Topographic effects on the wind‐driven ocean circulation

Abstract

This is a study of the influence of bottom topography of an ocean basin on the wind‐driven, barotropic ocean circulation. A detailed investigation is made of the role of vorticity transfer to the ocean bottom in the presence of varying topography. It is shown that the wind‐driven gyre over the topography of the North Atlantic has a transport in the western part of the basin only half of that obtained in an ocean of constant depth.     

Baroclinic and topographic influences on the transport in western boundary currents

Abstract

One of the central unsolved theoretical problems of the large scale ocean circulation is concerned with explaining the very large transports measured in western boundary currents such as the Gulf Stream and the Kuroshio. The only theory up to now that can explain the size of these transports is that of non-linear recirculation in which the advective terms in the momentum equations became important near the western boundary. In this paper an alternative explanation is suggested. When bottom topography and baroclinic effects are included in a wind-driven ocean model it is shown that the western boundary current can have a transport larger than that predicted from the wind stress distribution even when the nonlinear advective terms are ignored. The explanation lies in the presence of pressure torques associated with bottom topography which can contribute to the vorticity balance in the same sense as the wind stress curl.

Three numerical experiments have been carried out to explore the nature of this process using a three dimensional numerical model. The first calculation is done for a baroclinic ocean of constant depth, the second for a homogeneous ocean with an idealized continental slope topography, and the third for a baroclinic ocean with the same continental slope topography. The nature of the vorticity balance and of the circulation around closed paths is examined in each case, and it is shown that bottom pressure torques lead to enhanced transport in the western boundary current only for the baroclinic case with variable depth.     

Wind forcing of the Ganga-Brahmaputra river plume

Ocean Dynamics - Response of Ganga-Brahmaputra river plume to wind forcing in the Bay of Bengal is studied using a numerical ocean circulation model. Four different wind forcing scenarios, namely,...     

Six circumpolar currents—on the forcing of the Antarctic Circumpolar Current by wind and mixing

The transport of the Antarctic Circumpolar Current (ACC) is influenced by a variety of processes and parameters. A proper implementation of basin geometry, ocean topography and baroclinicity is known to be a fundamental requisite for a realistic simulation of the circulation and transport. Other, more subtle parameters are those of eddy-induced transports and diapycnal mixing of thermohaline tracers or buoyancy, either treated by eddy resolution or by a proper parameterization. Quite a number of realistic numerical simulations of the circulation in the Southern Ocean have recently been published. Many concepts on relations of the ACC transport to model parameters and forcing function are in discussion, however, without much generality and little success. We present a series of numerical simulations of circumpolar flow with a simplified numerical model, ranging from flat-bottom wind-driven flow to baroclinic flow with realistic topography and wind and buoyancy forcing. Analysis of the balances of momentum, vorticity, and baroclinic potential energy enables us to develop a new transport theory, which combines the most important mechanisms driving the circulation of the ACC and determining its zonal transport. The theory is based on the importance of the bottom vertical velocity in generating vorticity and shaping the baroclinic potential energy of the ACC. It explains the breaking of the -constraint by baroclinicity and brings together in one equation the wind and buoyancy forcing of the current. The theory emphasizes the role of Ekman pumping and eddy diffusion of buoyancy to determine the transport. It also demonstrates that eddy viscosity effects are irrelevant in the barotropic vorticity balance and that friction arises via eddy diffusion of density. In this regime, the classical Stommel model of vorticity balance is revived where the bottom friction coefficient is replaced by (with the Gent–McWilliams coefficient and the baroclinic Rossby radius ) and a modified wind curl forcing appears.     

Response of the equatorial Pacific thermocline to climate warming

Climate models project a significant shoaling of the thermocline over the western equatorial Pacific Ocean under global warming, which has been generally regarded as a direct response to surface wind change. This study investigates the formation processes for the equatorial Pacific thermocline response to CO₂ quadrupling using the Community Earth System Model version 1 (CESM1). In particular, an overriding method is applied to isolate and quantify the wind stress effect and the direct radiative effect of CO₂ emissions. Results show that both effects of the wind stress and direct radiative forcing are equally important for shoaling the equatorial thermocline, with the former responsible for its upper portion change and the latter for its lower portion change. Further passive tracer experiments with the ocean component of the CESM1 verify the role of ocean surface warming in shoaling the equatorial thermocline and identify the ocean circulation change in response to the surface warming as its dynamic cause of formation.     

A numerical study of the string function using a primitive equation ocean model

Abstract

We use results from a primitive-equation ocean numerical model (SCRUM) to test a theoretical 'string function' formulation put forward by Tyler and Käse in another article in this issue. The string function acts as a stream function for the large-scale potential energy flow under the combined beta and topographic effects. The model results verify that large-scale anomalies propagate along the string function contours with a speed correctly given by the cross-string gradient. For anomalies having a scale similar to the Rossby radius, material rates of change in the layer mass following the string velocity are balanced by material rates of change in relative vorticity following the flow velocity. It is shown that large-amplitude anomalies can be generated when wind stress is resonant with the string function configuration.     

