Wind-driven Ocean Circulation Research Articles

A simple model for the three-dimensional, thermally and wind-driven ocean circulation

As a generalization to box models of the large-scale, thermally and wind-driven ocean circulation, nonlinear equations, describing the evolution of two vectors characterizing the state of the ocean, are derived for a rectangular ocean on an f -plane. These state vectors represent the basin-averaged density gradient and the overall angular momentum vector of the ocean. Neglecting rotation, the Howard-Malkus loop oscillation is retrieved, governed by the Lorenz equations. This has the equations employed in box models, in the restricted sense where no distinction is made between the restoring time scales of the temperature and salinity fields, as a special case. In another approximation, with rotation included, the equations are equivalent to a set E. N. Lorenz introduced to describe the “simplest possible atmospheric general circulation model”. Although the atmospheric circulation may be chaotic, parameter values in the ocean are such that the circulation is steady or, at most, exhibits a self-sustained oscillation. For a purely thermally forced ocean, this is always a unique state. Addition of a wind-induced horizontal circulation allows for multiple equilibria, despite the neglect of the salinity field. DOI: 10.1034/j.1600-0870.1994.t01-3-00008.x

A simple model for the symmetry properties of nonlinear wind driven ocean circulation

Abstract It is shown that the symmetry properties of barotropic nonlinear wind driven ocean circulation, as presented in the numerical simulations of Veronis (1966a, b), can easily be derived analytically for large Ekman number, the so-called “small beta regime”, and for any strength of the nonlinearity, by a perturbation expansion in the inverse Ekman number. The solution is a superposition of a vorticity monopole, dipole and quadrupole, the symmetry properties of which are qualitatively the same as those of the Veronis' sequence. It is also shown that the Veronis' sequence does not lead to the inertial Fofonoff (1954) mode, but that the latter is the limit of another sequence in the parameter plane spanned by the Rossby and Ekman numbers.

Rectification of the wind-driven ocean circulation on the beta plane

Abstract A nonlinear Stommel model of the ocean circulation on the beta plane, driven by a time periodic wind stress, is investigated in order to study symmetry properties of the observed time-mean ocean gyres. Due to the presence of vorticity advection terms the model will have a steady or rectified response to fluctuating wind fields. In this paper a small inverse Ekman number, “the small beta regime”, is considered. It is demonstrated that for this case all qualitative features of the residual circulation, obtained numerically by Veronis (1970). are reproduced in an analytical way. They include the dipole character of the gyre, its maximum symmetry breaking around the north-south axis for intermediate Reynolds numbers, measuring the ratio of vorticity forcing and dissipation, and the maximum residual response for intermediate forcing frequencies.

On steady, frictional wind-driven ocean circulation with topography in a circumpolar basin

Abstract An analytical boundary layer solution is developed for barotropic, steady, frictional, wind-driven flow over a meridionally aligned top-hat ridge in a circumpolar basin on a local β-plane. Classical Sverdrup dynamics cannot hold in a basin with no meridional barriers. With a top-hat ridge, frictional boundary layers exist adjacent to the depth discontinuities which can support along- and cross-ridge transport. The boundary layers thus provide a mechanism for transporting fluid across latitudes of zero wind stress curl. The relevance of this simple model to the dynamics of the Southern Ocean is discussed.

The Wind-driven Circulation: Quasi-geostrophic Simulations and Theory for Nonsymmetric Winds

Abstract Simulations of the wind-driven Ocean circulation, carded out with an eddy-resolving quasi-geostrophic numerical model, and symmetric, idealized wind forcing have a large-scale structure that is predicted wen by the steady nonlinear theory of Rhines and Young. The sharp jet and inertial recirculation am often confined weft inside the region of closed hyperbolic characteristics, defined by that theory, and hence do not affect the Sverdrup-dynamics part of the gyre. The characteristics make possible simple predictions about the development of the circulation, including time dependence and eddy stirring. By tilting the line of vanishing Ekman pumping away from the east-west orientation (as it is tilted in the North Atlantic, and less so the North Pacific), we explore a family of circulations. As the tilt of the wind held is increased, characteristics originating at the eastern boundary begin to thread through the energetic region occupied by the free jet. Then, extensive new branches of eddy-driven f...

