gravitational symmetric and baroclinic instability of the ocean mixed layer abstract a hierarchy of hydrodynamical instabilities controlling the transfer of buoyancy through the oceanic mixed layer is reviewed if a resting ocean of horizontally uniform stratification is subject to spatially uniform buoyancy loss at the sea surface then gravitational instability ensues in which buoyancy is drawn from depth by upright convection but if spatial inhomogeneities in the ambient stratification or the forcing are present as always exist in nature then horizontal density gradients will be induced and within a rotation period horizontal currents in thermal wind balance with those gradients will be set up within the mixed layer there are two important consequences on the convective process upright convection will become modified by the presence of the thermal wind shear fluid parcels are exchanged not along vertical paths but rather along slanting paths in symmetric instability theoretical considerations suggest that this slantwise convection sets the potential vorticity of th

potential vorticity dynamics of tropical instability vortices abstracttropical instability vortices tivs in the equatorial pacific exhibit energetic horizontal and vertical circulation characterized by regions of high rossby number and low richardson number their strong anticyclonic vorticity and vertical shear can influence the broader scale circulation by driving lateral mixing and vertical exchange between the ocean surface and interior the authors use a set of nested high resolution simulations of the equatorial pacific with a finest grid size of 3 km to examine the vortex dynamics associated with tiv core water formation tiv cores are characterized by low values of the ertel potential vorticity pv as the relative vorticity is anticyclonic with magnitude comparable to the local coriolis parameter a study of the variation of pv and other scalars along lagrangian fluid parcel tracks entering the tivs shows that the low pv water in their cores is a mix of equatorial undercurrent euc water and north equatorial counter current necc water the euc water

upstream control of the frontal jet regulating plankton production in the alboran sea western mediterranean using a coupled physical biological model we document that a 30 km wide meandering jet constitutes a major source of biological enrichment in the alboran sea western mediterranean even in the absence of wind forcing and tidal dynamics the level of enrichment is shown to vary markedly during the year depending on the upstream characteristics of the jet as it exits from the gibraltar strait when its intensity is sufficiently low and characterized by weaker cross frontal density gradients during winter spring the jet is weakly nonlinear and may not fulfill the necessary conditions for frontogenesis it then remains weakly productive in the case of stronger jet intensity 1 1 sv accompanied by stronger cross frontal density and velocity gradients within the alboran sea during summer autumn the frontal jet becomes strongly nonlinear and ageostrophic with large cross frontal vorticity changes on the order of planetary vorticity under these conditions upward vertical velocities in the range 10 50 m d 1 supply nutrients into the euphotic layer more effectively and support high level frontogenesis induced phytoplankton production on the anticyclonic side of the main jet axis the strong eddy pumping mechanism also provides a comparable level of plankton production within strongly nonlinear elongated cyclonic eddies along the outer periphery of the frontal jet the plankton biomass is advected partially by the jet along its trajectory and dispersed within the basin by mesoscale eddies and meanders

frontogenesis subduction and cross front exchange at upper ocean fronts the subduction of water at upper ocean fronts driven by internal instabilities is investigated a simple analytic model which assumes conservation of potential density and potential vorticity is used to characterize the expected structure of subducted parcels as a function of the surface layer depth and the length scale of the parcel parcels subducted from a deep surface layer will be characterized by anomalously low potential vorticity and anticyclonic circulation while shallow surface layers result in subducted parcels with high potential vorticity and cyclonic circulation a nonlinear isopycnal primitive equation model is used to demonstrate how baroclinic instability and the resulting frontogenesis force the subduction of parcels below and across the front frontogenesis generates vertical velocities of 0 30 m d and ageostrophic cross front flows of 3 to 5 cm s the subduction is achieved by the deep ageostrophic flow which carries water from the surface layer below and across the front the subducted parcels quickly develop a circulation through balanced adjustment anticyclonic for deep surface layers and cyclonic for shallow surface layers the characteristics of parcels subducted in winter conditions closely resemble a class of eddies called submesoscale coherent vortices the horizontal and vertical scales of the vortices are determined by the frontogenetic mechanism and the depth of the surface layer the total permanent subduction rate is estimated to be 20 m yr for frontal subduction driven by frontogenesis although local and temporary subduction can be much larger the subducted anticyclonic vortices are often coupled to upper ocean cyclonic vortices thus forming a baroclinic dipole that propagates at approximately 3 5 cm s and is capable of transporting the anomalous water properties far from the region of formation similarities with observations in the north atlantic subtropical convergence zone and near the gulf stream are discussed

intensification of ocean fronts by down front winds abstract many ocean fronts experience strong local atmospheric forcing by down front winds that is winds blowing in the direction of the frontal jet an analytic theory and nonhydrostatic numerical simulations are used to demonstrate the mechanism by which down front winds lead to frontogenesis when a wind blows down a front cross front advection of density by ekman flow results in a destabilizing wind driven buoyancy flux wdbf equal to the product of the ekman transport with the surface lateral buoyancy gradient destabilization of the water column results in convection that is localized to the front and that has a buoyancy flux that is scaled by the wdbf mixing of buoyancy by convection and ekman pumping suction resulting from the cross front contrast in vertical vorticity of the frontal jet drive frontogenetic ageostrophic secondary circulations ascs for mixed layers with negative potential vorticity the most frontogenetic ascs select a preferred cross front width and do not translate with

linear instability of a mixed layer front the linear instabilities of a geostrophically balanced frontal jet are computed numerically in an effort to understand the origin of intense small scale cold core features observed in the north atlantic subtropical convergence zones during the frontal air sea interaction experiment fasinex a simple analytic continuously stratified basic state is used to represent the observed frontal structure the most unstable linear modes have e folding timescales of 2 3 days alongfront wavelengths near 70 km and significant asymmetry across the front the results provide indirect evidence that baroclinic instability of the frontal jet is a possible source of the cold core features observed during fasinex

