A zero potential vorticity model of the North Brazilian Coastal Current

The North Brazilian Coastal Current (NBCC) is idealized as an inertial, surface layer jet of equatorial origin, intruding along the coast into a northern water mass of constant, positive potential vorticity. Dissipation is accounted for by supposing that some equatorial water leaks out in the northwest corner of the intrusion. The problem is closed by adopting the free streamline boundary condition (between the northern and equatorial water masses) of continuous layer depth and velocity.Calculations are made for flow (intruding and return) supposed parallel to the coast; this approximation is verified à posteriori. The results show a narrow intrusion region along the coast, equatorial fluid flowing northwestward next to the coast, peeling off and returning along the boundary streamline. When no leakage is postulated, the northern limit of the intrusion becomes a stagnation point where the coast and the boundary streamline meet. With substantial leakage postulated, the flow chokes at some limiting latitude, where the inviscid inertial model breaks down. However, a realistic intrusion-return flow pattern is calculated south of the choking latitude for a number of different illustrative cases. The key control parameter is the potential vorticity of the northern water mass, or in a nondimensional form, the ratio of the rest-depths, at a given latitude, of the equatorial and northern water masses.The model accounts for a number of observed facets of NBCC behavior, notably its seasonal cycle, magnitude of the transports, intrusive and return flow

Vortex pair model of Langmuir circulation

Accumulating evidence shows spacing and length of surface convergences associated with Langmuir circulation to be random variables, their strength also variable, their lifetime limited. Analysis of several sets of quantitative observations reveals the probability distribution of windrow spacing to be lognormal. This suggests generation of surface convergences at random times and locations on the sea surface. Moving shear stress anomalies, under wind gusts or breaking long waves, are capable of generating surface convergence in their wakes, and are the type of random event likely responsible for the stochastic properties of windrows. The generation mechanism envisaged is a “forced” version of the Craik-Leibovich “CL2” theory, Stokes drift tilting the vertical vortex lines at the edges of stress anomalies. This contrasts with the feedback mechanism of the CL2 theory operating on infinitesimal spanwise disturbances. Realistic shear stress anomalies produce vortex pairs strong enough to account for Langmuir circulation without feedback amplification. A vortex pair just under the sea surface induces motion bringing the vortices together at first, and then causing them to dive deep into the mixed layer. This inviscid kinematic effect limits the surface presence of convergences, and accounts for the finite lifetime of windrows without even taking into account viscous decay. Converging motion at the surface, and low eddy viscosity, combine to channel the downward momentum transfer from the air flow into descending branches of the Langmuir circulation. One result is the increase of windward surface velocity in the convergences

Retroflection and leakage in the North Brazil Current: Critical point analysis

In an attempt to throw light on the complex flow pattern of the North Brazil Current near its point of separation from the coast, the flow in the neighborhood of boundary- and internal stagnation points ( critical points ) has been analyzed. The underlying hypothesis is that fluid masses of widely different potential vorticity come in contact near such points. In a one-and-a-half layer idealization of inertial, frictionless flow the key control parameter is the ratio of potential vorticities of the converging fluids. This determines the angle of flow after separation, and, for given buoyancy and depth scale, the volume of each kind of fluid transported past the stagnation point. A quasi-geostrophic calculation also gives a realistic picture of the streamline field near a stagnation point. Using the analytical results, a critical point analysis has been carried out on the observed pressure field of the separating North Brazil Current. The results support the idea of direct leakage along the coast into the Guiana Current. They also suggest a second, indirect route of water transport from the North Brazil Current to the North Equatorial Current, via the interior of the cyclonic gyre between the North Equatorial Counter Current and the North Equatorial Current

The thermohaline driving mechanism of oceanic jet streams

Worthington (1972a) advanced the hypothesis that winter cooling of the Gulf Stream south of New England is the cause of the Stream\u27s winter intensification. That loss of buoyancy should result in increased velocity and transport in an oceanic jet stream seems at first paradoxical...

The non-wavelike response of a continental shelf to wind

An overlooked aspect of continental shelf wave generation by wind is that a non-wavelike flow field may accompany the waves. To explore this possibility, we calculate the response of an inclined plane shelf to suddenly applied alongshore wind, affecting a finite portion of the coast. The calculations are based on the classical theory of continental shelf waves, supposing low frequency motions and invoking the boundary layer approximation (alongshore scales much longer than cross-shore ones). The results reveal non-wavelike circulations, with or without bottom friction, on a shelf of finite or unlimited width, unaffected by changing offshore boundary conditions. In the frictionless case, the principal new feature is an accelerating coastal jet that feeds offshore Ekman transport, drawing the fluid from the outer shelf of the downwave half-space. Continental shelf waves accompany the coastal jet on a shelf of finite width, their properties varying with the shelf-edge boundary condition. With bottom friction, the non-wavelike circulation has the character of an arrested topographic wave, a steady-state flow that develops on a gradually expanding portion of the inner shelf. This takes over the role of the coastal jet in the frictionless solution and satisfies mass balance by feeding offshore or onshore Ekman transport. The outer shelf is occupied by time-dependent closed circulations

What controls the rate of equatorial warm water mass formation?