Flow separation and unsteadiness in a rotating sliced cylinder

Abstract The rotating sliced cylinder model has its origins in simulations of the large scale wind-driven ocean circulation. The model consists of a rotating circular cylinder with a sloping planar base and a lid which rotates at a rate slightly different from that of the background rotation. Numerical models for the inviscid flow, the boundary-layer flow and the viscous flow equations in this configuration are described and the flow patterns produced by them are compared. Laboratory experiments were also performed and the results are presented as validation of the numerical models. The unsteadiness of the flow in some parameter regimes which was noted by other authors (Beardsley, 1969, 1973a, b and Beardsley and Robbins, 1975) appears to be caused by instability of the separated boundary-layer flow. The separated flow has some unique features due to the effect of the driving force exerted on the flow by the rotating lid and these are also described.

Wind-driven ocean circulation and equilibrium statistical mechanics

Wind-driven ocean circulation and equilibrium statistical mechanics

A multilayer model of the thermohaline and wind-driven ocean circulation : Huang, R.X. and Kirk Bryan, 1987. J. phys. Oceanogr., 17(11):1909–1924

A multilayer model of the thermohaline and wind-driven ocean circulation : Huang, R.X. and Kirk Bryan, 1987. J. phys. Oceanogr., 17(11):1909–1924

Wind-driven ocean circulation transition to barotropic instability

This article deals with the ocean circulation driven by steady zonal winds, and damped by bottom and biharmonic friction, when represented by the simple barotropic vorticity equation. A double gyre antisymmetrical wind stress pattern in a square basin is considered. Wind forcing and dissipation parameters are chosen within the ranges of what has been used in previous studies. The flow characteristics for both steady and unsteady situations are tentatively described as functions of model external parameters through the analysis of a large set of numerical experiments. Functional relations are derived for the mid-latitude jet parameters (length, width and transport) on the basis of scaling arguments. With the diagrams established for these quantities in forcing and dissipation parameter relations allow quantitative predictions of model response to a wide range of parameter choices to be made. The transition to barotropic instability is interpreted by analysing and comparing the spin-up phase of different numerical experiments leading either to stable or unstable solutions. Two major types of destabilization are identified, namely through meandering of the mid-latitude eastward jet and Rossby wave radiation from the westward return flow. The characteristics of the flows are shown to be highly sensitive to the external parameter changes. Competition between eddy kinetic energy level and eastward jet extension appears to consttitute the key point of this class of solutions, controlling in particular the intensity of transport in the inner gyres, driven by the eddy field on the two sides of the mid-basin jet, in a very similar manner to that of the more complex multilayered EGCMs.

On the application of asymptotic analysis to the dynamical theory of the pole tide

Summary. This article examines the effects of boundaries on the pole tide in an ocean of constant depth. The cyclically continuous global ocean solutions to Laplace's tidal equations with the pole tide forcing are used as the particular solutions to the problem. The approach here is to find approxi- mate asymptotic solutions to the homogeneous tidal equations which can be added to the global particular solutions so that the normal component of velocity will vanish at the boundary. At the very long period of the pole tide, the unforced motions are assumed to be non-divergent, and so only the homogeneous vorticity equation must be solved. The first case considered is a zonal ocean bounded by parallels of latitude equidistant from the equator. Asymptotic solutions are found in order to satisfy the zonal boundary condition, and this gives rise to a narrow zonal boundary current. The contribution of these solutions is exponentially small compared to the forced global pole tide except in the immediate vicinity of the northern and southern boundaries. Next, the effect of meridional boundaries is considered. When a linear form of bottom friction is assumed, two approximate homogeneous solutions are found to construct a general solution that satisfies the meridional boundary conditions. One solution decays exponentially in longitude and gives rise to a western boundary current, while the other solution is indepen- dent of longitude. The meridional boundary conditions are used to match the homogeneous and particular solutions, and so the solution for the interior of the ocean satisfies the eastern boundary condition. The resulting solution for the pole tide has a western boundary current term, while over the majority of the ocean domain the solution has a term varying with the wavelength of the forcing (the global solution) and a zonal motion term used to satisfy the eastern boundary condition. Comparisons are made with the wind-driven ocean circulation problem.

