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Articles 241 - 270 of 2497
Full-Text Articles in Entire DC Network
Ellipsoidal Vortex In A Nonuniform Flow: Dynamics And Chaotic Advections, V. V. Zhmur, E. A. Ryzhov, K. V. Koshel
Ellipsoidal Vortex In A Nonuniform Flow: Dynamics And Chaotic Advections, V. V. Zhmur, E. A. Ryzhov, K. V. Koshel
Journal of Marine Research
Quasi-geostrophic dynamics of an ellipsoidal vortex embedded in a nonuniform flow is studied in the approximation of the infinitely deep rotating ocean with a constant buoyancy frequency. The vortex core is an ellipsoid with a constant vorticity different from the background vorticity value. The core is shown to move along with the flow and to deform under the effect of it. Regimes of the core's behavior depend on the flow characteristics and the initial values of the vortex parameters (the shape and the orientation relative to the flow). These regimes are (i) rotation (along with the eccentricity oscillation), (ii) oscillation …
Secondary Toroidal Vortices Above Seamounts, Valery N. Zyryanov 0
Secondary Toroidal Vortices Above Seamounts, Valery N. Zyryanov 0
Journal of Marine Research
The classical Taylor-Couette flow appears in a homogeneous fluid between two coaxial cylinders rotating with different angular velocities. The stability loss by a Taylor-Couette flow leads to a bifurcation and generation of Taylor toroidal vortices. In this study we consider an analog to this effect in the case of seamounts in a homogeneous ocean on a f-plane. A seamount is approximated by two coaxial cylinders with heights h1, h2 standing one upon the other, the lower cylinder having a larger diameter. Taylor-Couette flow forms in a circular area above the ledge as follows from the differential …
Topographic Rectification In A Stratified Ocean, K. H. Brink
Topographic Rectification In A Stratified Ocean, K. H. Brink
Journal of Marine Research
Mean flow generation by oscillating currents is considered in an idealized stratified ocean with a corrugated shelf-slope topography. Numerical model results for near-bottom mean along-isobath flow show a general parameter dependence similar to that found with no stratification (Brink, 2010). Stratification, however, makes the interior rectified flow depth-dependent, and usually bottom-intensified. Scalings for both the mean flow and its vertical dependence are developed and evaluated. Two crude comparisons against observed mean oceanic flows suggest that the present results may parameterize the mean flow magnitude correctly.
Rossby Wormholes, David P. Marshall
Rossby Wormholes, David P. Marshall
Journal of Marine Research
The influence of bottom topography on the westward propagation of long, baroclinic Rossby waves is studied analytically in a two-layer ocean model. In the limit of a thin upper layer, scaling analysis suggests that the waves should be relatively insensitive to variable bottom topography however, this insensitivity can break down in regions of closed f/H contours, where f is the Coriolis parameter and H the ocean depth. An integral constraint is derived in the planetary-geostrophic limit, showing that the net radiative flux of upper layer thickness anomalies into a closed f/H contour, at its eastern margin, is balanced by an …
Fluid Mixing By Swimming Organisms In The Low-Reynolds-Number Limit, Eric Kunze
Fluid Mixing By Swimming Organisms In The Low-Reynolds-Number Limit, Eric Kunze
Journal of Marine Research
Recent publications in the fluid physics literature have suggested that low-Reynolds-number swimming organisms might contribute significantly to ocean mixing. These papers have focussed on the mass transport due to fluid capture and disturbance by settling or swimming particles based on classical fluid mechanics flows but have neglected the role of molecular property diffusion. Scale-analysis of the property conservation equation finds that, while properties with low molecular diffusivities can have enhanced mixing for typical volume fractions in aggregations of migrating zooplankton, this mixing is still well below that due to internal-wave breaking so unlikely to be important in the ocean.