a numerical modeling study of the east australian current encircling and overwashing a warm core eddy 1 warm core eddies wces often form in the meanders of western boundary currents wbcs wces are frequently overwashed with less dense waters sourced from the wbc we use the regional ocean modelling system to investigate the ocean state during the overwashing of one such wce in october 2008 in the east australian current eac comparisons of model outputs with satellite sea surface temperature and vertical profiles show that the model provides a realistic simulation of the eddy during the period when the eac encircled and then overwashed the eddy during the encircling stage an eddy with closed circulation persisted at depth in the surface eac water entered from the north encircled the eddy and exited to the east the overwashing stage was initiated by the expulsion of cyclonic vorticity for the following 8 days after the expulsion waters from the eac washed over the top of the eddy transferring heat and anticyclonic vorticity radially inward after approximately one rotation period of overwashing the eddy separated the overwashing creates a two layer system that forms a subsurface maximum velocity at the interface of the two layers analysis of water mass properties eulerian tracer dynamics and lagrangian particle tracks show that the original eddy sinks 10 50 m during the overwashing period overwashing has been observed in many wbcs and occurs in most wces in the western tasman sea

formation of interleaving layers in the bay of bengal abstract observations of the upper 200 m of the strongly stratified bay of bengal reveal a host of interleaving layers of watermass properties the features appear as isopycnal spice anomalies and form multiple parallel 10 m thin layers that are coherent over horizontal scales of 30 80 km they are coincident with anomalies in density stratification and in some cases with the vertical shear of horizontal velocity but are not aligned with isopycnals the cross isopycnal slopes of these prominent features are o 1 0 4 and are on average 5 to 10 times smaller than the expected slopes of passive tracer anomalies due to mesoscale stirring we present two alternate mechanisms by which such interleaving layers can be created from existing lateral spice gradients i stirring by vertically sheared submesoscale eddies and ii near inertial wave shear a numerical simulation of a density and spice front based on observations of a narrow and fast jet develops a submesoscale vortex that produces spice layering similar to our observations the layering suggests that even a weak vertical diffusivity would greatly enhance the horizontal mixing of spice at submesoscales the scales of the proposed processes through shear dispersion the analysis of the observations draws attention to the prevalence of submesoscale dynamics and niws with unusually high vertical wavenumbers in the bay of bengal

evolution of the instability of a mixed layer front observations from the frontal air sea interaction experiment fasinex indicating the presence of small scale cold core features in the north atlantic subtropical convergence zone motivated a recent linear analysis of the instability of a geostrophically balanced mixed layer front the results of that analysis suggested that the instability would preferentially form small scale cold core eddies at finite amplitude in the present study the finite amplitude evolution of the fastest growing mode of this nongeostrophic baroclinic instability is investigated numerically the linear prediction of cold core eddy formation is confirmed by the nonlinear calculation there are large horizontal and vertical heat and potential vorticity fluxes associated with the developing disturbance the heat flux is confined above the thermocline in the region of sloping frontal isotherms that provide the energy source for the instability but the potential vorticity fluxes are maximum 50 75 m deeper and reach into the thermocline a tongue of low potential vorticity fluid is advected 50 75 m downward along isopycnal surfaces from the cold side of the front into the thermocline at the mixed layer base the small scale potential vorticity structure has similarities to estimates of the upper ocean potential vorticity field obtained previously from fasinex observations the calculations illustrate the role that frontal instabilities may play in the flux of heat and potential vorticity from the mixed layer into the thermocline the evolution of the disturbance resembles baroclinic wave life cycles obtained in atmospheric models

inertia gravity waves spontaneously generated by jets and fronts part i different baroclinic life cycles abstract the spontaneous generation of inertia gravity waves in idealized life cycles of baroclinic instability is investigated using the weather research and forecasting model two substantially different life cycles of baroclinic instability are obtained by varying the initial zonal jet the wave generation depends strongly on the details of the baroclinic wave s development in the life cycle dominated by cyclonic behavior the most conspicuous gravity waves are excited by the upper level jet and are broadly consistent with previous simulations of o sullivan and dunkerton in the life cycle that is dominated by anticyclonic behavior the most conspicuous gravity waves even in the stratosphere are excited by the surface fronts although the fronts are no stronger than in the cyclonic life cycle the anticyclonic life cycle also reveals waves in the lower stratosphere above the upper level trough of the baroclinic wave these waves have not been previously identified in idealized simulations the sensiti

cyclonic eddies formed at the pacific tropical instability wave fronts 1 sea surface temperature images and surface drifter observations are compared to the results from a high resolution numerical simulation to study the properties of cyclonic eddies generated at the density front of the tropical instability waves in the tropical pacific ocean these cyclonic eddies of which the diameter is about 30 100 km and the vertical extent is limited to the upper 100 m in depth have physical characteristics similar to those of smaller submesoscale eddies at the midlatitudes according to the model they have highly coherent structures below the surface carrying cold and salty upwelled equatorial water probably rich in marine life the stretching and tilting of the upper layer of the ocean provides the main mechanism responsible for the intense cyclonic vorticity of the eddies involving complex evolution of the density field into occluded fronts

computing ocean surface currents over the coastal california current system using 30 min lag sequential sar images as compared with conventional methods for measuring ocean surface currents spaceborne synthetic aperture radar sar offers cloud penetrating ocean current observation capability at high spatial resolution while some studies have shown the potential of sar for studying ocean surface currents through feature tracking they have only analyzed a few images to demonstrate the basic measurement technique and no concise general technique has been developed this paper shows the application of the maximum cross correlation mcc method to generate ocean surface currents from nearly two years of available sequential spaceborne c band sar imagery from the envisat asar and ers 2 advanced microwave instrument sar sensors over the coastal california current system the data processing strategies are discussed in detail and results are compared with hf radar measured currents one dimensional wavenumber spectra of the sar derived surface currents agree with the k 2 power law as predicted by submesoscale resolution models comparisons with hf radar currents show encouraging results with mcc sar vectors oriented slightly counterclockwise relative to hf radar vectors mcc sar surface currents are found to have larger magnitudes than hf radar currents approx 11 cm s which may be due to the fact that sar penetrates only a few centimeters into the ocean surface whereas hf radar currents are averaged over the top 1 m of the ocean surface the larger part of this magnitude difference is contained in the along shore component which can be attributed to higher hf radar accuracy in the direct radial cross shore measurements as compared with along shore components derived from multiple cross shore radial measurements

