The equatorial dynamics of a shallow,homogeneous ocean

Abstract

It is shown that the linear equatorial dynamics of a shallow ocean is characterized by two boundary layers of width γ^? L and γL (γ is the Ekman number of the flow, assumed small, and L is a horizontal dimension of the basin). In the γ^? layer stress in the bottom Ekman layer is comparable to that in the surface Ekman layer. In the γ layer vertical friction is important throughout the depth of the ocean. Should the Rossby number ? be so large as to invalidate a linear theory (? > γ^5/3), then inertial effects become important at a distance ?^2/5 L from the equator. The role played in the circulation of the basin by the non-linear equatorial current first studied by Charney (1960) is shown to be similar to that of the γ layer of the linear theory. Though lateral friction is unimportant in a linear model of the flow, shear layers at the equator are found to be a necessary feature of non-linear flow.     

Mechanisms of bottom boundary fluxes in a numerical model of the Shetland shelf

Across-slope bottom boundary layer (BBL) fluxes on the shelf-edge connect this region to deeper waters. Two proposed ways in which across-slope BBL fluxes can occur, in regions that have a slope current aligned to the bathymetry, are the frictional veering of bottom currents termed the ‘Ekman drain’ and through local wind-forced downwelling (wind-driven surface Ekman flow with an associated bottom flow). We investigate the variability, magnitude and spatial scale of BBL fluxes on the Shetland shelf, which has a prominent slope current, using a high-resolution (～2 km) configuration of the MITgcm model. Fluxes are analysed in the BBL at the shelf break near the 200 m isobath and are found to have a seasonal variability with high/low volume transport in winter/summer respectively. By using a multivariate regression approach, we find that the locally wind-driven Ekman transport plays no explicit role in explaining daily bottom fluxes. We can better explain the variability of the across-slope BBL flux as a linear function of the speed and across-slope component of the interior flow, corresponding to an Ekman plus mean-flow flux. We estimate that the mean-flow is a greater contributor than the Ekman flux to the BBL flux. The spatial heterogeneity of the BBL fluxes can be attributed to the mean-flow, which has a much shorter decorrelation length compared to the Ekman flux. We conclude that both the speed and direction of the interior current determines the daily BBL flux. The wind does not explicitly contribute through local downwelling, but may influence the interior current and therefore implicitly the BBL fluxes on longer timescales.     

Study on linear and nonlinear bottom friction parameterizations for regional tidal models using data assimilation

Data assimilation technique (adjoint method) is applied to study the similarities and the differences between the Ekman (linear) and the Quadratic (nonlinear) bottom friction parameterizations for a two-dimensional tidal model. Two methods are used to treat the bottom friction coefficient (BFC). The first method assumes that the BFC is a constant in the entire computation domain, while the second applies the spatially varying BFCs. The adjoint expressions for the linear and the nonlinear parameterizations and the optimization formulae for the two BFC methods are derived based on the typical Largrangian multiplier method. By assimilating the model-generated ‘observations’, identical twin experiments are performed to test and validate the inversion ability of the presented methodology. Four experiments, which employ the linear parameterization, the nonlinear parameterizations, the constant BFC and the spatially varying BFC, are carried out to simulate the M₂ tide in the Bohai Sea and the Yellow Sea by assimilating the TOPEX/Poseidon altimetry and tidal gauge data. After the assimilation, the misfit between model-produced and observed data is significantly decreased in the four experiments. The simulation results indicate that the nonlinear Quadratic parameterization is more accurate than the linear Ekman parameterization if the traditional constant BFC is used. However, when the spatially varying BFCs are used, the differences between the Ekman and the Quadratic approaches diminished, the reason of which is analyzed from the viewpoint of dissipation rate caused by bottom friction. Generally speaking, linear bottom friction parameterizations are often used in global tidal models. This study indicates that they are also applicable in regional ocean tidal models with the combination of spatially varying parameters and the adjoint method.     