The Nonlinear Downstream Development Of Baroclinic Instability, Joseph Pedlosky
The Nonlinear Downstream Development Of Baroclinic Instability, Joseph Pedlosky
Journal of Marine Research
The downstream development in both space and time of baroclinic instability is studied in a nonlinear channel model on the f-plane. The model allows the development of the instability to be expressed on space and time scales that are long compared to the growth rates and wavelengths of the most unstable wave. The unstable system is forced by time-varying boundary conditions at the origin of the channel and so serves as a conceptual model for the development of fluctuations in currents like the Gulf Stream and Kuroshio downstream of their separation points from their respective western boundaries. The theory …
Meddy, Spiral Arms, And Mixing Mechanisms Viewed By Seismic Imaging In The Tagus Abyssal Plain (Sw Iberia), Haibin Song, Luis Menezes Pinheiro, Barry Ruddick, Francisco Curado Teixeira
Meddy, Spiral Arms, And Mixing Mechanisms Viewed By Seismic Imaging In The Tagus Abyssal Plain (Sw Iberia), Haibin Song, Luis Menezes Pinheiro, Barry Ruddick, Francisco Curado Teixeira
Journal of Marine Research
Seismic imaging of the water column is used to investigate the relative roles of thermohaline intrusive mixing and stirring (straining and shearing) by mesoscale eddies in the NE Atlantic, in and around a Meddy, and in waters between the Meddy and the coast of Portugal. The images show that mixing is virtually absent within the core but anomalously high in the top, bottom, and surrounding frontal region, as previously found by conventional means. In the immediate periphery of the Meddy, bands of water with numerous reflectors consistent with thermohaline intrusions, and with anomalously high mixing rate can be seen. We …
Anomalous Diffraction Approach To The Visible Spectra Of Absorption By Marine Particles With Power-Law Size Distributions, Maciej Matciak, Bożena Wojtasiewicz
Anomalous Diffraction Approach To The Visible Spectra Of Absorption By Marine Particles With Power-Law Size Distributions, Maciej Matciak, Bożena Wojtasiewicz
Journal of Marine Research
The spectral shape of the light absorption by marine particles with power-law size distribution was analyzed. The anomalous diffraction approximation (ADA) in its conventional form for optically “soft” homogenous particles was used to model the absorption cross section. Based on this theory, particular formulas describing the spectral shape of absorption of an assemblage of particles were derived. Exemplary calculations were performed for particles of selected shapes (spheres, thin cylinders and disks). The results suggest that relative absorption spectra of marine particles in many cases can be approximated by a simple formula, i.e. a power function of the ratio of their …
Linear Instability Of Uniform Shear Zonal Currents On The Β-Plane, Nathan Paldor, Yona Dvorkin, Doron Nof
Linear Instability Of Uniform Shear Zonal Currents On The Β-Plane, Nathan Paldor, Yona Dvorkin, Doron Nof
Journal of Marine Research
A unified formulation of the instability of a mean zonal flow with uniform shear is proposed, which includes both the coupled density front and the coastal current. The unified formulation shows that the previously found instability of the coupled density front on the f-plane has natural extension to coastal currents, where the instability exists provided that the net transport of the current is sufficiently small. This extension of the coupled front instability to coastal currents implies that the instability originates from the interaction between Inertia-Gravity waves and a vorticity edge wave and not from the interaction of the two …
Primary And Secondary Intrusions In Double-Diffusively Stable Vertical Gradients, Julian A. Simeonov
Primary And Secondary Intrusions In Double-Diffusively Stable Vertical Gradients, Julian A. Simeonov
Journal of Marine Research
The purpose of this paper is to show that molecularly-driven double-diffusive intrusions can produce significant lateral and vertical double-diffusive mixing even when the initial temperature and salinity are both stably stratified in the vertical. Assuming uniform density-compensated horizontal gradients and periodic disturbances, three-dimensional direct numerical simulations (DNS) for the fastest growing intrusion show that the latter equilibrates due to the generation of salt fingers which reduce the driving buoyancy pressure gradient. The DNS also provided statistical data for a new parameterization of the salt finger fluxes which includes the effects of shear and variable vertical gradients. This parameterization makes it …
