Note on the dynamics of the Gulf Stream

The nonlinear inertial terms have been neglected in Stommel\u27s and in Munk\u27s theory for the wind-driven ocean circulation. Using a method of successive approximations, the effect of these terms on the mass transport in the Gulf Stream region has been computed under greatly simplifying assumptions. These assumptions involve Reid\u27s model of the vertical density structure, which consists of an exponential decrease in the density upward to the thermocline and a homogeneous upper layer...

Large-scale circulation with small diapycnal diffusion: The two-thermocline limit

The structure and dynamics of the large-scale circulation of a single-hemisphere, closed-basin ocean with small diapycnal diffusion are studied by numerical and analytical methods. The investigation is motivated in part by recent differing theoretical descriptions of the dynamics that control the stratification of the upper ocean, and in part by recent observational evidence that diapycnal diffusivities due to small-scale turbulence in the ocean thermocline are small (≈0.1 cm2 s−1). Numerical solutions of a computationally efficient, three-dimensional, planetary geostrophic ocean circulation model are obtained in a square basin on a mid-latitude β-plane. The forcing consists of a zonal wind stress (imposed meridional Ekman flow) and a surface heat flux proportional to the difference between surface temperature and an imposed air temperature. For small diapycnal diffusivities (vertical: κv ≈0.1 – 0.5 cm2 s−1, horizontal: κh ≈105 – 5 × 106 cm2 s−1), two distinct thermocline regimes occur. On isopycnals that outcrop in the subtropical gyre, in the region of Ekman downwelling, a ventilated thermocline forms. In this regime, advection dominates diapycnal diffusion, and the heat balance is closed by surface cooling and convection in the northwest part of the subtropical gyre. An ‘advective’ vertical scale describes the depth to which the wind-driven motion penetrates, that is, the thickness of the ventilated thermocline. At the base of the wind-driven fluid layer, a second thermocline forms beneath a layer of vertically homogeneous fluid (‘mode water’). This ‘internal’ thermocline is intrinsically diffusive. An ‘internal boundary layer’ vertical scale (proportional to κv1/2) describes the thickness of this internal thermocline. Two varieties of subtropical mode waters are distinguished. The temperature difference across the ventilated thermocline is determined to first order by the meridional air temperature difference across the subtropical gyre. The temperature difference across the internal thermocline is determined to first order by the temperature difference across the subpolar gyre. The diffusively-driven meridional overturning cell is effectively confined below the ventilated thermocline, and driven to first order by the temperature difference across the internal thermocline, not the basin-wide meridional air temperature difference. Consequently, for small diapycnal diffusion, the abyssal circulation depends to first order only on the wind-forcing and the subpolar gyre air temperatures. The numerical solutions have a qualitative resemblance to the observed structure of the North Atlantic in and above the main thermocline (that is, to a depth of roughly 1500 m). Below the main thermocline, the predicted stratification is much weaker than observed