On the influence of frictional parameterization in wind-driven ocean circulation models

In a series of numerical experiments the wind-driven ocean circulation is studied in an idealized, rectangular model ocean, which is forced by steady zonal winds and damped by lateral and/or bottom friction. The problem as described by the barotropic vorticity equation is characterized by a Rossby number ( R) and horizontal and/or vertical Ekman numbers ( E L, E B) only. With free-slip conditions at the boundaries steady solutions for all chosen values of R are obtained, provided the diffusivity is sufficiently large. For both the forms of frictional parameterization a northern boundary current emerges with an eastward penetration scale depending on R. The recirculation pattern in the oceanically relevant ‘intermediate’ range of R is strongly affected by the type of friction. If lateral diffusion dominates bottom friction, a strong recirculating sub-gyre emerges in the northwestern corner of the basin. Its shape resembles the vertically integrated transport fields in recent eddy resolving model (EGCM) studies. The maximum transport is increased to values several times larger than the Sverdrup transport. The increase in transport is coupled with a development of closed contours of potential vorticity, enabling a nearly free inertial flow. This behaviour provides a sharp contrast to the bottom friction case (Veronis) where inertial recirculation only takes place with values of R so large that the eastward jet reaches the eastern boundary. It is shown that the linear friction law puts a strong constraint on the flow by preventing an intense recirculation in a small part of the basin. A reduction of the diffusivity ( E L) in the lateral friction case leads to quasi-steady solutions. The interaction with eddies becomes an integral part of the time mean energetics but does not influence the recirculation character of the flow. The main conclusion of the study is that the horizontal structure of the EGCM-transport fields can be explained in terms of a steady barotropic model where lateral friction represents the dominant dissipation mechanism.

Numerical Model Studies of the Winter-Storm Response of the West Florida Shelf

Abstract The wintertime, wind-driven Ocean circulation on the West Florida Continental Shelf is studied within the framework of a linearized storm-surge model. The model bathymetry incorporates a realistic shelf, extending from New Orleans to the southern tip of Florida, and a deep ocean region. The boundary condition at the coast is that there is no normal flow. At the open boundaries, located off the shelf in deep water, the adjusted sea level is fixed at zero. It is found that 1) a coastally trapped response is achieved within one local inertial period following the imposition of the wind; 2) the curved coast forces a mass exchange between the coastal water and the deep ocean; 3) this exchange leads to the generation of a series of mesoscale eddies along the shelf edge; and 4) these eddies give rise to long-period, shelf-wide oscillations that persist beyond the local spin-up time. A hindcast of the wind-driven flow on the West Florida Shelf for a particular period (11–25 March 1978) that contains the ...

Asymptotic Analysis of the Agulhas and Brazil Current Systems

An asymptotic analysis is carried out of a linear and a nonlinear transport model of the large-scale wind-driven ocean circulation in the subtropical region of the Atlantic and Indian Oceans. The complicated geometry with a continent that terminates in mid-ocean is reflected in both models into the Atlantic Ocean through free boundary layers. It is shown that inertia must be incorporated to be able to produce a significant retroflection of the Agulhas Current south of Africa. In such a model the transport of the Return Agulhas Current becomes large when the wind stress curl decreases substantially over the north–south scale of an inertial boundary layer region around South Africa. The reason is that the overshooting Agulhas Current can then “unload” more of its transport eastward into the Sverdrup regime. The remainder of the transport bends westward into the free boundary layer. Wind stress curls calculated from the observed wind field over the Indian Ocean show such a rapid decrease. Thus the existence of a stagnation point near South Africa is shown to be a consequence of the large-scale conditions especially over the Indian Ocean part of the domain. The length scale that results from a formal asymptotic analysis for the distance of that retroflection point to the southern tip of the peninsula and the associated transport of the Return Agulhas Current agree with values from observations. Without the fast latitudinal variation of the wind stress curl the transport of the Brazil Current would he of the same order as that in the Agulhas. Almost the full Agulhas Current would then flow around South Africa and proceed as a westward jet into the Atlantic Ocean.

