitudes on spherical harmonic representations of the ocean tides the ocean tides are first estimated in bins of size 2 834 in longitude by 1 in latitude and then smoothed to 1 by 1 grids within 66 latitude the orthotide response formalism of groves and reynolds 1975 is used to represent the diurnal and semidiurnal ocean tides while a constant admittance is assumed across narrow bandwidths around each of the monthly mm fortnightly mf and termensual mt tidal components comparisons of the t p ocean tide models to tide gauge observations indicate their accuracies to be of the order of 2 3 cm the t p derived ocean tide models remove approximately 20 cm2 more of the t p measured sea surface variance than the cartwright and ray 1991 tide model and show a 19 cm2 and 15 cm2 improvement over the schwiderski 1980a b and cartwright and ray 1991 tide models respectively when compared to tide gauge estimates of the ocean tides

how can we improve a global ocean tide model at a regional scale a test on the yellow sea and the east china sea a global ocean model has been developed within the context of topex poseidon t p on the basis of a finite element hydrodynamic modeling approach combined with data assimilation based on the representer method the solution produced at global scale represents a spectacular improvement over what was available before the era of t p typically the mean discrepancy between the main tidal components and a hundred in situ tide gauges is 1 7 cm for m2 and 1 cm or less for the other components however the accuracies of this solution and of that produced by different authors within the t p tide working group are all worse near coastlines and over continental shelves this is the case for our finite element solution fes fes94 1 solution over the yellow sea and the east china sea ys ecs where the discrepancy is 33 cm for the m2 tide and 9 cm for the k1 tide when compared to a set of 192 tide gauges distributed along the coastlines this is due largely to the complex geometry of the basin and the limited knowledge of the bathymetry the aim of this paper is to investigate how our fes model can be improved with a dedicated application focused on one of the most energetic coastal basins the ys ecs 180 gigawatts for m2 i e 8 of the global energy dissipated in the whole ocean for this application a finite grid was implemented with a resolution down to 5 km along the coasts and over the continental shelf break particular attention was paid to bathymetry by complementing the etop05 database with regional maps sensitivity tests to the tuning of the bottom friction and the nonlinear interactions between the diurnal and semidiurnal components allow us to investigate the impact of dissipation parameterization and to produce an optimal solution without any data assimilation for nine main components of the tidal spectrum improvement by a factor of 2 m2 distance to the observations is now 17 5 cm global variance of 92 cm and k1 is 4 cm global variance of 21 cm as nonlinear components are significant over these basins the two main quarterdiurnal components are calculated the improvements are explained by five points 1 the choice of a mixed friction 2 a refinement of the mesh 3 a choice of reliable boundary conditions 4 a refined topography and 5 the use of a specific friction coefficient 1 5 10 3 surprisingly the energy budget for the m2 component leads to a dissipation similar to the value estimated by the global fes94 1 this is a major result of this study which leads us to the conclusion that when forcing a regional model with sea level boundary conditions along the open limits the simulated velocity field adjusts to the tuning of friction coefficients in order to dissipate the same amount of energy made available at its open boundaries

ocean tidal heating in icy satellites with solid shells abstract as a long term energy source tidal heating in subsurface oceans of icy satellites can influence their thermal rotational and orbital evolution and the sustainability of oceans we present a new theoretical treatment for tidal heating in thin subsurface oceans with overlying incompressible elastic shells of arbitrary thickness the stabilizing effect of an overlying shell damps ocean tides reducing tidal heating this effect is more pronounced on enceladus than on europa because the effective rigidity on a small body like enceladus is larger for the range of likely shell and ocean thicknesses of enceladus and europa the thin shell approximation of beuthe 2016 is generally accurate to less than about 4 explaining enceladus endogenic power radiated from the south polar terrain by ocean tidal heating requires ocean and shell thicknesses that are significantly smaller than the values inferred from gravity and topography constraints the time averaged surface distribution of ocean tidal heating is distinct from that due to dissipation in the solid shell with higher dissipation near the equator and poles for eccentricity and obliquity forcing respectively this can lead to unique horizontal shell thickness variations if the shell is conductive the surface displacement driven by eccentricity and obliquity forcing can have a phase lag relative to the forcing tidal potential due to the delayed ocean response for europa and enceladus eccentricity forcing generally produces greater tidal amplitudes due to the large eccentricity values relative to the obliquity values despite the small obliquity values obliquity forcing generally produces larger phase lags due to the generation of rossby haurwitz waves if europa s shell and ocean are respectively 10 and 100 km thick the tide amplitude and phase lag are 26 5 m and

