wave diffraction by multiple arbitrary shaped cracks in an infinitely extended ice sheet of finite water depth flexural gravity wave interactions with multiple cracks in an ice sheet of infinite extent are considered based on the linearized velocity potential theory for fluid flow and thin elastic plate model for an ice sheet both the shape and location of the cracks can be arbitrary while an individual crack can be either open or closed free edge conditions are imposed at the crack for open cracks zero corner force conditions are further applied at the crack tips the solution procedure starts from series expansion in the vertical direction based on separation of variables which decomposes the three dimensional problem into an infinite number of coupled two dimensional problems in the horizontal plane for each two dimensional problem an integral equation is derived along the cracks with the jumps of displacement and slope of the ice sheet as unknowns in the integrand by extending the crack in the vertical direction into the fluid domain an artificial vertical surface is formed on which an orthogonal inner product is adopted for the vertical modes through this the edge conditions at the cracks are satisfied together with continuous conditions of pressure and velocity on the vertical surface the integral differential equations are solved numerically through the boundary element method together with the finite difference scheme for the derivatives along the crack extensive results are provided and analysed for cracks with various shapes and locations including the jumps of displacement and slope diffraction wave coefficient and the scattered cross section

size distribution and shape properties of relatively small sea ice floes in the antarctic marginal ice zone in late winter in the marginal sea ice zone miz where relatively small ice floes are dominant the floe size distribution is an important parameter affecting melt processes given the larger cumulative perimeter of multiple small floes compared with a single ice floe of the same area smaller ice floes are therefore subject to increased lateral melt however the available data have been very limited so far analysis of sea ice in the sea of okhotsk revealed that while floe size distribution is basically scale invariant a regime shift occurs at a size of about 40 m in order to extend this preliminary result to the antarctic miz and further examine the controlling factors the first concurrent ice floe size and ice thickness measurements were conducted in the northwestern weddell sea and off wilkes land around 64 s 117 e with a heli borne digital video camera in the late winter of 2006 and 2007 respectively the floe sizes ranged from 2 to 100 m our analysis shows 1 the scale invariance and regime shift are confirmed in both regions 2 the floe size at which regime shift occurs slightly increases from 20 to 40 m with ice thickness consistent with the theory of the flexural failure of sea ice and 3 the aspect ratio is 1 6 1 9 on average close to the previous results based on these results the processes affecting the floe size distribution and the subsequent implications on melt processes are discussed by applying a renormalization group method to interpret the scale invariance in floe size distribution the fractal dimension is related to the fragility of sea ice these results indicate the importance of wave ice interaction in determining the floe size distribution

surface wave propagation in shallow water beneath an inhomogeneous ice cover abstract the scattering of flexural gravity waves in a layer of shallow fluid beneath an ice cover with irregularities is investigated the irregularities considered are the ice edges cracks areas of finely broken ice and ice ridges even this idealized problem formulation demonstrates that the accumulated effect of a large number of irregularities may lead to complete dissipation of the energy of wind waves and swells the analysis shows a strong scattering of such waves by periodic linear irregularities in the sea ice cover the authors employ the shallow water approximation which makes the results applicable for ocean shelf areas

characteristics of sea ice floe size distribution in the seasonal ice zone 1 the size distribution of sea ice floes was observed by coordinated landsat imagery and video monitoring conducted from an icebreaker and a helicopter for an area 38 km 26 km in seasonal sea ice in the southern sea of okhotsk in february 2003 the combination of imagery on several scales allowed measurements of ice floes over three orders of magnitude from 1 m to 1 5 km two different regimes were observed floes larger than about 40 m have a power law number density with an exponent of 1 87 in the lower range of earlier results below 40 m the power law exponent is 1 15 the cause of these two different regimes is hypothesized to lie in the effects of swell on floes of different sizes and thicknesses the importance of the floe size distribution for lateral melting is elucidated