Interactions between wind and tidally induced currents in coastal and shelf basins

This paper addresses the impact of atmospheric variability on ocean circulation in tidal and non-tidal basins. The data are generated by an unstructured-grid numerical model resolving the dynamics in the coastal area, as well as in the straits connecting the North Sea and Baltic Sea. The model response to atmospheric forcing in different frequency intervals is quantified. The results demonstrate that the effects of the two mechanical drivers, tides and wind, are not additive, yet non-linear interactions play an important role. There is a tendency for tidally and wind-driven circulations to be coupled, in particular in the coastal areas and straits. High-frequency atmospheric variability tends to amplify the mean circulation and modify the exchange between the North and the Baltic Sea. The ocean response to different frequency ranges in the wind forcing is area-selective depending on specific local dynamics. The work done by wind on the oceanic circulation depends strongly upon whether the regional circulation is tidally or predominantly wind-driven. It has been demonstrated that the atmospheric variability affects the spring-neap variability very strongly.     

Numerical study of circulation and temperature-salinity distributions in the Bras d’Or Lakes

The Bras d’Or Lakes (BdOL) are a large, complex and virtually land-locked estuary in central Cape Breton Island of Nova Scotia and one of Canada’s charismatic ecosystems, sustaining ecological and cultural communities unique in many aspects. The BdOL comprise two major basins, many deep and shallow bays, several narrow channels and straits and a large, geologically complex watershed. Predictive knowledge of the water movement within the estuary is a key requirement for effective management and sustainable development of the BdOL ecosystem. A three-dimensional (3D) primitive-equation ocean circulation model is used to examine the estuary’s response to tides, winds and buoyancy forcing associated with freshwater runoff in a series of numerical experiments validated with empirical data. The model results generate intense, jet-like tidal flows of about 1 m s^?1 in the channels between the basins and connecting them to the ocean and relatively weak tidal currents in other regions, which agrees well with previous observations and numerical results. Wind forcing and buoyancy forcing associated with river runoff play important roles in generating the significant sub-tidal circulations in the estuary, including narrow channels, deep basins and shallow bays. The circulation model is also used to reconstruct the 3D circulation and temperature-salinity distributions in the summer months of 1974, when current and hydrographic measurements were made at several locations. The sub-tidal circulation in the estuary produced by the model is characterised by wind and barometric set-up and set-down in different sections of the system, and a classic two-layer estuarine circulation in which brackish, near-surface waters flow seaward from the estuary into the Atlantic Ocean, and deep salty waters flow landward through the major channel. The model results reproduce reasonably well the overall features of observed circulation and temperature-salinity fields made in the BdOL in 1974 but generally underestimate the observed currents and density stratification. The model discrepancies reflect the use of spatially mean wind forcing and spatially and monthly mean surface heat flux and the inability of the coarse model horizontal resolution (～500 m) to resolve narrow channels and straits.     

Variations of tidally driven three-layer residual circulation in fjords

Residual, or tidally averaged, circulation in fjords is generally assumed to be density driven and two layered. This circulation consists of a thin surface layer of outflow and a thick bottom layer of sluggish inflow. However, development of different vertical structures in residual circulation in fjords can arise from wind, remote, and tidal forcing that may modify the two-layer circulation. Particularly, theoretical results of tidal residual flows in homogeneous semienclosed basins indicate that their vertical structure is determined by the dynamical depth of the system. This dynamical depth can be considered as the ratio between the water column depth and the depth of frictional influence in an oscillatory flow (inverse of Stokes number). When the frictional depth occupies the entire water column, the tidal residual flow is one layered as in shallow basins. But when the frictional depth is only a small portion of the water column (>6 times smaller), the tidal residual is three layered. In relatively deep fjords (say deeper than 100 m), where frictional depths typically occupy a small portion of the water column, the tidal residual flow is expected to be three layered. Ample observational evidence presented here shows a three-layered exchange flow structure in fjords. On the basis of observational and theoretical evidence, it is proposed that the water exchange structure in deep fjords (more than six frictional layers deep, or inverse Stokes number >6) is tidally driven and is three layered. The tidally driven three-layer structure of residual flows could be regarded in some cases as the fundamental structure. However, this structure will only be observed sporadically as it will be masked by wind forcing, remote forcing from the ocean, and freshwater pulses.     

Internal Variability Of The North Atlantic Wind-Driven Ocean Circulation

A new approach to understand the physical processes that govern internal variability of the large scale North Atlantic ocean circulation is outlined and current methods and results are reviewed. In this approach, based on the theory of dynamical systems, internal variability is viewed as arising through successive transitions when parameters are changed. The potential of the approach is demonstrated through analysesof solutions of intermediate complexity models of the wind-driven ocean circulation in the North Atlantic. In a quasi-geostrophic modelfor the flow in a rectangular basin with idealized wind forcing, the basic transitions are already found and physical mechanisms at work can be described in detail. Qualitatively, this transition behavior remains robust in more realistic models, having shallow water dynamics, realistic wind forcingand continental geometry, although patterns and time scales changethrough the model hierarchy. The relevance of the results is discussed inrelation to those of observations and of ocean general circulation models.     