inversion of submesoscale patterns from a high resolution solomon sea model feasibility assessment a high resolution realistic numerical model of the solomon sea which exhibits a high level of variability at mesoscales and submesoscales is used to explore new avenues for data assimilation image data assimilation represents a powerful methodology to integrate information from high resolution observations such as satellite sea surface temperature or chlorophyll or high resolution altimetric sea surface height that will be observed in the forthcoming swot mission the present study investigates the feasibility and accuracy of the inversion of the dynamical submesoscale information contained in high resolution images of sea surface temperature sst or salinity sss to improve the estimation of oceanic surface currents the inversion method is tested in the context of twin experiments with sst and sss data provided by a model of the solomon sea for that purpose synthetic tracer images are built by binarizing the norm of the gradient of sst sss or spiciness the binarized tracer images are compared to the dynamical image which is derived from the finite size lyapunov exponents the adjustment of the dynamical image to the tracer image provides the optimal correction to be applied on the surface velocity field the method is evaluated by comparing the result of the inversion to the reference model solution the feasibility of the inversion of various images sst sss both sst and sss or spiciness is explored on two small areas of the solomon sea we show that errors in the surface velocity field can be substantially reduced through the inversion of tracer images

diagnosis of 3d vertical circulation in the upwelling and frontal zones east of hainan island china abstractusing the generalized omega equation and cruise observations in july 2012 this study analyzes the 3d vertical circulation in the upwelling region and frontal zone east of hainan island china the results show that there is a strong frontal zone in subsurface layer along the 100 m isobath which is characterized by density gradient of o 10 4 kg m 4 and vertical eddy diffusivity of o 10 5 10 4 m2 s 1 the kinematic deformation term sdef ageostrophic advection term sadv and vertical mixing forcing term smix are calculated from the observations their distribution patterns are featured by banded structure that is alternating positive negative alongshore bands distributed in the cross shelf direction correspondingly alternating upwelling and downwelling bands appear from the coast to the deep waters the maximum downward velocity reaches 5 10 5 m s 1 within the frontal zone accompanied by the maximum upward velocity of 7 10 5 m s 1 on two sides the dynamic diagnosis indicates that sadv

sensitivity of cyclogenesis to sea surface temperature in the northwestern atlantic during the intensive observation period 15 13 15 february 1997 of the fastex experiment a major cyclone crossed the atlantic ocean from the newfoundland basin to southern iceland its surface low center deepened by 17 hpa in 7 h when the perturbation crossed the north atlantic current nac from cold 38c to warm water 158c to elucidate the role of sea surface temperature sst and air sea fluxes in the dynamics of oceanic cyclones three nonhydrostatic mesoscale simulations were performed the first one is a control experiment with a realistic sst field describing in detail the oceanic front associated with the nac system the two following simulations are sensitivity experiments where the sst front is removed the first one uses a uniformly cold sst equal to 38c and the second one uses a uniformly warm sst equal to 158c the frontogenetic function and the vertical velocity sources in the lower atmospheric layers of the three simulations were diagnosed in the control simulation the surface heat fluxes were found to be negative in the perturbation warm sector and positive in the region behind the cold front as reported by numerous authors this pattern of surface heating and cooling did not intensify the cyclone except in the occlusion when the phasing with the sst front occurs this configuration enhances the horizontal gradient of surface buoyancy flux across the occlusion which increases the buoyancy flux source of vertical velocity w when the sst front is removed the surface heat fluxes are strongly affected in magnitude and in spatial variability the marine atmospheric boundary layer mabl stability the convective activity the warm advection in the core of the wave and the heating depth are strongly affected by the different surface flux fields there are several consequences i the uniform ssts tend to decrease the cold front intensity of the wave ii a weaker buoyancy flux source of vertical velocity is found above a uniform cold sst across the occlusion in comparison with the control case and iii surprisingly a weaker w buoyancy flux source is also found above a uniform warm sst because of a higher heating depth vertical velocity depends not only on the buoyancy flux forcing but also on the thermal wind the turbulent momentum and the thermal wind imbalance forcings the thermal wind forcing and the thermal wind imbalance forcing were the most sensitive to the sst compared to the turbulent momentum forcing this result means that i the feed back of the ageostrophic circulation induced by the surface is greater on the kinematic forcings than on the turbulent forcings and ii the turbulent momentum forcing does not play a crucial role in cyclogenesis above a uniform warm sst the strongest intensity of the occlusion is due to the strongest w thermal wind forcing and w thermal wind imbalance forcing in the mabl in spite of a weaker w buoyancy flux forcing than in the control case this result is explained by the convective activity that increases the low level convergence and vorticity spinup this point means that latent heat release and baroclinicity are in tight interaction in the first 12 h and at the scale of the simulation domain the three cyclones evolve similarly but at a small scale their internal structures diverge strongly and rapidly the scale at which the surface turbulent fluxes act on the dynamics of marine cyclones is therefore important finally the cyclone simulated in the warm sst case developed more rapidly than those simulated in the real and the cold sst cases this behavior is attributed to the strong positive surface heat fluxes because they preconditioned the mabl by moistening and heating the low levels during the incipient stage of the cyclone development

finescale vertical structure of the upwelling system off southern peru as observed from glider data abstractthe upwelling system off southern peru has been observed using an autonomous underwater vehicle a slocum glider during october november 2008 nine cross front sections have been carried out across an intense upwelling cell near 14 s during almost two months profiles of temperature salinity and fluorescence were collected at less than 1 km resolution between the surface and 200 m depth estimates of alongshore absolute geostrophic velocities were inferred from the density field and the glider drift between two surfacings in the frontal region salinity and biogeochemical fields displayed cross shore submesoscale filamentary structures throughout the mission those features presented a width of 10 20 km a vertical extent of 150 m and appeared to propagate toward the shore they were steeper than isopycnals and kept an aspect ratio close to f n the inverse of the prandtl ratio these filamentary structures may be interpreted mainly as a manifestation of submesoscale turbulence through sti

upwelling filaments off cap blanc interaction of the nw african upwelling current and the cape verde frontal zone eddy field 1 the hydrographical and dynamical properties of the upwelling filaments forming off cap blanc mauritania are investigated using remotely sensed and in situ data collected in april may 2009 during the strongest upwelling season the area is situated at the southern edge of the nw african upwelling system where the cape verde frontal zone cvfz separates warmer saltier north atlantic central water nacw and cooler fresher south atlantic central water sacw sea surface temperature images indicated the presence of an upwelling filament extending 280 km offshore rooted over the cap blanc promontory and entrained around a warm core anticyclonic eddy after this filament started to decay a new cold filament developed at the approximate same location high resolution moving vessel profiler mvp and acoustic doppler current profiler adcp surveys of these mesoscale structures revealed that both filaments were carrying south atlantic central water sacw offshore through an intense jet like flow similarity of the relative vorticity structure across the filament with that of the tangent eddy suggested that the latter was responsible for the offshore current tracking of this eddy in altimetric data demonstrated that it originated from the cvfz as implied by its hydrographic structure altimetric data also revealed that another anticyclonic structure centered over the cap blanc promontory was responsible for the northwestward advection of sacw into the base of the filament the results support the idea that some upwelling filaments can be produced by the interaction of an external eddy field including topographic eddies with the upwelled water