the response of ice floes to ocean waves a precise linear mathematical theory is reported to model the response of a solitary ice floe in ocean waves allowing the floe to bend with the passing wave both infinite and finite water depths are considered and the model is also extended to include a pair of separated floes of different length the case of n floes then being a natural and straightforward development for a single ice floe perfect transmission is achieved whenever the wavelength beneath the ice couples perfectly to the length of the ice floe then the strains induced in the bending ice floe reach a maximum and because multiple cycle tuning can occur in floes which are long compared to the wavelength strain response amplitude operators raos are complicated by considering the case of infinite stiffness heave and roll raos are also found for typical ocean wave periods and these agree well with two dimensional rigid body models finally ice floes of different diameters but constant 1 m thickness are subjected to spectral forcing and the strain spectral density for each is found spectral density envelopes increase gradually with floe diameter achieving a maximum value for a floe of about 102m thereafter strains never decrease below those for the 80 m curve owing to multiple cycle tuning this may explain the presence of zones within an ice field where floe size never exceeds some prescribed value results obtained from the complete theory for two adjacent floes do not differ significantly from those found by applying the single floe model serially except when the separation is very small

a fresh look at how ocean waves and sea ice interact because of their capacity to alter floe size distribution and concentration and consequently to influence atmosphere ocean fluxes there is a compelling justification and demand to include waves in

water wave transmission and energy dissipation by a floating plate in the presence of overwash a numerical model based on the two phase incompressible navier stokes equations is used to study transmission of regular water waves by a thin floating plate in two dimensions the model is shown to capture the phenomenon of waves overwashing the plate and the generation of turbulent bores on the upper plate surface it is validated against laboratory experimental measurements in terms of the transmitted wave field and overwash depths for a set of incident wave periods and steepness values corresponding simulations are performed for a thick plate that does not experience overwash which are validated using experiments where an edge barrier prevents thin plate overwash the model accurately reproduces i the linear relationship between the transmitted and incident amplitudes for the thick plate and ii the decrease in proportion of incident wave transmission for the thin plate as incident steepness increases model outputs are used to link the decreasing transmission to wave energy dissipation in the overwash particularly where bores collide and in the surrounding water particularly at the plate ends it is shown that most energy dissipation occurs in the overwash for the shortest incident waves tested and in the surrounding water for the longer incident waves further evidence is given that overwash suppresses plate motions and causes asymmetry in plate rotations

cretaceous climate a comparison of atmospheric simulations with the geologic record abstract atmospheric simulations using realistic cretaceous geography 100 million years ago suggest that paleography is an important factor governing the nature of the circulation the simulated cretaceous atmospheric circulations are markedly different both from the present day atmospheric circulation and from the classical hypotheses of a weaker circulation and poleward displacement of circulation features e g the subtropical high therefore they pose specific questions which can be tested against the geologic record aspects of the cretaceous simulations are verified in comparisons with the geologic record the simulations serve to guide areas of future paleoclimatic research and to formulate better the nature of the problem of warm equable climates

ice coupled wave propagation across an abrupt change in ice rigidity density or thickness the model of fox and squire 1990 1991 1994 which discusses the oblique propagation of surface gravity waves from the open sea into an ice sheet of constant thickness and properties is augmented to include propagation across an abrupt transition of properties within a continuous ice sheet or across two dissimilar ice sheets that abut one another but are free to move independently rigidity thickness and or density may change across the transition allowing for example the modeling of ice coupled waves into across and out of refrozen leads and polynyas across cracks and through coherent pressure ridges reflection and transmission behavior is reported for various changes in properties under both types of transition conditions

reflection and transmission characteristics at the edge of shore fast sea ice the reflection and transmission of ocean waves at a sea ice boundary is reconsidered the sea ice is modelled as a continuous thin elastic plate of uniform thickness floating on water of arbitrary constant depth unlike earlier solutions matching of potentials between the free surface domain and the ice covered domain is done at all depths previous solutions were incompletely matched as the potentials in each domain were deficient in the present solution a number of the infinity of evanescent modes which were hitherto ignored are included in the solution and allow matching to be carried out by minimization of an integrated error term from surface to seafloor reflection and transmission are found to be markedly influenced by the inclusion of these modes suggesting that conclusions based on the incomplete potentials may be substantially in error