Sediment dynamics in the Black Sea: numerical modelling and remote sensing observations

Here, we address the sediment dynamics in the Black Sea based on analysis of remote sensing data from the Medium Resolution Imaging Spectrometer and numerical simulations with Nucleus for European Modelling of the Ocean model. Boundary conditions consist of realistic meteorological forcing, including significant wave height generated by wave prediction model. A number of sensitivity runs was analysed with the aim to find the most suitable parameters governing sediment fluxes. The comparison between numerical simulations and remote sensing data gives credibility to the quality of simulations. The combined effect of wind waves and currents in the bed layer controls the sediment resuspension that appears to be the major basin-wide source of sediment. Sensitivity experiments included or excluded different forcing terms, e.g. sediment flux from rivers enable to determine the spatial extensions of different point sources. It is concluded that wind-wave forcing is manifested in the sediment dynamics through episodic high energy events contributing to the increase of horizontal sediment fluxes over the northwestern shelf. Both satellite images and numerical model simulations demonstrated that the penetration of suspended sediment into the basin interior was governed by the dynamics of coastal and open-ocean eddies. While fine sediment at sea surface could cross the continental slope propagating into the open ocean, coarser fractions follow the bottom and their penetration into the open ocean is limited. The conclusion is thus that the deposition patterns correlate with the specific shape of Black Sea topography, and the largest depositions are observed in the area of continental slope.     

A 3-D coastal tidal rectification process: observations, theory and experiments

In homogeneous rotating fluid, when there is an oscillating forcing in the interior fluid with a period long enough for an Ekman layer to develop, there is an interaction between the oscillatory Ekman layer and the vertical wall, since the latter imposes an alternating adjustment flow confined near the wall. As a result, this coastal rectification process leads to a Lagrangian transport along the coast. The Ekman number, the Rossby number and the temporal Rossby number of the forcing flow are the governing parameters of that mechanism which can be described by a simplified analytical model taking into account both the vertical time-dependent structure of the current and the presence of the wall. The model shows that the residual (rectified) current flowing with the coast to its right results from the strong nonlinear interaction between along- and cross-shore tidal currents leading to asymmetrical momentum exchanges between the Ekman bottom layer and the coastal boundary layer. The model provides simple scaling laws for the maximum intensity and width of the residual current. The latter is significantly larger than the friction (Stokes) lateral boundary layer of the forcing flow. A comprehensive set of experiments is performed in the 13 m diameter rotating tank by oscillating an 8 m×2 m horizontal plate and vertical wall in a homogeneous fluid at rest in solid-body rotation and measuring the two horizontal components of the current at several locations and depths above the central part of the plate. The predicted and experimentally measured maximum intensity and width of the residual current are in very good agreement, within the range of validity of the model, i.e. when the Ekman number is sufficiently small. However experiments also show that the residual current still occurs when the Ekman layer thickness is of the same order as the fluid depth, but it is then confined to a narrower band along the vertical wall. The flow structure found experimentally is also correctly described by a numerical model developed by Zhang et al. (1994). Current measurements in the Eastern part of the English Channel near the French coast reveal a significant coastal residual current flowing Northward and the coastal rectification process described here may account for part of it.     

风驱动下f-平面准地转三维海洋环流的形成及总质量守恒的应用

将理想化的南中国海海盆在垂直方向上划分为Ekman层、惯性层和摩擦层. Ekman层中的运动由大气风应力驱动,其底部的扰动压力将作为其下惯性层中运动的上边界条件. 惯性层中的运动是由f 平面三维非线性方程在准地转近似下位势涡度守恒控制,由此得到控制惯性层中运动关于扰动压力的三维椭圆型方程. 在惯性层以下考虑到深层的海盆水平尺度很小,由此引进带有底部摩擦的线性控制方程,方程的边界条件为惯性层和摩擦层交界面上的扰动压力连续,沿海盆边界假定海水与相邻的固壁间无热量交换,由此设在海盆边界上扰动温度为零. 在此基础上分别利用惯性层和摩擦层中的椭圆型控制方程计算了相应层次上冬、夏季的扰动压力和准地转流. 结果表明冬季各层上以气旋式环流为主,且随深度的增加流速减小;夏季各层上以反气旋式环流为主,流速也随深度增加而减小. 这在一定程度上和观测事实相符.     