destruction of potential vorticity by winds the destruction of potential vorticity pv at ocean fronts by wind stress driven frictional forces is examined using pv flux formalism and numerical simulations when a front is forced by downfront winds that is winds blowing in the direction of the frontal jet a nonadvective frictional pv flux that is upward at the sea surface is induced the flux extracts pv out of the ocean leading to the formation of a boundary layer thicker than the ekman layer with nearly zero pv and nonzero stratification the pv reduction is not only active in the ekman layer but is transmitted through the boundary layer via secondary circulations that exchange low pv from the ekman layer with high pv from the pycnocline extraction of pv from the pycnocline by the secondary circulations results in an upward advective pv flux at the base of the boundary layer that scales with the surface nonadvective frictional pv flux and that leads to the deepening of the layer at fronts forced by both downfront winds and a destabilizing atmospheric buoyancy flux f b the critical parameter that determines whether the wind or the buoyancy flux is the dominant cause for pv

baroclinic instability and submesoscale eddy formation in weakly stratified oceans under cooling 1 numerical experiments with a three dimensional nonhydrostatic model have been performed to investigate baroclinic instability and submesoscale eddy formation in weakly stratified oceans under cooling two types of baroclinic instability can exist in a two layered ocean where the convectively formed deep mixed layer overlies the weakly stratified lower layer one rapidly develops in the mixed layer with short wavelengths shallow mode and the other occupies the whole ocean depth with long wavelengths deep mode when a background flow is deep the shallow mode develops first but the deep mode replaces it in several days in contrast only the shallow mode is excited in the mixed layer overlying the strongly stratified layer the linear stability analysis explains these results well despite active cooling subsequently formed eddies restratify the mixed layer and modify water density over the whole depth when a background flow is shallow baroclinic instability is confined to the mixed layer and produces a dipole of surface intensified cyclonic eddy and middepth intensified anticyclonic eddy both of which are of submesoscale 10 km the anticyclonic eddy consisting of convectively formed but weakly stratified water moves across the front to ventilate the deep layer where convection does not reach locally in this way density modification extends below the mixed layer surface cooling as well as baroclinicity enhances restratification of the mixed layer and density modification at depths by activating submesoscale eddy formation the results can explain the restratification of the deep mixed layer observed during a cooling season and the origins of submesoscale coherent vortices recently detected in polar oceans

observations of near inertial internal gravity waves radiating from a frontal jet abstractshipboard adcp and towed ctd measurements are presented of a near inertial internal gravity wave radiating away from a zonal jet associated with the subtropical front in the north pacific three dimensional spatial surveys indicate persistent alternating shear layers sloping downward and equatorward from the front as a result depth integrated ageostrophic shear increases sharply equatorward of the front the layers have a vertical wavelength of about 250 m and a slope consistent with a wave of frequency 1 01f they extend at least 100 km south of the front time series confirm that the shear is associated with a downward propagating near inertial wave with frequency within 20 of f a slab mixed layer model forced with shipboard and ncep reanalysis winds suggests that wind forcing was too weak to generate the wave likewise trapping of the near inertial motions at the low vorticity edge of the front can be ruled out because of the extension of the features well south of it instead the authors

sea surface temperature fronts in the california current system from geostationary satellite observations 1 sea surface temperature sst fronts are determined for the 2001 2004 time period from geostationary operational environmental satellites goes data in the california current system ccs the probability of detecting a sst front at an individual pixel location in the ccs is presented as a bi monthly climatology fronts clearly indicate the seasonal evolution of coastal upwelling as well as meanders and filaments that are often linked with irregularities in coastline geometry winter is characterized by low frontal activity along the entire coast fronts first appear close to the coast during spring particularly south of cape blanco where upwelling favorable winds are already persistent the area of high frontal activity continues to increase during summer especially between monterey bay and cape blanco extending more than 300 km from the coast the region with high frontal activity widens at 2 6 km day 1 off northern baja california a band with persistent fronts is found close to the coast year round but there is no evidence of a seasonal widening of the area of higher activity during fall the weakening of upwelling favorable winds leads to a gradual decrease in frontal activity an empirical orthogonal function eof decomposition reveals the development of sst fronts associated with seasonal upwelling for locations north of monterey bay with less summer intensification to the south the first appearance of fronts close to the coast during spring and the occurrence of the fronts offshore later in the season are represented by additional statistically significant eof modes

mesoscale to submesoscale transition in the california current system part ii frontal processes this is the second of three papers investigating the regime transition that occurs in numerical simulations for an idealized equilibrium subtropical eastern boundary upwelling current system similar to the california current the emergent upper ocean submesoscale fronts are analyzed from phenomenological and dynamical perspectives using a combination of composite averaging and separation of distinctive subregions of the flow the initiating dynamical process for the transition is near surface frontogenesis the frontal behavior is similar to both observed meteorological surface fronts and solutions of the approximate dynamical model called surface dynamics i e uniform interior potential vorticity q and diagnostic force balance in the intensification of surface density gradients and secondary circulations in response to a mesoscale strain field however there are significant behavioral differences compared to the surface dynamics model wind stress acts on fronts through nonlinear ekman transport and creation and destruction of potential vorticity the strain induced frontogenesis is disrupted by vigorous submesoscale frontal instabilities that in turn lead to secondary frontogenesis events submesoscale vortices and excitation of even smaller scale flows intermittent submesoscale breakdown of geostrophic and gradient wind force balance occurs during the intense frontogenesis and frontal instability events