atmospheric circulation during warm geologic periods is the equator to pole surface temperature gradient the controlling factor paleoclimatologists have hypothesized that the equator to pole surface temperature gradient is a dominant control on the paleocirculation of the oceans and the atmosphere atmospheric simulations using realistic cretaceous 100 m y ago geography are used to examine quantitatively the relationships between paleogeography surface temperature gradients and the nature of the atmospheric circulation these results raise questions concerning the classical theories and interpretations of warm paleoclimates and suggest that paleogeography is an important factor governing the nature of the circulation

strain in shore fast ice due to incoming ocean waves and swell using a development from the theoretical model presented by fox and squire 1990 this paper investigates the strain field generated in shore fast ice by normally incident ocean waves and swell after a brief description of the model and its convergence normalized absolute strain relative to a 1 m incident wave is found as a function of distance from the ice edge for various wave periods ice thicknesses and water depths the squared transfer function giving the relative ability of incident waves of different periods to generate strain in the ice is calculated and its consequences are discussed the ice is then forced with a pierson moskowitz spectrum and the consequent strain spectra are plotted as a function of penetration into the ice sheet finally rms strain computed as the incoherent sum of the strains resulting from energy in the open water spectrum is found the results have implications to the breakup of shore fast ice and hence to the floe size distribution of the marginal ice zone

wave response of an ice floe of arbitrary geometry 1 a fully three dimensional model for the motion and bending of a solitary ice floe due to wave forcing is presented this allows the scattering and wave induced force for a realistic ice floe to be calculated these are required to model wave scattering and wave induced ice drift in the marginal ice zone the ice floe is modeled as a thin plate and its motion is expanded in the thin plate modes of vibration the modes are substituted into the integral equation for the water this gives a linear system of equations for the coefficients used to expand the ice floe motion solutions are presented for the ice floe displacement the scattered energy and the time averaged force for a range of ice floe geometries and wave periods it is found that ice floe stiffness is the most important factor in determining ice floe motion scattering and force however above a critical value of stiffness the floe geometry also influences the scattering and force

seismic stratigraphy of the west shetland drift implications for late neogene paleocirculation in the faeroe shetland gateway 1 the morphology and anatomy of a late neogene contourite drift on the british margin of the faeroe shetland channel is investigated in unprecedented detail using industrial two dimensional and three dimensional seismic data the west shetland drift is constructed by a succession of mounded asymmetric strata that in the basin and on the midslope has accumulated on a regional unconformity of early pliocene age the midslope component of the drift system forms a 400 m thick convex elongate sedimentary body that can be traced from the outlet of the norwegian channel and 250 km southwest along the shetland margin contourite drifts occupying the basin are evident as a succession of sheeted mounded and wavy migrating units intercalated by three mega debrite sequences the seismic architecture of the west shetland drift and tentative age estimates of its bounding surfaces suggests that it formed rapidly 5 10 cm kyr 1 by alongslope transport of hemipelagic sediments derived from the nw european shelf the change from erosion nondeposition to enhanced contourite drift accumulation during the early pliocene suggests that a moderate thermohaline current regime prevailed in the faeroe shetland channel prior to the main phase of northern hemisphere glaciation at 3 0 2 5 ma a reduction in meridional heat transport associated with a decrease in the flux of north atlantic deep waters may have been an important factor for the growth of northern hemisphere ice sheets