Effects of the bottom boundary condition in numerical investigations of dense water cascading on a slope

The flow of dense water along continental slopes is considered. There is a large literature on the topic based on observations and laboratory experiments. In addition, there are many analytical and numerical studies of dense water flows. In particular, there is a sequence of numerical investigations using the dynamics of overflow mixing and entrainment (DOME) setup. In these papers, the sensitivity of the solutions to numerical parameters such as grid size and numerical viscosity coefficients and to the choices of methods and models is investigated. In earlier DOME studies, three different bottom boundary conditions and a range of vertical grid sizes are applied. In other parts of the literature on numerical studies of oceanic gravity currents, there are statements that appear to contradict choices made on bottom boundary conditions in some of the DOME papers. In the present study, we therefore address the effects of the bottom boundary condition and vertical resolution in numerical investigations of dense water cascading on a slope. The main finding of the present paper is that it is feasible to capture the bottom Ekman layer dynamics adequately and cost efficiently by using a terrain-following model system using a quadratic drag law with a drag coefficient computed to give near-bottom velocity profiles in agreement with the logarithmic law of the wall. Many studies of dense water flows are performed with a quadratic bottom drag law and a constant drag coefficient. It is shown that when using this bottom boundary condition, Ekman drainage will not be adequately represented. In other studies of gravity flow, a no-slip bottom boundary condition is applied. With no-slip and a very fine resolution near the seabed, the solutions are essentially equal to the solutions obtained with a quadratic drag law and a drag coefficient computed to produce velocity profiles matching the logarithmic law of the wall. However, with coarser resolution near the seabed, there may be a substantial artificial blocking effect when using no-slip.     

An analytical model for ice-edge upwelling

Abstract

This paper presents an analytical, two-dimensional model of the wind-induced homogeneous circulation near the edge of an ice pack floating on the ocean surface. It is shown that a vertical shear layer arises under the ice edge, by which the wind-driven geostrophic motion in the open ocean is matched to the flow region underneath the ice. As in coastal upwelling models, this shear layer consists of a thin E ^1/2-layer inside a thicker E ^1/4-layer (E being the Ekman number). Under certain conditions the shear layer produces a vertical mass flux from the bottom to the surface Ekman layer. Near the surface this upwelling flux is concentrated in the narrow E ^1/2-layer. Comparison with observations of upwelling at the edge of a polar ice pack shows good agreement.     

Estimation of friction parameters and laws in 1.5D shallow-water gravity currents on the f-plane, by data assimilation

A 1.5-dimensional, 1.5-layer shallow water model and an ensemble Kalman filter are used to evaluate the feasibility of estimating friction parameters and determining friction laws of oceanic gravity currents. The two friction laws implemented are a linear Rayleigh friction and a quadratic drag law. We demonstrate that the assimilation procedure rapidly estimates the total frictional force, whereas the distinction between the two laws is evolving on a slower time scale. We also demonstrate that parameter estimation can, in this way, choose between different parametrisations and help to discriminate between physical laws of nature by estimating the coefficients presented in such parametrisations.     

Dense water formation and cascading in the Gulf of Thermaikos (North Aegean), from observations and modelling

Observations of dense water formation on the shelf of the Gulf of Thermaikos (North Aegean) are presented, based mainly on continuous monitoring of temperature and currents, during the winter of 2001–2002, at an instrumented mooring and a CTD survey carried out in early February 2002. A 2.5-month realistic simulation, corresponding to the period of observation, was performed to investigate the processes of dense water formation and cascading. The simulation is first compared to the main characteristics of the dense water, time variation of bottom temperature and spatial distribution of the dense water on the shelf. Subsequently, the simulation is used (a) to show that the formation of dense water takes place within the semi-enclosed Thessaloniki Bay and (b) to explain the intermittence of cascading out of the bay in relation to wind variations. The pathways of the dense water through the shelf are investigated with an emphasis on the role of the bottom slope and friction in the Ekman layer. The export of dense water towards the open sea occurs primarily along the slope bounding the western coast.     