Effects Of Surface Quasi-Geostrophic Turbulence On Phytoplankton Competition And Coexistence, Coralie Perruche, Pascal Rivière, Guillaume Lapeyre, Xavier Carton, Philippe Pondaven
Effects Of Surface Quasi-Geostrophic Turbulence On Phytoplankton Competition And Coexistence, Coralie Perruche, Pascal Rivière, Guillaume Lapeyre, Xavier Carton, Philippe Pondaven
Journal of Marine Research
This paper aims at studying numerically the competition between two mutually exclusive phytoplankton species in a fully-turbulent field consisting of interacting mesoscale and submesoscale structures. A simple NPPZD ecosystem model is embedded in a Surface Quasi-Geostrophic model which is able to reproduce frontogenesis and the associated nutrient vertical pump. The two simulated phytoplankton species differ by their size and their affinity for nutrients. In this study, we rationalize the role played by eddies and filaments in the distribution of the two phytoplankton species. We show that the SQG dynamics are responsible for the coexistence of the two phytoplankton species on …
Modeling The Evolution Of Intrathermocline Lenses In The Atlantic Ocean, B. N. Filyushkin, M. A. Sokolovskiy
Modeling The Evolution Of Intrathermocline Lenses In The Atlantic Ocean, B. N. Filyushkin, M. A. Sokolovskiy
Journal of Marine Research
The existence of a tongue of Mediterranean Water (MW) at the depths of 500–1500 m is a characteristic feature of the hydrological regime in the northeastern part of the Atlantic Ocean. Anticyclonic eddies filled with MW (meddies or lenses) are observed in this region. They are identified via their high temperature and salinity anomalies, which compensate in density, yielding nearly homogeneous meddy cores. The analysis of historical observations has showed that approximately 100 lenses can exist simultaneously in this part of the ocean. High concentration of large water volumes (>4000 km3 each) can be found both in the …
Modeling Of The M2 Surface And Internal Tides And Their Seasonal Variability In The Arctic Ocean: Dynamics, Energetics And Tidally Induced Diapycnal Diffusion, B. A. Kagan, E. V. Sofina, A. A. Timofeev
Modeling Of The M2 Surface And Internal Tides And Their Seasonal Variability In The Arctic Ocean: Dynamics, Energetics And Tidally Induced Diapycnal Diffusion, B. A. Kagan, E. V. Sofina, A. A. Timofeev
Journal of Marine Research
Modeling results for the M2 surface and internal tides in the Arctic Ocean (AO) are presented. These incorporate the data on tidal dynamics and energetics and tidally induced diapycnal diffusion. A modified version of the 3D finite-element hydrostatic model QUODDY-4 is used as a basis for modeling. It is shown that the predicted surface tide differs slightly from that obtained from other tidal models, whereas the internal tidal waves (ITW) are less than those in oceans of moderate and low latitudes. It also appears that ITW themselves belong to the family of trapped waves. This finding, together with the …
On Trend Analysis In Climatic Time Series, With Application To Surface Temperature, Victor Privalsky, Marina Fortus, Vladimir Komchatov, Eugene Borisov
On Trend Analysis In Climatic Time Series, With Application To Surface Temperature, Victor Privalsky, Marina Fortus, Vladimir Komchatov, Eugene Borisov
Journal of Marine Research
The deletion of a trend as an initial step in the analysis of climatic time series may result in the elimination of low-frequency components which constitute an integral part of climatic variability. An example is given here showing that linear trend deletion from the time series of the World Ocean annual sea-surface temperature (1850–2009) reduces the low-frequency (from 0.02 year–1 to 0.001 year–1) part of the time series spectrum by ∼40% to 80% thus severely distorting the spectrum of climate. As an additional result, it is shown that the current warming can be explained in full within …
The Arrested Agulhas Retroflection, Doron Nof, Volodymyr Zharkov, Joseph Ortiz, Nathan Paldor, Wilton Arruda, Eric Chassignet
The Arrested Agulhas Retroflection, Doron Nof, Volodymyr Zharkov, Joseph Ortiz, Nathan Paldor, Wilton Arruda, Eric Chassignet
Journal of Marine Research