evolution of early cenozoic marine temperatures the equator to high southern latitude sea surface and vertical temperature gradients are reconstructed from oxygen isotope values of planktonic and benthic foraminifers for the following five time intervals late paleocene early eocene early middle eocene late eocene and early oligocene paleotemperatures are calculated using standard oxygen isotope temperature equations with adjustments to account for 1 variations in sea water 18o related to changes in global ice volume over time and 2 latitudinal gradients in surface water 18o these reconstructions indicate that sea surface temperatures sst of the southern oceans in the early eocene were as high as 15 c whereas temperatures during the late paleocene and early middle eocene reached maximum levels of 10 12 c by the late eocene and early oligocene high latitude sst had declined to 6 and 4 c respectively for most of the early paleogene low latitude sub tropical temperatures remained constant and well within the range of holocene temperatures 24 ndash 25 c but by the late eocene and early oligocene declined to values in the range of 18 to 22 c the late paleogene apparent decline in tropical temperatures however might be artificial because of dissolution of near surface foraminifera tests which biased sediment assemblages toward deeper dwelling foraminifera moreover according to recent plate reconstructions it appears that the majority of sites upon which the late eocene and early oligocene tropical temperatures were previously established were located either in or near regions likely to have been influenced by upwelling global deepwater temperature on average paralleled southern ocean sst for most of the paleogene we speculate based on the overall timing and character of marine sea surface temperature variation during the paleogene that some combination of both higher levels of greenhouse gases and increased heat transport was responsible for the exceptional high latitude warmth of the early eocene

modeling of in situ crystallization processes in the permian mafic layered intrusion of mont collon dent blanche nappe western alps abstract the mont collon mafic complex is one of the best preserved examples of the early permian magmatism in the central alps related to the intra continental collapse of the variscan belt it mostly consists 95 vol of ol hy normative plagioclase wehrlites olivine and cpx gabbros with cumulitic structures crosscut by acid dikes pegmatitic gabbros troctolites and anorthosites outcrop locally a well preserved cumulative sequence is exposed in the dents de bertol area center of intrusion p t calculations indicate that this layered magma chamber emplaced at mid crustal levels at about 0 5 gpa and 1100 c the mont collon cumulitic rocks record little magmatic differentiation as illustrated by the restricted range of clinopyroxene mg number mg cpx 83 89 whole rock incompatible trace element contents e g nb zr ba vary largely and without correlation with major element composition these features are characteristic of an in situ crystallization process with variable amounts of interstitial liquid l trapped between the cumulus mineral phases la icpms measurements show that trace element distribution in the latter is homogeneous pointing to subsolidus re equilibration between crystals and interstitial melts a quantitative modeling based on langmuir s in situ crystallization equation successfully duplicated the ree concentrations in cumulitic minerals of all rock facies of the intrusion the calculated amounts of interstitial liquid l vary between 0 and 35 for degrees of differentiation f of 0 to 20 relative to the least evolved facies of the intrusion l values are well correlated with the modal proportions of interstitial amphibole and whole rock incompatible trace element concentrations e g zr nb of the tested samples however the in situ crystallization model reaches its limitations with rock containing high modal content of ree bearing minerals i e zircon such as pegmatitic gabbros dikes of anorthositic composition locally crosscutting the layered lithologies evidence that the mont collon rocks evolved in open system with mixing of intercumulus liquids of different origins and possibly contrasting compositions the proposed model is not able to resolve these complex open systems but migrating liquids could be partly responsible for the observed dispersion of points in some correlation diagrams absence of significant differentiation with recurrent lithologies in the cumulitic pile of dents de bertol points to an efficiently convective magma chamber with possible periodic replenishment

a warm equable cretaceous the nature of the problem abstract the nature of the problem of warm equable paleoclimates is defined by investigating the mid cretaceous period the problem consists of three components 1 defining precisely the climatic state during any specified interval of geologic time 2 specifying the external climatic forcing factors which may have been important and 3 understanding the climatic response to any specific modifying influence these components are characterized by limitations of critical importance in understanding paleoclimates the nature of the problem of a warm cretaceous is defined both qualitatively and quantitatively within these limits