Equatorial warm water formation is one important factor in the mass balance of Tropical Surface Water (TSW) in the Atlantic Ocean; another is drainage by the North Brazilian Coastal Current (NBCC). Both are affected by the depth of the TSW layer at the western boundary: deepening of this layer increases the transport of the NBCC and reduces warm water mass formation by shortening the eastern upwelling zone. Strengthening westward wind-stress steepens the thermocline in the western sector of the equatorial band, enhances upwelling in the eastern sector, affecting mass balance on both counts. Recirculation of TSW via a loop containing the North Equatorial Counter Current (NECC), and inflow from the south at the eastern boundary are also important elements of this mass balance: they depend on the wind-stress field over a wider region.The various elements of this mass balance are parameterized in terms of western boundary layer depth and wind-stress in the western sector. The resulting first order equation describes the response of the system to the annual cycle of wind-stress. With quantitative inputs typical of the equatorial Atlantic, output variables are simulated realistically: upwelling varies from 3 to 18 × 106 m3/s, NBCC transport from 13 to 26 × 106 m3/s, both in accord with observation, as is simulated storage, and TSW depth. An interesting finding is that the east-west length of the upwelling region varies relatively little while everything except storage varies in phase with the wind-stress (the storage lags by 2 months). The lesser variation of upwelling sector length comes about because the steepening of the thermocline in response to increasing wind-stress is accompanied by deepening in the western end, necessary to allow the escape of excess fluid.The results show the interplay of wind-stress, upwelling and western boundary current transport in the control of the oceanic heat gain in the equatorial band

Warm water mass formation

Seasonal heat storage, massive upwelling, and cold water advection are shown by a thermodynamic model of the interacting atmospheric and oceanic mixed layers

Vorticity Balance of Outcropping Isopycnals

The authors extend Marshall and Nurser\u27s analysis of potential vorticity (PV) flux into outcropping isopycnic layers of the oceanic thermocline to the nonstationary case, allowing for the seasonal migration of isopycnal surfaces under surface heating and cooling. The most important new result is that the bulk of the surface PV flux arising from seasonal heating is used up in creating stratification as an isopycnal outcrop moves northward, extending the stratified layers of the thermocline. Residual PV transport (flux times the separation distance between adjacent isopycnals) reaching the interior thermocline is small in quiescent regions where only mean advection (connecting to subduction or upwelling at the outcrop) operates, and is given by Marshall and Nurser\u27s formula, unaffected by the migration of the isopycnals. Where geostrophic turbulence is vigorous, it supports another pathway of PV transport, via Reynolds flux of vorticity. Larger PV transports are then possible within the range of action of the geostrophic turbulence in locations where Ekman transport only partly balances wind stress

Instability waves in the Gulf Stream front and its thermocline layer

We carried out linear instability calculations on a three layer Gulf Stream front model in an attempt to elucidate the interaction of the thermocline layer with surface slopewater shoreward of the front. The basic state is geostrophic balance and constant potential vorticity in the two active layers, but the perturbations are ageostrophic. We found the flow to be unstable to long wave perturbations, the wavelength of the most unstable wave to be of the order of 10 radii of deformation. The instability is mainly baroclinic, 75–85% of the energy supply to the growing perturbation coming from basic flow potential energy. Calculated wavelengths, phase speeds and growth rates, using parameters typical of the Gulf Stream, are similar to those observed. The eigenfunctions of the perturbations show peak cross-front thermocline motions near the inflection points of a frontal wave, and a cyclonic eddy with closed streamlines under a trough, an anticyclonic eddy under a crest. The combined flow (basic state plus perturbation) in the thermocline layer follows the surface streamlines closely, except for small cross-stream anomalies, shoreward just upstream of a wave crest, seaward upstream of a trough. Calculated trajectories have characteristics similar to those observed by RAFOS floats, except that they suggest exchange of thermocline waters exclusively with slopewater

Vorticity balance of boundary currents

Friction at the seafloor acts as a source of potential vorticity (PV) for individual isopycnic layers of a boundary current. The rate of PV transport (flux times layer thickness) equals, to a good approximation, the divergence of alongstream shear stress in the bottom boundary layer at the seafloor, which in turn equals the alongstream gradient of Montgomery potential. Mean PV transport is continuous along isopycnals between the bottom boundary layer and a boundary current in statistically steady state. Within the boundary current, Reynolds flux of vorticity transports PV. The divergence of this transport balances planetary vorticity advection and other terms in the vorticity equation. PV transport is equivalent to horizontal shear force, and its continuity from the seafloor to the interior of the boundary current implies that the total shear force exerted by the seafloor over the broad footprint of an isopycnic layer acts as much increased shear over the shallow depth of the same layer offshore. A drag law of the bottom boundary layer connects shear stress at the seafloor to velocity outside the boundary layer, a similarity argument yields the functional form of the shear stress gradient-friction velocity relationship, and hence the boundary condition on PV transport from the seafloor. This is neither free-slip nor no-slip, but closer to the latter