Gravity current down a steeply inclined slope in a rotating fluid

The sinking of dense water down a steep continental slope is studied using laboratory experiments, theoretical analysis and numerical simulation. The experiments were made in a rotating tank containing a solid cone mounted on the tank floor and originally filled with water of constant density. A bottom gravity current was produced by injecting more dense coloured water at the top of the cone. The dense water plume propagated from the source down the inclined cone wall and formed a bottom front separating the dense and light fluids. The location of the bottom front was measured as a function of time for various experimental parameters. In the majority of runs a stable axisymmetric flow was observed. In certain experiments, the bottom layer became unstable and was broken into a system of frontal waves which propagated down the slope. The fluid dynamics theory was developed for a strongly non-linear gravity current forming a near-bottom density front. The theory takes into account both bottom and interfacial friction as well as deviation of pressure from the hydrostatic formula in the case of noticeable vertical velocities. Analytical and numerical solutions were found for the initial (t < 1/f), intermediate (t 1/f), and main (t 1/f) stages, where f is the Coriolis parameter. The model results show that during the initial stage non-linear inertial oscillations are developed. During the main stage, the gravity current is concentrated in the bottom layer which has a thickness of the order of the Ekman scale. The numerical solutions are close to the same analytical one. Stability analysis shows that the instability threshold depends mainly on the Froude number and does not depend on the Ekman number. The results of laboratory experiments confirm the similarity properties of the bottom front propagation and agree well with the theoretical predictions.     

Boundary layer dissipation and the nonlinear interaction of equatorial baroclinic and barotropic rossby waves

Two-layer equatorial primitive equations for the free troposphere in the presence of a thin atmospheric boundary layer and thermal dissipation are developed here. An asymptotic theory for the resonant nonlinear interaction of long equatorial baroclinic and barotropic Rossby waves is derived in the presence of such dissipation. In this model, a self-consistent asymptotic derivation establishes that boundary layer flows are generated by meridional pressure gradients in the lower troposphere and give rise to degenerate equatorial Ekman friction. That is to say, the asymptotic model has the property that the dissipation matrix has one eigenvalue which is nearly zero: therefore the dynamics rapidly dissipates flows with pressure at the base of the troposphere and creates barotropic/baroclinic spin up/spin down. The simplified asymptotic equations for the amplitudes of the dissipative equatorial barotropic and baroclinic waves are studied by linear theory and integrated numerically. The results indicate that although the dissipation slightly weakens the tropics to midlatitude connection, strong localized wave packets are nonetheless able to exchange energy between barotropic and baroclinic waves on intraseasonal timescales in the presence of baroclinic mean shear. Interesting dissipation balanced wave-mean flow states are discovered through numerical simulations. In general, the boundary layer dissipation is very efficient for flows in which the barotropic and baroclinic components are of the same sign at the base of the free troposphere whereas the boundary layer dissipation is less efficient for flows whose barotropic and baroclinic components are of opposite sign at the base of the free troposphere.     

Synergy of satellite remote sensing and numerical modeling for monitoring of suspended particulate matter

Monitoring and modeling of the distribution of suspended particulate matter (SPM) is an important task, especially in coastal environments. Several SPM models have been developed for the North Sea. However, due to waves in shallow water and strong tidal currents in the southern part of the North Sea, this is still a challenging task. In general there is a lack of measurements to determine initial distributions of SPM in the bottom sediment and essential model parameters, e.g., appropriate exchange coefficients. In many satellite-borne ocean color images of the North Sea a plume is visible, which is caused by the scattering of light at SPM in the upper ocean layer. The intensity and length of the plume depends on the wave and current climate. It is well known that the SPM plume is especially obvious shortly after strong storm events. In this paper a quasi-3-D and a 3-D SPM transport model are presented. Utilizing the synergy of satellite-borne ocean color data with numerical models, the vertical exchange coefficients due to currents and waves are derived. This results in models that for the first time are able to reproduce the temporal and spatial evolution of the plume intensity. The SPM models consist of several modules to compute ocean dynamics, the vertical and horizontal exchange of SPM in the water column, and exchange processes with the seabed such as erosion, sedimentation, and resuspension. In the bottom layer, bioturbation via benthos and diffusion processes is taken into account.Responsible Editor: Jörg-Olaf Wolff     

Inertial effects in an oceanic circulation model

Abstract

The flow in a mechanically driven thin barotropic rotating fluid system is analysed. The linear theory of Baker and Robinson (1969) is modified and extended into the non-linear regime.