a wave based model for the marginal ice zone including a floe breaking parameterization 1 the marginal ice zone miz is the boundary between the open ocean and ice covered seas where sea ice is significantly affected by the onslaught of ocean waves waves are responsible for the breakup of ice floes and determine the extent of the miz and floe size distribution when the ice cover is highly fragmented its behavior is qualitatively different from that of pack ice with large floes therefore it is important to incorporate wave ice interactions into sea ice ocean models in order to achieve this goal two effects are considered the role of sea ice as a dampener of wave energy and the wave induced breakup of ice floes these two processes act in concert to modify the incident wave spectrum and determine the main properties of the miz a simple but novel parameterization for floe breaking is derived by considering alternatively ice as a flexible and rigid material and by using current estimates of ice critical flexural strain and strength this parameterization is combined with a wave scattering model in a one dimensional numerical framework to evaluate the floe size distribution and the extent of the miz the model predicts a sharp transition between fragmented sea ice and the central pack thus providing a natural definition for the miz reasonable values are found for the extent of the miz given realistic initial and boundary conditions the numerical setting is commensurate with typical ice ocean models with the future implementation into two dimensional sea ice models in mind

explanations of the tertiary global cooling trend abstract a series of general circulation model experiments are performed to examine the role of paleogeography as an explanation of the tertiary global cooling trend systematic long term variations in topography and land sea distribution are potential causes of long term climate change however climate model sensitivity experiments indicate a geographically related cooling during the last 20 million years but not a long term cenozoic trend coarse resolution changes in geography throughout the tertiary may not be the explanation of the tertiary global cooling trend either a series of events some geographically related or another forcing factor most probably atmospheric co2 concentration are offered as alternative explanations of the tertiary global cooling trend

geophysical and oceanographic information in the marginal ice zone from ocean wave measurements consequent to recent experiments in marginal ice zones miz advances in remote sensing and theoretical progress studies have been published which invoke wave ice interactions to explain or predict certain geophysical phenomena while admirable and desirable in principle these works are based on a refutable surface boundary condition intended for a sheet or plate of solid ice rather than a medium made up of individual ice floes a case is argued for prudence as derived results may originate entirely from the application of an inappropriate miz model

hydroelastic wave diffraction by a vertical cylinder a linear three dimensional problem of hydroelastic wave diffraction by a bottom mounted circular cylinder is analysed the fluid is of finite depth and is covered by an ice sheet which is clamped to the cylinder surface the ice stretches from the cylinder to infinity in all lateral directions the hydroelastic behaviour of the ice sheet is described by linear elastic plate theory and the fluid flow by a potential flow model the two dimensional incident wave is regular and has small amplitude an analytical solution of the coupled problem of hydroelasticity is found by using a weber transform we determine the ice deflection and the vertical and horizontal forces acting on the cylinder and analyse the strain in the ice sheet caused by the incident wave

response of a circular ice floe to ocean waves a new model is presented to reproduce the behavior of a solitary circular flexible ice floe brought into motion by the action of long crested sea waves the intended application of the work is ultimately a fully three dimensional analogue of a marginal ice zone miz through which ocean waves propagate allowing the attenuation and directional advance to be forecast and validated against observations existing theory does not treat directional changes correctly to enable a check to be made on the model two independent methods are developed an expansion in the eigenfunctions of a thin circular plate and the more general method of eigenfunctions used to construct a green s function for the floe displacement and three dimensional scattering patterns in the water surrounding the floe are given for several floe geometries the model is also used to investigate the strain field generated in the floe its surge response and the energy initiated in the water encircling it finally with the aim of understanding how floes herd together to form cohesive structures in the miz the force induced on floes of various thicknesses and diameters is plotted

energy transport in the marginal ice zone a novel approach to modeling ocean wave scattering in the marginal ice zone that uses the coherent potential approximation to compute the energy transport velocity is reported the necessary theory is developed by considering sea ice floes to be thin elastic beams governed by the euler bernoulli equation with the open water surrounding each floe subject to the same equation with its material coefficients set to be very small quantities this mathematical stratagem facilitates the solution of the problem and yields interesting results about the speed at which wave energy propagates through a marginal ice zone the dispersion relation for a random mixture of ice floes and water and the mean free path or attenuation coefficient results from the model are compared with data reported by wadhams et al 1988