Paleoceanographic proxy data indicate that the Agulhas leakage into the South Atlantic was dramatically reduced during glacial times. In our former papers, we suggested that this was due to a northward shift of the zero wind stress curl that, in turn, forced the retroflection to occur farther north, where the slant of the coastline relative to the north is steep. In the present paper, we propose that strong westerlies (0.4 Pa, implying a wind speed of ∼12 m s–1 at zero degrees centigrade), which were supposedly common during glaciations, can also arrest the leakage. This arrest occurred because the …
Variational Assimilation Of Glider Data In Monterey Bay, Chudong Pan, Max Yaremchuk, Dmitri Nechaev, Hans Ngodock
Variational Assimilation Of Glider Data In Monterey Bay, Chudong Pan, Max Yaremchuk, Dmitri Nechaev, Hans Ngodock
Journal of Marine Research
Temperature and salinity profiles observed by gliders in the Monterey Bay in August 2003 are assimilated into NCOM model in the framework of a 3dVar scheme with a hybrid background error covariance (BEC) representation. The model performance is validated against independent mooring observations for the assimilation runs with 1-hour analysis cycle. In the first experiment the background error statistics was estimated using the ensemble of model states spanning the entire observation period, whereas in the second experiment the BEC information was acquired by averaging over the 3day floating temporal window (FTW) centered at the analysis time. It is found that …
A Tribute To Melvin E. Stern (1929–2010), George Veronis
A Tribute To Melvin E. Stern (1929–2010), George Veronis
Journal of Marine Research
Melvin Stern was a brilliant theoretician who introduced a number of innovative ideas in oceanography. These include his (a) penetrating introduction of double diffusive processes, (b) introduction of MODONS, the important, small scale, coherent features in the ocean, (c) incisive studies of rotating hydraulics, (d) investigation into bores, jumps and boundary flows, (e) analyses of the role of vortices in ocean dynamics, and (f) frequent contributions to instabilities in the ocean. He tended to think very intuitively, not unlike Henry Stommel. When he introduced a new idea, he accompanied it with a very thorough analysis. Generally speaking, he communicated most …
A Multispecies Tree Ring Reconstruction Of Potomac River Streamflow (950-2001), R. Stockton Maxwell, Amy E. Hessl, Edward R. Cook, Neil Pederson
A Multispecies Tree Ring Reconstruction Of Potomac River Streamflow (950-2001), R. Stockton Maxwell, Amy E. Hessl, Edward R. Cook, Neil Pederson
Faculty & Staff Scholarship
Millennial length reconstruction of Potomac River StreamflowInstrumental record does represent the past milleniumImprovement upon the previous reconstruction
Annual Seroprevalence Of Yersinia Pestis In Coyotes As Predictors Of Interannual Variation In Reports Of Human Plague Cases In Arizona, United States, Heidi E. Brown, Craig E. Levy, Russell E. Enscore, Martin E. Schriefer, Thomas J. Deliberto, Kenneth L. Gage, Rebecca J. Eisen
Annual Seroprevalence Of Yersinia Pestis In Coyotes As Predictors Of Interannual Variation In Reports Of Human Plague Cases In Arizona, United States, Heidi E. Brown, Craig E. Levy, Russell E. Enscore, Martin E. Schriefer, Thomas J. Deliberto, Kenneth L. Gage, Rebecca J. Eisen
United States Department of Agriculture Wildlife Services: Staff Publications
Although several health departments collect coyote blood samples for plague surveillance, the association between reported human cases and coyote seroprevalence rates remains anecdotal. Using data from an endemic region of the United States, we sought to quantify this association. From 1974 to 1998, about 2,276 coyote blood samples from four Arizona counties were tested for serological evidence of exposure to Yersinia pestis, the causative agent of plague. Using a titer threshold presumed to be indicative of recent infection (serum titers of ≥1:256), we found a statistically significant relationship between years with > 17% sero-positive coyotes and years with two or …
Editorial, Kenneth H. Brink
Editorial, Kenneth H. Brink
Journal of Marine Research
With the completion of Volume 67 of the Journal of Marine Research, George Veronis is stepping down after having served as editor for 37 years. In the Journal’s 73-year history, there have been only three editors, and George has served the longest. During George’s tenure, the Journal has prospered and it has strengthened its position as one of the best oceanographic scholarly Journals. The entire oceanographic community should be grateful for George’s commitment to excellence, hard work and commitment. His accomplishments with the Journal are most impressive.