An internal parameter, the “local Rossby number”, is indicative of the onset of nonlinear effects. If this parameter is 0(1) then inertial effects are as important as Coriolis accelerations in the interior of the transport-turning western boundary layer and both of its Ekman layers. The inertial effects in the Ekman layers, ignored in previous explorations of non-linear wind driven oceanic circulation, are retained here and calculated using an approximation of the Oseen type. The circulation problem is reduced to a system of scalar equations in only two independent variables; the system is valid for non-small local Rossby number provided only that the approximate total vorticity is positive.

To complete the solution for small Rossby number a boundary condition for the inertially induced transport is needed. It is found by examining the dynamics controlling this additional transport from the western boundary layer as the transport recirculates through the rest of the ocean basin. The strong constraint of total recirculation within the western boundary layer (zero net inertial transport) is derived.

The calculated primary inertial effects are in agreement with the observations of the laboratory model of Baker and Robinson (1969).

The analysis indicates the extent to which three-dimensional non-linear circulation can be reduced to a two dimensional problem.     

Turbulence avoidance and the wind-driven transport of plankton in the surface Ekman layer

Observations of turbulence avoidance in zooplankton are compared to estimates of the wind-driven turbulence in the upper ocean. Plankton that avoid wind-driven turbulence by moving deeper are no longer transported by the wind-driven Ekman currents near the surface because they are no longer near the surface. Here, a threshold level of turbulence that triggers an avoidance response is estimated, and is used to infer the wind speed and water column stratification conditions that would lead to zooplankton leaving the Ekman layer. Turbulence avoidance is argued to lead to near-shore retention in wind-driven upwelling systems, and to a reduction of the delivery of zooplankton to Georges Bank from the deeper waters of the Gulf of Maine.     

The nonlinear spin-up of a stratified ocean

Abstract

The adjustment of a nonlinear, quasigeostrophic, stratified ocean to an impulsively applied wind stress is investigated under the assumption that barotropic advection of vortex tube length is the most important nonlinearity. The present study complements the steady state theories which have recently appeared, and extends earlier, dissipationless, linear models.

In terms of Sverdrup transport, the equation for baroclinic evolution is a forced advection-diffusion equation. Solutions of this equation subject to a “tilted disk” Ekman divergence are obtained analytically for the case of no diffusion and numerically otherwise. The similarity between the present equation and that of a forced barotropic fluid with bottom topography is shown.

Barotropic flow, which is assumed to mature instantly, can reverse the tendency for westward propagation, and thus produce regions of closed geostrophic contours. Inside these regions, dissipation, or equivalently the eddy field, plays a central role. We assume that eddy mixing effects a lateral, down-gradient diffusion of potential vorticity; hence, within the closed geostrophic contours, our model approaches a state of uniform potential vorticity. The solutions also extend the steady-state theories, which require weak diffusion, by demonstrating that homogenization occurs for moderately strong diffusion.

The evoiution of potential vorticity and the thermocline are examined, and it is shown that the adjustment time of the model is governed by dissipation, rather than baroclinic wave propagation as in linear theories. If dissipation is weak, spin-up of a nonlinear ocean may take several times that predicted by linear models, which agrees with analyses of eddy-resolving general circulation models. The inclusion of a western boundary current may accelerate this process, although dissipation will still play a central role.     

On the magnitude of upwelling fluxes in shelf-break canyons

A hydrodynamic model is employed to derive the magnitude of on-shelf fluxes through a shelf-break canyon for a wide range of canyon sizes and ambient oceanic conditions. Predicted canyon-upwelling fluxes are of the order of 0.05–0.1 Sv (1 Sv=1 million m³/s), being several orders of magnitude greater than upslope fluxes in the bottom Ekman layer on the ambient continental slope. On the basis of ∼150 simulations conducted, a bulk formula of upwelling flux in a submarine canyon is derived. For typical conditions, the upwelling flux varies quadratically with forcing strength (speed of incident flow), linearly with canyon depth, and is inversely proportional to the buoyancy frequency of the density stratification inside the canyon. Other parameters such as density stratification above shelf-break depth and bottom friction are found to have minor influences on the resultant canyon-upwelling flux.     