submesoscale impacts on horizontal and vertical transport in the gulf of mexico 1 impacts of submesoscale processes on transport are investigated numerically in an energetic mesoscale flow with an ocean model run at two horizontal resolutions 1 and 5 km the focus is the northwestern gulf of mexico where the loop current eddies are surrounded by smaller vortices by increasing the horizontal resolution the number and strength of submesoscale eddies and vorticity filaments within the mixed layer increase dramatically and with them the vertical velocities inside the coherent eddies and at their peripheries increased vertical velocities for increasing resolution are associated to near inertial motions and they are not limited to the mixed layer but are found at all depths horizontal velocities on the contrary are similar lagrangian isobaric tracers are deployed close to the surface and at 100 m and three dimensional neutrally buoyant particles are released close to the surface at the base of the mixed layer and at 100 m the modeled horizontal dispersion curves for each deployment depth are independent of the kind of particles and of horizontal resolution close to the ocean surface however convergence zones generated by submesoscale ageostrophic motions and resolved at 1 km resolution influence the details of the tracer distributions vertical dispersion increases by several folds for increasing resolution at all depths explored with the largest differences found close to the surface therefore submesoscales processes play a fundamental role in driving vertical transport in eddy dominated flows both within and below the mixed layer for times comparable to the eulerian time scale

waveform inversion of oscillatory signatures in long period events beneath volcanoes 1 the source mechanism of long period lp events is examined using synthetic waveforms generated by the acoustic resonance of a fluid filled crack we perform a series of numerical tests in which the oscillatory signatures of synthetic lp waveforms are used to determine the source time functions of the six moment tensor components from waveform inversions assuming a point source the results indicate that the moment tensor representation is valid for the odd modes of crack resonance with wavelengths 2l n 2w n n 3 5 7 where l and w are the crack length and width respectively for the even modes with wavelengths 2l n 2w n n 2 4 6 a generalized source representation using higher order tensors is required although the efficiency of seismic waves radiated by the even modes is expected to be small we apply the moment tensor inversion to the oscillatory signatures of an lp event observed at kusatsu shirane volcano central japan our results point to the resonance of a subhorizontal crack located a few hundred meters beneath the summit crater lakes the present approach may be useful to quantify the source location geometry and force system of lp events and opens the way for moment tensor inversions of tremor

mixed layer instabilities and restratification abstract the restratification of the oceanic surface mixed layer that results from lateral gradients in the surface density field is studied the lateral gradients are shown to be unstable to ageostrophic baroclinic instabilities and slump from the horizontal to the vertical these instabilities which are referred to as mixed layer instabilities mlis differ from instabilities in the ocean interior because of the weak surface stratification spatial scales are o 1 10 km and growth time scales are on the order of a day linear stability analysis and fully nonlinear simulations are used to study mlis and their impact on mixed layer restratification the main result is that mlis are a leading order process in the ml heat budget acting to constantly restratify the surface ocean climate and regional ocean models do not resolve the scales associated with mlis and are likely to underestimate the rate of ml restratification and consequently suffer from a bias in sea surface temperatures and ml depths in a

submesoscale eddy vertical covariances and dynamical constraints from high resolution numerical simulations abstractwe analyze high resolution 1 km simulations of the western pacific gulf of mexico and arabian sea to understand submesoscale eddy dynamics a mask based on the okubo weiss parameter iso

sub mesoscale lateral density structure in the oceanic surface mixed layer 1 we investigate the horizontal scales of density variability in the surface mixed layer sml in the north pacific subtropical front stf during a period of highly variable atmospheric forcing wavelet analysis shows that horizontal density variability is not restricted to scales l 10 km as previously suggested but extends to l 2 km the limiting l varies strongly with location and corresponds to a local internal rossby radius that accounts for transient stratification above the seasonal thermocline density compensation in the sml achieved when temperature and salinity effects cancel in their effect on density occurs at 30 n at the climatological front associated with the northern boundary of the stf where large thermohaline gradients are observed at 28 n however temperature gradients within the sml are not compensated by salinity and horizontal density gradients result in 2 l 10 km our observations suggest dynamic processes restratify the sml at scales rarely resolved by numerical models of the sml

sub surface small scale eddy dynamics from multi sensor observations and modeling the study of mesoscale and submesoscale hereafter sub mesoscale hydrodynamic features is essential for understanding thermal and biogeochemical exchanges between coastal areas and the open ocean in this context a glider mission was conducted in august 2008 closely co located and almost simultaneously launched with a jason 2 altimetric pass to fully characterize the currents associated with regional sub mesoscale processes regularly observed to the north of mallorca mediterranean sea a synoptic view from satellite remote sensing fields before and during the glider mission provided a descriptive picture of the main surface dynamics at the balearic basin scale to quantify the absolute surface geostrophic currents the coastal altimetry derived current computation was improved and cross compared with its equivalent derived from glider measurements model simulations were then validated both qualitatively and statistically with the multi sensor observations the combined use of modeling and multi sensor observational data reveals the baroclinic structure of the balearic current and the northern current and a small scale anticyclonic eddy observed northeast of the mallorca coast current 15 cm s 180 m deep this mesoscale structure partially intercepted by the glider and along track altimetric measurements is marked by relatively strong salinity gradients and not as is more typical temperature gradients finally the use of the validated model simulation also shows that the geostrophic component of this small scale eddy is controlled by sub surface salinity gradients we hypothesize that this structure contains recently modified atlantic water arriving from the strait of ibiza due to a northerly wind which strengthens the northward geostrophic circulation

rapid changes in mixed layer stratification driven by submesoscale instabilities and winds 1 submesoscale eddies generated by baroclinic instability of upper ocean fronts lead to rapid restratification of the mixed layer on a time scale of days this restratification can be opposed by a down front wind stress acting in the direction of the geostrophic velocity that drives a surface ekman flow from the dense side to the light side of the front to arrest the slumping of isopycnals a scaling diagnostic is suggested to determine whether the effect of eddies or wind dominates under different conditions using a numerical model we investigate the juxtaposition of submesoscale eddies and down front winds acting on the mixed layer by estimating the eddy induced overturning stream function in the mixed layer we separate the along and cross isopycnal fluxes of buoyancy associated with submesoscale mixed layer eddies and demonstrate the need for parameterization of the advective along isopycnal flux though the cross front transport of buoyancy induced by the down front component of the wind opposes restratification by mixed layer eddies it becomes diminished as the eddies and growth of the frontal instability disrupt alignment between the wind and frontal axis

lagrangian drifter dispersion in the southwestern atlantic ocean abstractin the framework of monitoring by ocean drifters mondo project a set of lagrangian drifters were released in proximity of the brazil current the western branch of the subtropical gyre in the south atlantic ocean the experimental strategy of deploying part of the buoys in clusters offers the opportunity to examine relative dispersion on a wide range of scales adopting a dynamical systems approach the authors focus their attention on scale dependent indicators like the finite scale lyapunov exponent fsle and the finite scale mean square relative velocity fsrv between two drifters as a function of their separation and compare them with classic time dependent statistical quantities like the mean square relative displacement between two drifters and the effective diffusivity as functions of the time lag from the release the authors find that dependently on the given observable the quasigeostrophic turbulence scenario is overall compatible with their data analysis with discrepancies fr