Larval Responses To Turbulence And Temperature In A Tidal Inlet: Habitat Selection By Dispersing Gastropods?, Heidi L. Fuchs, Andrew R. Solow, Lauren S. Mullineaux
Larval Responses To Turbulence And Temperature In A Tidal Inlet: Habitat Selection By Dispersing Gastropods?, Heidi L. Fuchs, Andrew R. Solow, Lauren S. Mullineaux
Journal of Marine Research
Marine larval dispersal is affected by hydrodynamic transport and larval behavior, but little is known about how behavior affects large-scale patterns of dispersal and recruitment. Intertidal habitats are characterized by strong and variable turbulence relative to shelf and pelagic waters, so larval responses to turbulence may affect both dispersal and habitat selection. This study combined observations and theoretical approaches to model gastropod larval responses to multiple physical variables in a well-mixed tidal inlet. Physical measurements and larvae were collected in July 2004 in Barnstable Harbor, Massachusetts (USA). Physical measurements were incorporated in an advection-diffusion model where larval vertical velocity is …
Oxygen Isotope Ratio, Barium And Salinity In Waters Around The North American Coast From The Pacific To The Atlantic: Implications For Freshwater Sources To The Arctic Throughflow, Michiyo Yamamoto-Kawai, Eddy C. Carmack, Fiona A. Mclaughlin, Kelly K. Falkner
Oxygen Isotope Ratio, Barium And Salinity In Waters Around The North American Coast From The Pacific To The Atlantic: Implications For Freshwater Sources To The Arctic Throughflow, Michiyo Yamamoto-Kawai, Eddy C. Carmack, Fiona A. Mclaughlin, Kelly K. Falkner
Journal of Marine Research
In 2002, oxygen isotope ratios of water (H218O/H216O), dissolved barium, and salinity were measured in surface waters around northern North America to identify freshwater sources and to provide a large-scale background for interpretation of regional inputs and processes. Oxygen isotope ratios showed that precipitation, river runoff, and sea ice meltwater were all significant contributors to the freshwater carried by the coastal component of the Arctic throughflow. Precipitation and runoff contributed <40% and >60%, respectively, to the freshwater found in surface waters along the Pacific coast. Sea ice meltwater contributed up to 65% to waters residing near …40%>
Onset Of Time-Dependence In A Double-Gyre Circulation: Barotropic Basin Modes Versus Classical Baroclinic Modes, Hristina G. Hristova, Henk A. Dijkstra, Michael A. Spall
Onset Of Time-Dependence In A Double-Gyre Circulation: Barotropic Basin Modes Versus Classical Baroclinic Modes, Hristina G. Hristova, Henk A. Dijkstra, Michael A. Spall
Journal of Marine Research
Using a fully-implicit high-resolution two-layer quasi-geostrophic model combined with pseudo-arclength continuation methods, we perform a bifurcation analysis of double-gyre ocean flows to study their initial oscillatory instabilities. In this model, both wind- and thermally-forced flows can be represented. We demonstrate that on the branch of anti-symmetric steady-state solutions the ratio, Ω, of the flow advective speed to the long internal Rossby wave speed determines the type of oscillatory modes to first become unstable. This is the same nondimensional parameter that controls the shape of the geostrophic contours in the linear limit of the circulation. For large values of Ω, the …
Upwelling Limitation By Onshore Geostrophic Flow, P. Marchesiello, P. Estrade
Upwelling Limitation By Onshore Geostrophic Flow, P. Marchesiello, P. Estrade
Journal of Marine Research
Although coastal upwelling has now been the subject of many studies, the only available dynamical upwelling index is derived from a simple relation between upwelling intensity and alongshore winds stress. In this study, we first present a primitive equation model simulation of the New Caledonia island region to show that upwelling intensity can be limited by onshore geostrophic flow. Then, we propose a new analytical model accounting for the effect of onshore geostrophic flow on the structure of upwelling. The analytical model is shown to match remarkably well the solution of the primitive equation model. Used as an upwelling index, …
Oxygen Penetration Around Burrows And Roots In Aquatic Sediments, F. J. R. Meysman, O. S. Galaktionov, R. N. Glud, J. J. Middelburg
Oxygen Penetration Around Burrows And Roots In Aquatic Sediments, F. J. R. Meysman, O. S. Galaktionov, R. N. Glud, J. J. Middelburg
Journal of Marine Research