Ocean wave imaging mechanism by imaging radar

Analytical representations of the high frequency spectra of ocean wave and its variation due to the variation of ocean surface current are derived from the wave-number spectrum balance equation. The ocean surface imaging formulation of real aperture radar (RAR) is given using electromagnetic wave backscattering theory of ocean surface and the modulations of ocean surface winds, currents and their variations to RAR are described. A general representation of the phase modulation induced by the ocean surface motion is derived according to standard synthetic aperture radar (SAR) imaging theory. The detectability of ocean current and sea bottom topography by imaging radar is discussed. The results constitute the theoretical basis for detecting ocean wave fields, ocean surface winds, ocean surface current fields, sea bottom topography, internal wave and so on.     

A numerical study of island wakes in the Southern California Bight

With the existence of eight substantial islands in the Southern California Bight, the oceanic circulation is significantly affected by island wakes. In this paper a high-resolution numerical model (on a 1 km grid), forced by a high-resolution wind (2 km), is used to study the wakes. Island wakes arise due both to currents moving past islands and to wind wakes that force lee currents in response. A comparison between simulations with and without islands shows the surface enstrophy (i.e., area-integrated square of the vertical component of vorticity at the surface) decreases substantially when the islands in the oceanic model are removed, and the enstrophy decrease mainly takes place in the areas around the islands. Three cases of wake formation and evolution are analyzed for the Channel Islands, San Nicolas Island, and Santa Catalina Island. When flows squeeze through gaps between the Channel Islands, current shears arise, and the bottom drag makes a significant contribution to the vorticity generation. Downstream the vorticity rolls up into submesoscale eddies. When the California Current passes San Nicolas Island from the northwest, a relatively strong flow forms over the shelf break on the northeastern coast and gives rise to a locally large bottom stress that generates anticyclonic vorticity, while on the southwestern side, with an adverse flow pushing the main wake current away from the island, positive vorticity has been generated and a cyclonic eddy detaches into the wake. When the northward Southern California Countercurrent passes the irregular shape of Santa Catalina Island, cyclonic eddies form on the southeastern coast of the island, due primarily to lateral stress rather than bottom stress; they remain coherent as they detach and propagate downstream, and thus they are plausible candidates for the submesoscale “spirals on the sea” seen in many satellite images. Finally, the oceanic response to wind wakes is analyzed in a spin-up experiment with a time-invariant wind that exhibits strips of both positive and negative curl in the island lee. Corresponding vorticity strips in the ocean develop through the mechanism of Ekman pumping.     

Detecting surface geostrophic currents using wavelet filter from satellite geodesy

According to the features of spatial spectrum of the dynamic ocean topography (DOT),wavelet filter is proposed to reduce short-wavelength and noise signals in DOT. The surface geostrophic currents calculated from the DOT models filtered by wavelet filter in global and Kuroshio regions show more detailed information than those from the DOT models filtered by Gaussian filter. Based on a satellite gravity field model (CG01C) and a gravity field model (EGM96),combining an altimetry-derived mean sea surface height model (KMSS04),two mean DOT models are estimated. The short-wavelength and noise signals of these two DOT models are removed by using wavelet filter,and the DOT models asso-ciated global mean surface geostrophic current fields are calculated separately. Comparison of the surface geostrophic currents from CG01C and EGM96 model in global,Kuroshio and equatorial Pacific regions with that from oceanography,and comparison of influences of the two gravity models errors on the precision of the surface geostrophic currents velocity show that the accuracy of CG01C model has been greatly improved over pre-existing models at long wavelengths. At large and middle scale,the surface geostrophic current from satellite gravity and satellite altimetry agrees well with that from oceanography,which indicates that ocean currents detected by satellite measurement have reached relatively high precision.