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Joseph Pedlosky

Abstract

A two-layer baroclinic flow on an f plane is rendered locally stable by sufficiently strong Ekman-layer friction except in an interval of length 2a in the downstream direction in which the friction is reduced. The localized marginally stable modes are found by matching the solutions found separately in each region where the friction is uniform.

It is shown that localized baroclinic instabilities, anchored to the local unstable zone, are possible as long as the interval length exceeds a critical value on the order of the Rossby deformation radius. The most unstable perturbation modes consist of two coupled vortices in each layer squeezed toward the downstream edge of the unstable zone. Slightly supercritical states will lead to growth. The growth rate remains substantial until the interval length becomes small with respect to a deformation radius.

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Joseph Pedlosky

Abstract

A study of finite-amplitude baroclinic instability for a two-layer system with small but non-zero dissipation is presented. The presence of dissipation, however slight, allows the existence of steady finite-amplitude wave solutions. For sufficiently small friction, however, the steady wave may be unstable if a certain criterion, presented in this paper, is satisfied. Calculations indicate that in such cases a continuous, slow, periodic amplitude pulsation exists which is independent of the initial conditions.

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Joseph Pedlosky

Abstract

The Rossby normal modes of a two-layer fluid in a meridional channel of width L∗ are altered by the presence of a meridional flow with a small vertical shear. The stability of the modes in the presence of the weak shear is considered. It is found that the joint presence of the Rossby modes and the vertical shear leads to baroclinic instability even for arbitrarily small values of the shear.

The results are used to explain previous numerical calculations of the persistent instability of meridional flows when the ratio βL2D/V > 1, where V is the magnitude of the shear, β is the planetary vorticity gradient, and L D is the deformation radius. If the flow were zonal it would be stable for such weak shears.

The growth rates are weak when βL2D/V ≫ 1 and each unstable mode exists in a narrow range of meridional wavenumber. The asymptotic results qualitatively agree with the earlier numerical results at moderate values of the same parameter.

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Joseph Pedlosky

Abstract

The problem of the reflection of unstable baroclinic waves from straight boundaries inclined with respect to latitude circles is studied. The basic flow in which the incident unstable wave is embedded is a flow with only vertical shear flowing parallel to the boundary. The analysis is done for a two-layer model on the β plane.

For a wave packet centered on the most unstable wave, the reflection process produces two reflected modes, each trapped to the boundary. The trapping scale is of the order of the Rossby radius of deformation. This trapping occurs whenever the current is inclined with respect to a latitude circle, in which case all shears, no matter how small, will support unstable waves.

It is argued that the trapped character of the reflected disturbance will produce a rectified current along the boundary with a net barotropic component.

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Joseph Pedlosky

Abstract

A model of wave-mean-field interaction in a baroclinic flow is formulated for the case where the ratio of the current width L to the Rossby deformation radius R is large for waves whose zonal wavelength is O(R). In this limit sufficient simplifications occur in the dynamical problem for the wave evolution to allow the examination of the wave amplitude behavior at larger effective supercritically than in previous weakly nonlinear theories. The model is shown, however, to contain within it the earlier theories.

Detailed numerical calculations with the model predict amplitude vacillation for fairly large values of the ratio E½/Ro, where E is the Ekman number and Ro the Possby number. Examination of the wave amplitude as a function of L/R shows that the velocity of the perturbations remains of the same order as the mean, although the total available potential energy of the mean exceeds its kinetic energy by a factor of L 2/R 2.

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Joseph Pedlosky

Abstract

A constant potential vorticity model is used to investigate the relation between the properties of an equatorward-directed western boundary current and the formation of the Equatorial Undercurrent (EUC) in the western equatorial oceans.

It is shown that the value of the Bernoulli function at the equator, undetermined in earlier purely inertial EUC models, is fixed by the bifurcation latitude of the western boundary current that feeds the EUC. This is an additional example of the nonlocal forcing of the EUC by the subtropical gyre.

The constant potential vorticity model yields reasonable values for the initial EUC core velocities for a bifurcation latitude on the order of 6° from the equator.

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Joseph Pedlosky

Abstract

A nonlinear inertial model of a steady-state coastal upwelling circulation is presented. The model describes a longshore equatorward current and countercurrent structure which is independent of any parameterization of turbulent mixing. Solutions for flat and sloping bottoms are presented.

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Joseph Pedlosky

Abstract

Weakly nonlinear theory is developed for finite-amplitude dynamics of a slightly dissipative baroclinic wave at the point of minimum critical shear in the β-plane two-layer model. At this parameter setting the nonlinear theory provides a simple manifestation of critical layer dynamics since the Doppler-shifted frequency vanishes in one of the two layers. Calculations show that when the dissipation is proportional to the potential vorticity and is weak, the new equilibrium steady state has uniform potential vorticity in the critical layer although this is not required for wave stabilization. The spatial harmonics of the fundamental play an important role in both the transient and final state. For a weakly dissipative flow, the potential vorticity due to the harmonics is conserved along streamlines of the fundamental wave. An analytical theory is given for the equilibrated wave amplitude based on the assumption of uniform potential vorticity in the critical layer, and this prediction agrees well with the calculations.

Potential vorticity smoothing does not occur when either dissipation or time dependence becomes large.

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Joseph Pedlosky

Abstract

An adiabatic, inertial, and quasigeostrophic model is used to discuss the interaction of surface Ekman transport with an island. The theory extends the recent work of Spall and Pedlosky to include an analytical and nonlinear model for the interaction. The presence of an island that interrupts a uniform Ekman layer transport raises interesting questions about the resulting circulation. The consequential upwelling around the island can lead to a local intake of fluid from the geostrophic region beneath the Ekman layer or to a more complex flow around the island in which the fluid entering the Ekman layer on one portion of the island's perimeter is replaced by a flow along the island's boundary from a downwelling region located elsewhere on the island. This becomes especially pertinent when the flow is quasigeostrophic and adiabatic. The oncoming geostrophic flow that balances the offshore Ekman flux is largely diverted around the island, and the Ekman flux is fed by a transfer of fluid from the western to the eastern side of the island. As opposed to the linear, dissipative model described earlier, this transfer takes place even in the absence of a topographic skirt around the island. The principal effect of topography in the inertial model is to introduce an asymmetry between the circulation on the northern and southern sides of the island. The quasigeostrophic model allows a simple solution to the model problem with topography and yet the resulting three-dimensional circulation is surprisingly complex with streamlines connecting each side of the island.

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Joseph Pedlosky

Abstract

A model of cross-gyre geostrophic flow is presented. It is a two-layer model of the (Northern Hemisphere) subtropical thermocline above a resting lower ocean. The northern boundary of the gyre is taken to be a latitude circle on which the Ekman pumping vanishes.

In distinction to previous theories, the meridional geostrophic velocity at the line of vanishing Ekman pumping is not zero. Instead, an internal mode is found which consists of southward, potential-vorticity-conserving flow in the lower layer and northward flow in the upper layer. There is net transport across the gyre boundary, in agreement with the Sverdrup relation.

The theory describes the longitudinal extent of the internal mode. Sufficient distortion of the isolines of potential vorticity by the wind-stress curl south of the gyre boundary is required in order to allow the flux of fluid in the internal mode to penetrate into the subtropical gyre. The model is presented as an additional example of gyre ventilation, in this case due to interaction with a neighboring gyre rather than the sea surface. Attention is drawn to the similarity of the calculated flow with the circulation pattern for the eastern North Atlantic proposed by Saunders.

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