A note on the overall vorticity balance in wind-driven ocean circulation

Some constraints resulting from a required overall vorticity balance in an ocean forced by a net wind-stress curl are considered. It is pointed out that the Sverdrup balance holds for Ekman-geostrophic flow in an area-averaged sense even in the presence of topography. It is suggested that nonlinear stretching and twisting of vorticity in an inertial boundary current may provide a source of vorticity which may balance a net wind-stress curl, without help of frictional effects at the bottom or sides. It is also suggested that potential vorticity generated by the wind-stress curl can be balanced by other local potential vorticity sources in the top layer. At this stage no proof for the need of bottom or side friction in a generally stratified ocean exists, and a counterexample is also lacking, leaving the question open for further studies.

Eddy Lateral Vorticity Transport and the Equilibrium of the North Atlantic Subtropical Gyre

Abstract Oceanic gyres defined by the mean zero wind-stress curl lines have been the focus of wind-driven ocean circulation theory since its beginnings. In the face of single-signed vorticity input from the curl of the wind stress over a gyre, a mechanism to balance the wind vorticity input is required if an equilibrium is to be established. Traditional models have tended to restrict their allowable physics so that a dissipation mechanism is required for equilibrium. However, dissipation is not necessary, in principle, for equilibrium for a general fluid system. In fact, it has recently been shown that lateral eddy vorticity transport between gyres can provide an important part of the vorticity tendency required for equilibration in model oceanic systems. This note examines the possibility that in the North Atlantic subtropical gyre this process also might be important. After a brief review of the equilibration mechanisms possible in a primitive equation fluid, attention is focussed on estimates of the ed...

Model Studies of the Wind-Driven Transient Circulation in the Middle Atlantic Bight. Part 1: Adiabatic Boundary Conditions

Abstract A numerical model of the wind-driven transient ocean circulation in the Middle Atlantic Bight is described. The model incorporates realistic topography and covers the continental shelf between the coast and the 200 m isobath from Cape Hatteras to the southern tip of Nova Scotia. The traditional shallow-water dynamics are used, i.e., the vertically integrated and linearized equations for the flow of a homogeneous fluid driven by atmospheric pressure and wind stress fluctuations and damped by a quadratic bottom stress. The equations are integrated in time using a simple modification of Platzman's (1972) finite-difference scheme, with a 12.7 km grid spacing. At the coast, normal flow is required to vanish; at non-coastal boundaries, the equivalent surface elevation is held fixed. Several classes of initial value experiments are used to study the free and forced modes of this model, and the damped flow driven by a spatially uniform and stationary wind stress and by an idealized travelling synoptic-sc...

An unsteady wind-driven ocean circulation model

This model of a continuously stratified ocean, consisting of surface Ekman and thermal layers and a deep abyssal region, is driven by an unsteady surface wind stress. The model yields a nonlinear planetary wave equation for the surface temperature which is solved by the method of characteristics. Horizontal distributions of the surface temperature, the heat content and the potential energy are computed. For a model zonal wind stress relevant to the North Atlantic, a parameter sensitivity study is made.Long time scale observations of the heat content in the North Atlantic north of 45°N show that periods of heating and cooling of a few decades duration frequently occur. Using a zonal wind stress consisting of the superposition of a mean and two time harmonic components, secular variations in the surface temperature field manifest themselves as a beat period, provided the time harmonic frequencies are close together. Finally, to investigate the effects on the circulation produced by the changing intensity of the westerly winds, numerical results are presented for the case when the wind stress distribution oscillates in the north-south direction with time. Results from the study show that the heating and cooling periods of a few decades duration in the North Atlantic can be reproduced.