three dimensional structure and temporal evolution of submesoscale thermohaline intrusions in the north pacific subtropical frontal zone abstract four instances of persistent intrusive deformation of the north pacific subtropical front were tagged individually by a lagrangian float and tracked for several days each feature was mapped in three dimensions using repeat towed observations referenced to the float isohaline surface deformations in the frontal zone included sheetlike folds elongated in the alongfront direction and narrow tongues extending across the front all deformations appeared as protrusions of relatively cold and fresh water across the front no corresponding features of the opposite sign or isolated lenslike structures were observed the sheets were o 10 m thick protruded about 10 km into the warm saline side of the front and were coherent for 10 30 km along the front having about the same thickness and cross frontal extent as the sheets tongues extended less than 5 km along the front all of the intrusions persisted as long as they were followed several days to one week their structures evolved on both inertial

mesoscale to submesoscale transition in the california current system part i flow structure eddy flux and observational tests in computational simulations of an idealized subtropical eastern boundary upwelling current system similar to the california current a submesoscale transition occurs in the eddy variability as the horizontal grid scale is reduced to o 1 km this first paper in a series of three describes the transition in terms of the emergent flow structure and the associated time averaged eddy fluxes in addition to the mesoscale eddies that arise from a primary instability of the alongshore wind driven currents significant energy is transferred into submesoscale fronts and vortices in the upper ocean the submesoscale arises through surface frontogenesis growing off upwelled cold filaments that are pulled offshore and strained in between the mesoscale eddy centers in turn some submesoscale fronts become unstable and develop submesoscale meanders and fragment into roll up vortices associated with this phenomenon are a large vertical vorticity and rossby number a large vertical velocity relatively flat horizontal spectra contrary to the prevailing view of mesoscale dynamics a large vertical buoyancy flux acting to restratify the upper ocean a submesoscale energy conversion from potential to kinetic a significant spatial and temporal intermittency in the upper ocean and material exchanges between the surface boundary layer and pycnocline comparison with available observations indicates that submesoscale fronts and instabilities occur widely in the upper ocean with characteristics similar to the simulations

observed and simulated lagrangian and eddy characteristics of the east australian current and the tasman sea new insights into the lagrangian and eddy dynamical processes within the east australian current eac and the tasman sea are presented we briefly discuss the past campaigns undertaken to observe the eac and the tasman sea eddies as well as the motivation to renew the deployment of drifting buoys into the eac and the tasman sea the specific features discussed are motivated by the recent observing campaigns using drifting buoys and the availability of high spatial and temporal resolution estimates of the ocean state and circulation from eddy resolving models the interpretation of these features is also aided by other components of the ocean observing system the dynamics presented includes a transient eac separation through a vortex dipole b stratified vortex mergers and secondary circulation of eac eddies c eddy networks in the tasman sea and d formation and propagation of the eac separation point the importance of these dynamical features to the eac and the tasman sea and their implications for the observing system and modelling are discussed

two layer model of shear driven coastal upwelling in the presence of bottom topography a stratified two layer fluid is brought to solid body counterclockwise rotation inside a cylindrical tank having a conical bottom with a radial topographic ridge a stress is then applied to the top surface by means of a clockwise differentially rotating disk the resulting ekman layer flux causes the top layer to spin down and the interface to rise near the wall and to descend a t the centre of the tank as this process continues the interface front between the two layers intersects the disk surface and after that migrates away from the wall and allows the bottom fluid to contact the disk directly the migration of the front continues until a steady state is reached the front becomes stationary and the system is in geostrophic balance the first sign of upwelled flow at the surface always occurs as a high speed jet like plume at the bottom topography and only at a later time does a uniform upwelled flow appear a t the surface upstream of the topography this plume which always forms near the downstream edge of the topography migrates in advance of the upstream front to produce an upwelling maximum at the bottom topography the final width of the upstream flow in steady state conditions is estimated by a simple theoretical model which is in good agreement with the experimental results we have an experimental criterion to predict the occurrence of travelling baroclinic waves on the upstream front on the downstream side of the ridge large standing waves are observed with significant upwelling within them under some circumstances cyclones pinch off from the upstream front the plume on the ridge and the crests of the large downstream standing waves we present criteria to predict the occurrence of these pinch off processes

eddy induced mixed layer shallowing and mixed layer thermocline exchange the effects of eddies on the mixed layer and on the transfer of properties between the mixed layer and thermocline are studied in a high resolution model of an unstable front a spring scenario is considered with a mixed layer maintained against surface warming by wind mixing tilting of the buoyancy gradients by ageostrophic flow is found to shallow the mixed layer over the front giving a mixed layer as shallow as 10 m in some places compared with the equilibrium monin obukhov depth of 30 m away from the front variations of mixed layer depth with time and lateral advection lead to a subduction field that is substantially different from the vertical velocity field vertical velocities associated with the growing instabilities push tongues of a ventilation tracer initially only present within the surface layer down to depths of up to 100 m after 24 days a quarter of this ventilation tracer has been deposited in the thermocline conversely the vertical motions pull nutrients from the thermocline up into the mixed layer giving enhanced surface values along the front in the basin average the geostrophic eddies give vertical eddy diffusivities for a ventilation tracer of o 3 10 10 4m2s 1

generation of mesoscale gravity waves in upper tropospheric jet front systems abstract multiply nested mesoscale numerical simulations with horizontal resolution up to 3 3 km are performed to study the generation of mesoscale gravity waves during the life cycle of idealized baroclinic jet front systems long lived vertically propagating mesoscale gravity waves with horizontal wavelengths 100 200 km are simulated originating from the exit region of the upper tropospheric jet streak in a manner consistent with past observational studies the residual of the nonlinear balance equation is found to be a useful index in diagnosing flow imbalance and predicting wave generation the imbalance diagnosis and model simulations suggest that balance adjustment as a generalization of geostrophic adjustment is likely responsible for generating these mesoscale gravity waves it is hypothesized that through balance adjustment the continuous generation of flow imbalance from the developing baroclinic wave will lead to the continuous radiation of gravity waves