Residual vorticity induced by the action of tidal currents in combination with bottom topography in the Southern Bight of the North Sea

Abstract

Results are presented of calculations on the generation of residual vorticity by tidal currents over the bottom topography of the Southern Bight of the North Sea. A typical order of magnitude is 10^?6 to 10^?7 s ^?1. This is compared with current measurements on calm days, when similar magnitudes are found. At windspeeds less than about 5 m/s tidal generation of residual vorticity is important; at higher windspeeds wind effects begin to dominate. Our results are relevant in understanding the spatial variability of residual currents, because a non-zero vorticity implies the existence of horizontal gradients in the residual current field.     

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.     

A numerical study of the circulation and monthly-to-seasonal variability in the Caribbean Sea: the role of Caribbean eddies

This study examines the circulation and associated monthly-to-seasonal variability in the Caribbean Sea using a regional ocean circulation model. The model domain covers the region between 99.0 and 54.0°W and between 8.0 and 30.3°N, with a horizontal resolution of 1/6°. The ocean circulation model is driven by 6-hourly atmospheric reanalysis data from the National Center for Environmental Prediction and boundary forcing extracted from 5-day global ocean reanalysis data produced by Smith et al. (Mercator Newsletter 36:39–49, 2010), and integrated for 7 years. A comparison of model results with observations demonstrates that the regional ocean circulation model has skill in simulating circulation and associated variability in the study region. Analysis of the model results, as well as a companion model run that uses steady annual mean forcing, illustrates the role of Caribbean eddies for driving monthly-to-seasonal circulation variability in the model. It is found that vertically integrated transport between Nicaragua and Jamaica is influenced by the interaction between the density perturbations associated with Caribbean eddies and the Nicaraguan Ridge. The impact of Caribbean eddies squeezing through the Yucatan Channel is also discussed.     

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.     

ENSO循环之中的海气相互响应——对次表层海温和大气旋度的资料分析

利用美国国家环境预测中心（NCEP）和联合环境数据分析中心（JEDAC）资料，分别定义了表征海洋和大气变异的风场涡度指数和温度场指数，对热带太平洋海域的极值曲面上的温度距平、850 hPa风应力旋度进行了分析.结果显示，大气对海洋热力强迫的响应主要是Gill型，而大气又可以通过风应力旋度造成的Ekman抽吸作用来影响海洋，这种海气相互作用影响着ENSO循环的发展.通过简单的统计分析，解释了二者在ENSO循环之中所起的作用，并从资料中验证了El Nio事件具有3～4年的循环周期.这在一定程度上支持了ENSO的时滞振荡子和自然振荡子理论.     

Linear theory of the response of a two layer ocean to a moving hurricane‡

Abstract

This paper describes the linear response of an inviscid two‐layer model of a deep ocean on an f‐plane to a hurricane translating across the surface at constant speed. The forcing is a localized, radially‐symmetric pattern of positive wind stress curl and negative pressure anomaly. Only the steady state response is considered. The principal result is the identification of an internal wake in the lee of the storm, present when the translation speed of the storm exceeds the baroclinic long wave speed. The amplitude of the wake depends on the length of time over which the stress is experienced at a given point. The angle of the wedge filled by the wake is small, an effect due to the fact that the scale of a hurricane is typically larger than the baroclinic radius of deformation. After the wake disperses, a geostrophically balanced baroclinic ridge remains along the storm track.     

On the exact shape of the horizontal profile of a topographically rectified tidal flow

Abstract

Starting from the nonlinear shallow water equations of a homogeneous rotating fluid we derive the equation describing the evolution of vorticity by a fluctuating bottom topography of small amplitude, using a multiple scale expansion in a small parameter, which is the topographic length scale relative to the tidal wave length. The exact response functions of residual vorticity for a sinusoidal bottom topography are compared with those obtained by a primitive perturbation series and by harmonic truncation, showing the former to be invalid for small topographic length scales and the latter to be only a fair approximation for vorticity produced by planetary vortex stretching. In deriving the exact shape of the horizontal residual velocity profile at a step-like break in the bottom topography, it is shown that the Lagrangian profile only exists in a strip having the width of the amplitude of the tidal excursion at both sides of the break, and that it vanishes outside that interval. Moreover, in the limit of small amplitude topography at least, it vanishes altogether for the generation mechanism by means of planetary vortex stretching. The Eulerian profile is shown to extend over twice the interval of the Lagrangian profile both for production by vortex stretching and by differential bottom friction. These finite intervals over which the residual velocity profiles exist for a step-like topography are not reproduced by harmonic truncation of the basic equation. This method gives exponentially decaying profiles, indicating spurious horizontal diffusion of vorticity. In terms of orders of magnitude, the method of harmonic truncation is reliable for residual velocity produced by vortex stretching but it overestimates the residual velocity produced by differential bottom friction by a factor 2.