Asymptotic behaviour and stability results for an oceanographic model

Linear wind-driven oceanic circulation is governed by the Stokes’ equations and the continuity equation. The ratio of the vertical scale to the horizontal scale is very small for oceanic problems. Therefore, some terms in the equations can be neglected. The problem we have to solve is time-dependent and written in an open set R of R3. The unknown variables are the velocity of the current and the elevation of the sea surface. Discretization of the three-dimensional equations leads to numerical difficulties and very long computer time. That is why a method of separation of variables and expansion in Fourier series has been studied in a previous article [ll. Existence and uniqueness of the solution have been proved for the initial problem and the problem obtained after spectral expansion. We have also verified the convergence of the series in suitable functional spaces. Oceanographers are interested in steady-state circulation which is driven by a given wind-stress acting on an oceanic domain a. We will calculate this steady-state curtent as the limit of the time-dependent solution. This is justified by the results on the asymptotic behaviour of the solution which are given here: we will prove the existence and the uniqueness of the solution of the steady-state problem and the convergence of the timedependent solution towards the steady-state solution when time t + 00. The two-dimensional problem obtained after spectral expansion has been discretized by a finite difference method. Stability of the numerical scheme has been studied by a Fourier-type method. Numerical experiments have been carried out for different values of the parameters. In each case, they allow us to select the optimal time step.

Mesoscale eddies and general ocean circulation models

In a series of numerical experiments the wind-driven ocean circulation is studied in an idealized, rectangular model ocean, which is forced by steady zonal winds and damped by lateral and/or bottom friction. The problem as described by the barotropic vorticity equation is characterized by a Rossby number (R) and horizontal and/or vertical Ekman numbers (EL, EB) only.With free-slip conditions at the boundaries steady solutions for all chosen values of R are obtained, provided the diffusivity is sufficiently large. For both the forms of frictional parameterization a northern boundary current emerges with an eastward penetration scale depending on R. The recirculation pattern in the oceanically relevant ‘intermediate’ range of R is strongly affected by the type of friction. If lateral diffusion dominates bottom friction, a strong recirculating sub-gyre emerges in the northwestern corner of the basin. Its shape resembles the vertically integrated transport fields in recent eddy resolving model (EGCM) studies. The maximum transport is increased to values several times larger than the Sverdrup transport. The increase in transport is coupled with a development of closed contours of potential vorticity, enabling a nearly free inertial flow.This behaviour provides a sharp contrast to the bottom friction case (Veronis) where inertial recirculation only takes place with values of R so large that the eastward jet reaches the eastern boundary. It is shown that the linear friction law puts a strong constraint on the flow by preventing an intense recirculation in a small part of the basin.A reduction of the diffusivity (EL) in the lateral friction case leads to quasi-steady solutions. The interaction with eddies becomes an integral part of the time mean energetics but does not influence the recirculation character of the flow.The main conclusion of the study is that the horizontal structure of the EGCM-transport fields can be explained in terms of a steady barotropic model where lateral friction represents the dominant dissipation mechanism.

On the Generation of Mesoscale Eddies and their Contribution to the OceanicGeneral Circulation. I. A Preliminary Numerical Experiment

Abstract Numerical experiments on the wind-driven ocean circulation in a closed basin show that mesoscale eddiescan appear spontaneously during the integration of the equations of motion for a baroclinic ocean. For somevalues of the basic parameters governing the flow, the solutions reach a steady state while for other valuesfinite-amplitude eddies remain a part of the final statistically steady state. In the eddying cases the solutionscan be regarded as a mean flow upon which is superimposed a set of eddies which propagate westward at afew kilometers per day. The eddies typically have horizontal wavelengths of a few hundred kilometers. Analyses of die energetics show the eddies to be generated by the process of baroclinic instability. Thepotential energy of the mean flow is released to supply energy to the eddies. The computed Reynoldsstresses, while small compared to the terms in the geostrophic balance of the mean momentum equations, dohave a strong influence on the mean circulation and, in fact, the d...