a frontal challenge for climate models the ocean surface is filled with a convoluted web of fronts that separate waters of different temperatures and salinities see the figure just as thin ducts in the lung called alveoli facilitate the rapid exchange of gases when breathing fronts are the ducts through which heat carbon oxygen and other climatically important gases enter into the deep ocean a lack of observations however has hampered progress in understanding the dynamics of fronts which can be as narrow as hundreds of meters and as wide as tens of kilometers global satellite measurements of ocean surface velocities and air sea fluxes for instance are only available at resolutions of a few hundred kilometers although shipboard researchers can sample vertical ocean profiles down to centimeter scales only rarely do they collect profiles that are less than 100 km apart on page 318 of this issue d asaro et al 1 present a breakthrough in observing ocean fronts providing direct observations of the workings of the kuroshio front off japan on scales from kilometers to millimeters this detailed and wide ranging portrait was made possible by the development of towed instruments that continuously sample the waters behind a steaming ship the deployment of freely drifting instruments that follow ocean currents and the exercising of a great deal of ingenuity in keeping all these tools along the front for a few weeks in 2007

frontogenesis and frontal arrest of a dense filament in the oceanic surface boundary layer the evolution of upper ocean currents involves a set of complex poorly understood interactions between submesoscale turbulence e g density fronts and filaments and coherent vortices and smaller scale boundary layer turbulence here we simulate the lifecycle of a cold dense filament undergoing frontogenesis in the presence of turbulence generated by surface stress and or buoyancy loss this phenomenon is examined in large eddy simulations with resolved turbulent motions in large horizontal domains using sim 10 10 grid points steady winds are oriented in directions perpendicular or parallel to the filament axis due to turbulent vertical momentum mixing cold filaments generate a potent two celled secondary circulation in the cross filament plane that is frontogenetic sharpens the cross filament buoyancy and horizontal velocity gradients and blocks ekman buoyancy flux across the cold filament core towards the warm filament edge within less than a day the frontogenesis is arrested at a small width approx 100 text m primarily by an enhancement of the turbulence through a small submesoscale horizontal shear instability of the sharpened filament followed by a subsequent slow decay of the filament by further turbulent mixing the boundary layer turbulence is inhomogeneous and non stationary in relation to the evolving submesoscale currents and density stratification the occurrence of frontogenesis and arrest are qualitatively similar with varying stress direction or with convective cooling but the detailed evolution and flow structure differ among the cases thus submesoscale filament frontogenesis caused by boundary layer turbulence frontal arrest by frontal instability and frontal decay by forward energy cascade and turbulent mixing are generic processes in the upper ocean

frontal dynamics in a california current system shallow front 1 frontal processes and tracer structure 1 the three dimensional dynamics in a shallow front are examined using density and current data from two surveys 100 km offshore of monterey bay california survey 1 is forced by down front winds and both surveys have considerable cross front density gradients and flow curvature the maximum rossby numbers on the dense side reached maxima of 0 60 in survey 1 and 0 45 in survey 2 downwelling occurs in regions of confluence frontogenesis associated with potential vorticity pv change and thermal wind imbalance streamers of particulate matter and pv are advected southeastward by the frontal jet and downward nonlinear ekman currents advect dense water over light water in the presence of down front winds which leads to upwelling along the front and downwelling on the light side of the front at sites of active ageostrophic secondary circulation asc induced by frontogenesis or ekman effects the observed cross front ageostrophic velocity is consistent with the diagnosed vertical velocity furthermore in survey 2 ageostrophic divergence may play an important role at the curved front presumably counteracting quasi geostrophic frontogenesis due to isopycnal confluence downward frictional vertical pv flux below the surface extracts pv from the pycnocline and reinforces the frontogenetic vertical pv flux pv destruction at the surface is inferred from a low pv anomaly below the mixed layer in survey 2 since the magnitude of the frontogenetic asc is only twice the magnitude of ekman suction external forcing may have a considerable impact on the vertical heat and pv fluxes

mesoscale and submesoscale effects on mixed layer depth in the southern ocean the authors gratefully acknowledge support from the natural environment research council awards ne j010472 1 and ne j009857 1

parameterization of mixed layer eddies part ii prognosis and impact abstract the authors propose a parameterization for restratification by mixed layer eddies that develop from baroclinic instabilities of ocean fronts the parameterization is cast as an overturning streamfunction that is proportional to the product of horizontal buoyancy gradient mixed layer depth and inertial period the parameterization has remarkable skill for an extremely wide range of mixed layer depths rotation rates and vertical and horizontal stratifications in this paper a coarse resolution prognostic model of the parameterization is compared with submesoscale mixed layer eddy resolving simulations the parameterization proves accurate in predicting changes to the buoyancy the climate implications of the proposed parameterization are estimated by applying the restratification scaling to observations the mixed layer depth is estimated from climatology and the buoyancy gradients are from satellite altimetry the vertical fluxes are comparable to monthly mean air sea fluxes in large areas of

on frontal dynamics in two model oceans vertically homogeneous variable temperature layer models are often used to describe upper ocean variability the dynamics of jets and fronts included frontogenesis is known to have a preference for strong cyclonic shears when a frontal wave winds up ageostrophically one would expect intense cyclones and more diffuse anticyclones to be the result this is characteristic of both atmospheric weather and the oceanic equivalent the frontal dynamics of the variable temperature layer model is here compared with that of the three dimensional primitive equations the origin of the layer model whereas the primitive equation numerical experiments produce dynamics according to the above the cyclonic and anticyclonic shears and eddies are equally amplified in the corresponding variable temperature layer experiments it is suggested that thermal wind is basal to the desired frontal characteristics and that the layer description fails because of the way it has been defined to have none

oceanic restratification forced by surface frontogenesis potential vorticity pv conservation implies a strong constraint on the time evolution of the mean density at a given depth the authors show that on an f plane and in the absence of sources and sinks of pv it only depends on two terms namely the time evolution of the product between density anomaly and relative vorticity and the vertical pv flux this primitive equation result which applies at any depth suggests that the ageostrophic dynamics induced by baroclinic eddies strongly affect the mean oceanic stratification profile this result is illustrated for two simple initial value simulations of a baroclinic balanced jet for initial situations propitious to surface frontogenesis the simulations show a restratification over the whole water column characterized by the amplification in time of the brunt vaisala frequency in the upper oceanic layers in the absence of surface frontogenesis such as when the jet is initialized at the middepth of the water column the restratification is much weaker and slower because both simulations have similar kinetic energy and growth rate of baroclinic instability the results clearly reveal that the restratification is driven by surface frontogenesis in the first case and by vertical pv flux in the interior in the second case the authors also point out that the dynamics of the interior pv is tightly related to the surface dynamics because of total mass conservation