Diffusion is the dominant physical mechanism for the transfer of oxygen into fine-grained aquatic sediments. This diffusive uptake occurs at the sediment-water interface, but also at internal interfaces, such as along ventilated burrows or O2 releasing plant roots. Here, we present a systematic model analysis of the oxygen transfer at such biological interfaces. We list the equations for the O2 distribution, the flux, the oxygen penetration distance (OPD), the oxygenated sediment volume, and the irrigational oxygen uptake (IOU) as a function of biological parameters, such as burrow/root radius and burrow/root density. We also provide a set of computational …
Relative Displacement Probability Distribution Functions From Balloons And Drifters, J. H. Lacasce
Relative Displacement Probability Distribution Functions From Balloons And Drifters, J. H. Lacasce
Journal of Marine Research
The focus of relative (pair) dispersion studies in the atmosphere and ocean is often on the mean square particle separation or the Finite Scale Lyapunov Exponent. Much less attention has been paid to the probability density function (PDF) of pair separations, despite that this determines the dispersion. In two-dimensional (2-D), nondivergent, homogeneous flows, the PDF is governed by a Fokker-Planck equation. Analytical solutions exist for the turbulent inertial ranges, but these have rarely been compared to observations.We consider the analytical PDFs for the turbulent inertial ranges and derive a new solution for the 2-D energy range. We then compare the …
George Veronis: An Appreciation, K. H. Brink, K. K. Turekian
George Veronis: An Appreciation, K. H. Brink, K. K. Turekian
Journal of Marine Research
George Veronis was born in New Brunswick, New Jersey on June 3, 1926, one of six accomplished children of a Greek immigrant couple. He grew up in Easton, Pennsylvania, where his talent for mathematics was recognized early on. World War II interrupted his education, however, and he enlisted in the U.S. Navy where he served aboard submarines in the Pacific Ocean. With the end of the global conflict, George entered college on the G.I. Bill and graduated with a B.S. in Mathematics from nearby Lafayette College in 1950...
Impact Of High-Frequency Nonlinear Internal Waves On Plankton Dynamics In Massachusetts Bay, Zhigang Lai, Changsheng Chen, Robert C. Beardsley, Brian Rothschild, Rucheng Tian
Impact Of High-Frequency Nonlinear Internal Waves On Plankton Dynamics In Massachusetts Bay, Zhigang Lai, Changsheng Chen, Robert C. Beardsley, Brian Rothschild, Rucheng Tian
Journal of Marine Research
A simple Nutrient-Phytoplankton-Zooplankton (NPZ) model was coupled with the non-hydrostatic Finite-Volume Coastal Ocean Model (FVCOM-NH) to study the impact of high-frequency nonlinear internal waves on plankton dynamics in Massachusetts Bay (MB) during the stratified summer season. The temporal and spatial variability of phytoplankton concentration follows the vertical isopycnal displacement to the lowest order as the waves are generated by the semidiurnal tidal flow over Stellwagen Bank (SB) and propagate westward across MB. The tidally-averaged distribution of phytoplankton is characterized by three distinct zones of low subsurface concentration: (I) the western flank of Stellwagen Bank; (II) the center of Stellwagen Basin; …
Rapid Response Of The East Australian Current To Remote Wind Forcing: The Role Of Barotropic-Baroclinic Interactions, K. L. Hill, S. R. Rintoul, P. R. Oke, K. Ridgway
Rapid Response Of The East Australian Current To Remote Wind Forcing: The Role Of Barotropic-Baroclinic Interactions, K. L. Hill, S. R. Rintoul, P. R. Oke, K. Ridgway
Journal of Marine Research
The strength of the East Australian Current (EAC) is observed to vary in response to changes in basin-scale winds in the South Pacific, with a time lag of three years. First mode baroclinic Rossby waves would take 10–15 years to reach the western boundary from the center of the South Pacific, so a faster mechanism is needed to explain this link. We use an ocean general circulation model forced with idealized anomalies of wind stress curl to examine the mechanism responsible for the rapid response of the EAC. A curl perturbation in the central South Pacific produces baroclinic and barotropic …
Patchiness In Internal Tidal Beams, Hans Van Haren, Leo R. M. Maas, Theo Gerkema
Patchiness In Internal Tidal Beams, Hans Van Haren, Leo R. M. Maas, Theo Gerkema
Journal of Marine Research
Results are presented from measurements on internal tides and near-inertial motions, obtained using deep-towed acoustic Doppler current profilers along a single transect over the continental slope in the Bay of Biscay and, in another experiment, over a flank of Great Meteor Seamount in the Canary Basin. Each measurement lasted two days and involved repeated passage of the same track, making it possible to extract by harmonic analysis the semidiurnal (and, over Great Meteor Seamount, also the combined diurnal/near-inertial) signal. In the Bay of Biscay, the transect covered by the towing was sufficiently long to follow the internal semidiurnal tidal beam …