Wind-Induced Exchange in Semi-Enclosed Basins

The wind-induced circulation over laterally varying bathymetry was investigated in homogeneous and in stratified systems using the three-dimensional Regional Ocean Model (ROMS). For homogeneous systems, the focus was to describe the influence of the earth\u27s rotation on the lateral distribution of the flow with particular emphasis on the transverse circulation. Along-basin wind-stress with no rotation caused a circulation dominated by an axially symmetric transverse structure consisting of downwind flow over the shoals and upwind flow in the channel along the whole domain. Transverse circulation was important only at the head of the system where the water sank and reversed direction to move toward the mouth. The wind-induced flow pattern under the effects of the earth\u27s rotation depended on the ratio of Ekman depth (d) to the maximum basin\u27s depth (h). The solution tended to that described in a non-rotating system as h/d remained equal to or below one. For higher values of h/d, the longitudinal flow was axially asymmetric. Maximum downwind flow was located over the right shoal (looking downwind). The transverse component of velocity described three gyres. The main gyre was clockwise (looking downwind) and occupied the entire basin cross-section, as expected from the earth\u27s rotation and the presence of channel walls. The other two gyres were small and localized, and were linked to the lateral distribution of the along-channel velocity component, which in turn, was dictated by bathymetry. In stratified systems, the main focus was to study the interaction between the wind-driven and buoyancy-induced flow over laterally varying bathymetry. In particular the influence of the earth\u27s rotation and the transverse circulation were examined. The interaction between the wind-induced and buoyancy-driven flow was characterized by, the Wedderburn number ( We) which compares wind stress accelerations to baroclinic pressure gradient accelerations. The influence of the earth\u27s rotation was characterized by the inverse of h/d, i.e., the Ekman number. For both rotating and non-rotating systems under strong winds (We ≥ 1), the wind-induced pattern of downwind flow over the shoals and up-wind flow in the channel masked any effects of buoyancy driven flows as the water column remained nearly vertically homogeneous. For weak up-estuary winds (We [special characters omitted] 1), the gravitational circulation (with or without rotation) remained almost unaltered. Only the upper part of the water column was modified by the wind-stress, showing an increased surface mixed layer and reduction (increment) of the seaward flow with up-estuary (down-estuary) wind. The non-rotating experiments showed axially symmetric distribution of flow and salinity fields. Rotating cases under weak wind conditions showed low Ekman number, such that rotation effects translated into axial asymmetries of salinity and flow fields. The transverse circulation and the salinity field showed a distribution expected from the balance of the lateral density gradient force per unit mass and Coriolis accelerations. Rotating cases under strong wind conditions exhibited high Ekman numbers and tended to be axially symmetric, responding to a transverse balance between lateral pressure gradient and friction. Transverse flows showed two gyres located over the shoals in response to the lateral density gradient. These results compared favorably with a limited set of observations and are expected to motivate future measurements

The dynamical balance, transport and circulation of the Antarctic Circumpolar Current

The physical ingredients of the ACC circulation are reviewed. A picture of thecirculation is sketched by means of recent observations of the WOCE decade. Wepresent and discuss the role of forcing functions (wind stress, surfacebuoyancy flux) in the balance of the (quasi)-zonal flow, the meridionalcirculation and their relation to the ACC transport. Emphasis will be on theinterrelation of the zonal momentum balance and the meridional circulation, theimportance of diapycnal mixing and eddy processes. Finally, new model conceptsare described: a model of the ACC transport dependence on wind stress andbuoyancy flux, based on linear wave theory; and a model of the meridionaloverturning of the Southern Ocean, based on zonally averaged dynamics with eddyparameterization

Modeling circulation patterns induced by spatial cross-shore wind variability in a small-size coastal embayment

This contribution shows the importance of the cross-shore spatial wind variability in the water circulation in a small-sized micro-tidal bay. The hydrodynamic wind response at Alfacs Bay (Ebro River delta, NW Mediterranean Sea) is investigated with a numerical model (ROMS) supported by in situ observations. The wind variability observed in meteorological measurements is characterized with meteorological model (WRF) outputs. From the hydrodynamic simulations of the bay, the water circulation response is affected by the cross-shore wind variability, leading to water current structures not observed in the homogeneous-wind case. If the wind heterogeneity response is considered, the water exchange in the longitudinal direction increases significantly, reducing the water exchange time by around 20%. Wind resolutions half the size of the bay (in our case around 9 km) inhibit cross-shore wind variability, which significantly affects the resultant circulation pattern. The characteristic response is also investigated using idealized test cases. These results show how the wind curl contributes to the hydrodynamic response in shallow areas and promotes the exchange between the bay and the open sea. Negative wind curl is related to the formation of an anti-cyclonic gyre at the bay's mouth. Our results highlight the importance of considering appropriate wind resolution even in small-scale domains (such as bays or harbors) to characterize the hydrodynamics, with relevant implications in the water exchange time and the consequent water quality and ecological parameters.Peer ReviewedPostprint (author's final draft