a tale of two eddies the biophysical characteristics of two contrasting cyclonic eddies in the east australian current system mesoscale cyclonic eddies are known to be highly productive less well known are the dynamics and productivity of smaller cyclonic eddies known as frontal eddies that form on the landward side of western boundary currents in this study we investigate the physical and biogeochemical properties of two contrasting cyclonic eddies in the east australian current eac the first murphy a mesoscale cyclonic eddy that formed at 28 s with a diameter of 160 km and high surface chlorophyll a concentrations which lived 47 days the second freddy a smaller frontal eddy 35 km diameter that formed from a shelf water billow 7 days prior to sampling at 31 5 s and was advected off the shelf along the eac front from 200m to 4000m of water both eddies were at least 1000m deep with a similar steric height anomaly we introduce and employ the method of closest approach using shipboard adcp velocities to estimate the eddy centers which reveals significant tilting through the water column we estimate rotation rates of 4 10 days and 1 9 days and rossby numbers 0 25 0 1 and 0 6 0 1 from the surface to 600m for murphy and freddy respectively high resolution altimetry measurements from the saral altika satellite provide estimates of the ageostrophic component of rotation our results show that the frontal eddy is significantly more ageostrophic energetic and productive than the mesoscale cyclone despite its small size and short life 4 weeks we suggest that frontal eddies have potential to contribute significantly to the net productivity of the tasman sea region this article is protected by copyright all rights reserved

modulation of frontogenetic plankton production along a meandering jet by zonal wind forcing an application to the alboran sea we present a coupled physical biological modeling study to elucidate the changes in ageostrophic frontal dynamics and the frontogenetic plankton production characteristics of a meandering jet under the impacts of successive westerly easterly wind events combined with seasonal variations in the upstream transport and buoyancy flux characteristics of the jet using a case study for the alboran sea western mediterranean their nonlinear coupling is shown to result in different forms of physical and biological characteristics of the background jet structure that follows a meandering path around two anticyclonic gyres in the western and eastern basins and a cyclonic eddy in between the westerly downfront wind events broaden the jet and result in stronger cross frontal density contrast and intensify ageostrophic cross frontal secondary circulation thus they improve the frontogenetic plankton production with respect to the no wind case they also support higher production along the northern coast in response to wind induced coastal upwelling and spreading of resulting nutrient rich productive water by mesoscale stirring these features weaken gradually as the jet transport reduces in contrast stronger and longer lasting easterlies during the reduced jet transport phase weaken the currents and frontal density structure change the circular western alboran gyre to an elongated form and shift the main axis of the jet towards the southern basin then frontogenesis fails to contribute to phytoplankton production that becomes limited to the eddy pumping within cyclones apart from the frontogenetic production eddy pumping mesoscale stirring and diapycnal mixing of nutrients support intermittent and localized phytoplankton patches over the basin

dynamics of the upper oceanic layers in terms of surface quasigeostrophy theory in this study the relation between the interior and the surface dynamics for nonlinear baroclinically unstable flows is examined using the concepts of potential vorticity first it is demonstrated that baroclinic unstable flows present the property that the potential vorticity mesoscale and submesoscale anomalies in the ocean interior are strongly correlated to the surface density anomalies then using the invertibility of potential vorticity the dynamics are decomposed in terms of a solution forced by the three dimensional 3d potential vorticity and a solution forced by the surface boundary condition in density it is found that in the upper oceanic layers the balanced flow induced only by potential vorticity is strongly anticorrelated with that induced only by the surface density with a dominance of the latter the major consequence is that the 3d balanced motions can be determined from only the surface density and the characteristics of the basin scale stratification by solving an elliptic equation these properties allow for the possibility to reconstruct the 3d balanced velocity field of the upper layers from just the knowledge of the surface density by using a simpler model that is an effective surface quasigeostrophic model all these results are validated through the examination of a primitive equation simulation reproducing the dynamics of the antarctic circumpolar current

submesoscale instabilities in mesoscale eddies submesoscale processes have been extensively studied in observations and simulations of fronts recent idealized simulations show that submesoscale instabilities also occur in baroclinic mesoscale cyclones and anticyclones the instabilities in the anticyclone grow faster and at coarser grid resolution than in the cyclone the instabilities lead to larger restratification in the anticyclone than in the cyclone the instabilities also lead to changes in the mean azimuthal jet around the anticyclone from 2 km resolution but a similar effect only occurs in the cyclone at 0 25 km resolution a numerical passive tracer experiment shows that submesoscale instabilities lead to deeper subduction in the interior of anticyclonic than cyclonic eddies because of outcropping isopycnals extending deeper into the thermocline in anticyclones an energetic analysis suggests that both vertical shear production and vertical buoyancy fluxes are important in anticyclones but primarily vertical buoyancy fluxes occur in cyclones at these resolutions the energy sources and sinks vary azimuthally around the eddies caused by the asymmetric effects of the ekman buoyancy flux glider transects of a mesoscale anticyclone in the tasman sea show that water with low stratification and high oxygen concentrations is found in an anticyclone in a manner that may be consistent with the model predictions for submesoscale subduction in mesoscale eddies

the dilatancy diffusion hypothesis and earthquake predictability the dilatancy diffusion hypothesis was one of the first attempts to predict the form of potential geophysical signals that may precede earthquakes and hence provide a possible physical basis for earthquake prediction the basic hypothesis has stood up well in the laboratory where catastrophic failure of intact rocks has been observed to be associated with geophysical signals associated both with dilatancy and pore pressure changes in contrast the precursors invoked to determine the predicted earthquake time and event magnitude have not stood up to independent scrutiny there are several reasons for the lack of simple scaling between the laboratory and the field scales but key differences are those of scale in time and space and in material boundary con ditions coupled with the sheer complexity and non linearity of the processes involved upscaling is recognized as a difficult task in multi scale complex systems generally and in oil and gas reser voir engineering specifically it may however provide a clue as to why simple local laws for dila tancy and diffusion do not scale simply to bulk properties at a greater scale even when the fracture system that controls the mechanical and hydraulic properties of the reservoir rock is itself scale invariant