the island scale internal wave climate of moorea french polynesia 1 analysis of five year records of temperatures and currents collected at moorea reveal strong internal wave activity at predominantly semi diurnal frequencies impacting reef slopes at depths 30 m around the entire island temperature changes of 1 5 c to 3 c are accompanied by surges of upward and onshore flow and vertical shear in onshore currents superimposed on annual temperature changes of approximately 3 c internal wave activity is high from oct may and markedly lower from jun sep the offshore pycnocline is broadly distributed with continuous stratification to at least 500 m depth and a subsurface fluorescence maximum above the strong nutricline at approximately 200 m minimum buoyancy periods range from 4 8 to 6 min with the maximum density gradient occurring at 50 to 60 m depth in summer and deepening to approximately 150 to 200 m in winter the bottom slope angle around all of moorea is super critical relative to the vertical stratification angle suggesting that energy propagating into shallow water is only a portion of total incident internal wave energy vertical gradient richardson numbers indicate dominance by density stability relative to current shear with relatively limited diapycnal mixing coherence and lagged cross correlation of semi diurnal temperature variation indicate complex patterns of inter site arrival of internal waves and no clear coherence or lagged correlation relationships among island sides semi diurnal and high frequency internal wave packets likely arrive on moorea from a combination of local and distant sources and may have important impacts for nutrient and particle fluxes in deep reef environments

interdependence of internal tide and lee wave generation at abyssal hills global calculations abstractthe generation of internal waves at abyssal hills has been proposed as an important source of bottom intensified mixing and a sink of geostrophic momentum using the theory of bell previou

a topex poseidon global tidal model tpxo 2 and barotropic tidal currents determined from long range acoustic transmissions abstract tidal currents derived from the tpxo 2 global tidal model of egbert bennett and foreman are compared with those determined from long range reciprocal acoustic transmissions amplitudes and phases of tidal constituents in the western north atlantic are derived from acoustic data obtained in 1991 1992 using a pentagonal array of transceivers small spatially coherent differences between the measured and modeled tidal harmonic constants mostly result from smoothing assumptions made in the model and errors caused in the model currents by complicated topography to the southwest of the acoustical array acoustically measured harmonic constants amplitude phase of m2 tidal vorticity 3 8 10 9s 1 210 310 agree with those derived from the tpxo 2 model 2 5 10 9s 1 250 300 whereas harmonic constants of about 1 2 10 9s 1 350 360 are theoretically expected from the equations of motion harmonic constants in the north pacific ocean are determined using acoustic data from a triangular transceiver array deployed in 1987 these constants are consistent with those given by the tpxo 2 tidal model within the uncertainties tidal current harmonic constants determined from current meters do not generally provide a critical test of tidal models the tidal currents have been estimated to high accuracy using long range reciprocal acoustic transmissions these estimates will be useful constraints on future global tidal models

boundary mixing and the dynamics of three dimensional thermohaline circulations boundary mixing is implemented in an ocean general circulation model such that the vertical mixing coefficient ky is nonzero only near side boundaries and in convection regions the model is used in a highly idealized configuration with no wind forcing and very nearly fixed surface density to investigate the three dimensional dynamics of the thermohaline circulation for ky 5 20 3 1024 m2 s21 and lower the meridional overturning strength to great accuracy is proportional to meridional heat transport is proportional to the circulation 2 3 1 2 kk y y patterns resemble those from runs with uniform vertical mixing but vertical motion is entirely confined to the boundary regions near the western boundary there is upwelling everywhere near the eastern boundary there is a consistent pattern of downwelling above upwelling with downwelling reaching deeper at high latitudes this pattern is explained by convection and vertical advective diffusive balance underneath for ky 5 30 3 1024 m2 s21 and higher no steady solutions have been found the meridional overturning oscillates on a timescale of about 25 years a time averaged thermally direct overturning cell is not supported dynamically because convection extends longitudinally across the entire basin and upwelling near the western boundary does not lead to densities higher than at the eastern boundary assuming uniform upwelling in the west level isopycnals near the equator and level isopycnals along the eastern boundary south of the outcropping latitude permits the analytic determination of convection depth at the eastern wall and hence the density difference between the eastern and western walls this difference is at most one quarter the surface density difference between high and low latitudes and agrees in magnitude and latitudinal dependence with the numerical experiments scaling arguments estimate overturning strength as of the order of 10 3 106 m3 s21 and confirm the 2 3 power dependence onky the derivation also gives a dependence of overturning strength with latitude that agrees qualitatively with the numerical results the scaling for the dependence of meridional heat transport on latitude agrees well with the model results scaling for heat transport amplitude agrees less well but correctly predicts a weaker dependence on ky than maximum overturning