A method of calculating the total flow from a given sea surface topography

Using a simple dynamical model of a wind-driven ocean circulation of the Stommel type, and an analytical basis developed to objectively analyze the sea surface height residuals from an altimeter and, in the process, to determine the total flow instead of just the near surface geostrophic component associated with the given sea surface topography. The method is based on first deriving the solution to the forced problem for a given wind stress required to develop a hypothetical true or perfect data field and to establishing the basis for the objective analysis. The stream function and the surface height field for the forced problem are developed in terms of certain characteristic functions with the same expansion coefficients for both fields. These characteristic functions are simply the solutions for a homogeneous elliptic equation for the stream function and the solutions of an inhomogeneous balance equation for the height field. For the objective analysis, using a sample of randomly selected height values from the true data field, the height field characteristic functions are used to fit the given topography in a least squares sense. The resulting expansion coefficients then permit the synthesis of the total flow field via the stream function characteristic modes and the solution is perfectly well behaved even along the equator. The method of solution is easily adaptable to realistic ocean basis by straight forward numerical methods. The analytical basis of the theory and the results for an ideal rectangular basin on a beta plane are described

A laboratory study of the effects of a sloping side boundary on wind-driven circulation in a homogeneous ocean model

A laboratory model is used to investigate the effects of sloping boundaries on homogeneous wind-driven β-plane circulation. The very gentle slopes of real oceanic boundaries raise the possibility that dissipation by lateral diffusion of vorticity to the boundary is largely removed, leaving dissipation only in bottom Ekman layers. The laboratory model is a modification of the rotating ‘sliced-cylinder’ introduced by Pedlosky and Greenspan (1967) and Beardsley (1969) and in which flow is driven by a differentially rotating lid. The vertical wall is replaced with a side wall having a uniform 45° slope around the entire perimeter. This sloping boundary, like a continental slope, tends to steer the flow along the slope. In the geometry chosen for this study it also provides closed potential vorticity contours through every point in the basin, thus removing the blocked contours of the experiments with a vertical wall and the open contours of ocean basins that approach the equator. For cyclonic forcing there is a northward (Sverdrup) flow in the interior superimposed on a zonal flow so that a particle starts out at the southwest, enters the slope region in the northwest, circles cyclonically along a circle of constant radius (and depth) to a point on the southeast where it crosses constant depth contours and rejoins the original point. The direction of flow is reversed for anticyclonic forcing. The main dissipation of vorticity takes place in the southeast where the flow crosses constant depth contours. For cyclonic forcing the flow is stable and steady under all conditions achieved. For anticyclonic forcing the laboratory flow is unsteady under all conditions attainable and unstable to eddy shedding at sufficiently large Rossby or Reynolds numbers. At large Ekman numbers the onset of instability corresponds to shedding of cyclonic eddies in the region where the boundary current enters the interior, whereas at small Ekman numbers it corresponds to periodic breakup of an anticyclonic gyre in the ‘northwest’ and the formation of anticyclonic eddies. Eddies of both sign are shed when the forcing is sufficiently supercritical and the Ekman number small. A simple, qualitative argument explains why the cyclonic flow is stable and the anticyclonic flow is unstable when the system is nonlinear

On the additional boundary condition of wind-driven ocean models on the eastern coast

In the homogeneous model of the wind-driven ocean circulation, the dynamics of the basin interior is basically governed by the Sverdrup balance and the related no mass-flux condition on the eastern boundary of the basin, which we assume to be square for conceptual simplicity. In the presence of lateral diffusion of relative vorticity, the additional condition on the eastern boundary (like the conditions on the other boundaries) is not demanded on physical grounds but it is arbitrary to a large extent. Hence, certain choices of such boundary condition can produce overall solutions which are “far” from that of Sverdrup in the eastern part of the domain, without any physical reason. In the present note we show that this discrepancy can be strongly reduced if the adopted additional boundary condition has the same form as that implicitly satisfied by the Sverdrup solution. Unlike the common approach, a criterion is thus derived which selects a suitable partial slip boundary condition according to the specific wind-stress field which is taken into account