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Joseph Pedlosky

Abstract

A ventilated thermocline model is used to discuss the circulation of the warm water of the subtropical gyre. It is suggested on theoretical grounds that the warm water layers that outcrop well south of the zero wind-stress curl line are completely replenished by the mass flux pumped down from the upper Ekman layer while recirculation of mass through the western boundary current plays a relatively insignificant role for these layers. The recirculation seems, instead, to be confined to the deeper layers of the thermocline.

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Joseph Pedlosky

Abstract

The stability of the marginally stable baroclinic wave in a uniform zonal shear flow is studied. Although thesingle, marginally stable wave on a horizontally uniform baroclinic current has little or no cross-streamvariation, the present paper shows that such a baroclinic wave is itself unstable to waves whose meridionalscale is of the order of the Rossby deformation radius.

The implications of this result for oceanic mesoscale dynamics is discussed since the instability, whichoccurs in the form of a triad resonance, may provide an amplitude limiting mechanism ignored in single-wave stability analyses.

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Joseph Pedlosky

Abstract

The finite-amplitude dynamics of baroclinic disturbances in currents whose cross-stream structure varies in the downstream direction is investigated.

It is first shown under what circumstances downstream variations of the current properties influence the local stability of the current. For flows near the neutral curve only the potential vorticity in one of the fluid layers is significant in determining the local stability.

For currents which are locally stable at some downstream locations and unstable at others, it is shown that the disturbance amplitude depends on the entire upstream structure of the current. In particular, simple examples illustrate the lack of a local relationship between “local” stability characteristics and the disturbance intensity.

The linear initial value problem for uniform (in the downstream direction) currents is also discussed to elucidate the relation between the temporal and spatial stability problems.

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Joseph Pedlosky

Abstract

The response of a weakly stratified layer of fluid to a surface cooling distribution is investigated with linear theory in an attempt to clarify recent numerical results concerning the sinking of cooled water in polar ocean boundary currents.

A channel of fluid is forced at the surface by a cooling distribution that varies in the down-channel as well as the cross-channel directions. The resulting geostrophic flow in the central region of the channel impinges on its boundaries, and regions of strong downwelling are observed. For the parameters of the problem investigated, the downwelling occurs in a classical Stewartson layer but the forcing of the layer leads to an unusual relation with the interior flow, which is forced to satisfy the thermal condition on the boundary while the geostrophic normal flow in the interior is brought to rest in the boundary layer.

As a consequence of the layer’s dynamics, the resulting long-channel flow exhibits a nonmonotonic approach to the interior flow, and the strongest vertical velocities are limited to the boundary layer whose scale is so small that numerical models resolve the region only with great difficulty. The analytical model presented here is able to reproduce key features of the previous nonlinear numerical calculations.

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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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Joseph Pedlosky

Abstract

The finite-amplitude dynamics of a resonant triad of baroclinic waves in a slightly unstable barocliniccurrent is examined. The wave in the triad which is linearly unstable on the current is assumed to havenegligible cross-stream variation and therefore lacks a self-equilibrating mechanism. It is shown, however,that the triad cooperatively equilibrates although for certain initial conditions the amplitude of the wavesmay become quite large. The triad possesses the deformation radius as its characteristic scale in bothhorizontal directions. It is suggested, therefore, that this triad instability may be a mechanism for theproduction of intense mesoscale oceanic eddies. However, the dependence of the result on the choice ofinitial conditions does not make it possible to definitely scale the amplitudes with fixed and external oceanicparameters.

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Joseph Pedlosky

Abstract

Two very simple model equations, suggested by the form of the standard baroclinic instability dispersion relation. are studied to investigate the nature of the instability of zonally inhomogeneous flows. In particular, the simplifications of the model problems allow the consideration of examples in which the interval of instability is of the same order or even smaller than the characteristic wavelength of the free plane wave modes of the zonally homogeneous problem, a limit inaccessible to standard WKB procedures.

In both model problems it is shown that the zonally gravest mode always remain no matter how small the locally unstable interval may be. Further, this gravest mode is eddy-like rather than wave-like, i.e., it has no internal nodes. When the free wave solutions are allowed to propagate, the structures of the bound modes are altered. They are squeezed against the exit edges of the unstable domain but again one mode, the bound eddy mode, is always possible.

This study is complementary to the more elaborate WKB analyses recently published and, in agreement with these studies, it is shown that only local maxima in supercriticality are required to yield trapped modes. The bound eddy mode is, however,. a feature allowable only when WKB analysis fails.

It is suggested that such bound eddies, anchored to local maxima in supercriticality may be regarded as the preliminary stage for the production of isolated, coherent structures.

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Joseph Pedlosky

Abstract

A model of abyssal, subthermocline flow is presented for a basin in which a peninsula intrudes into the basin. The effect of the peninsula is to provide two “eastern” boundaries for the total basin. The latitude-independent baroclinic pressure and density anomalies on both these boundaries are determined by integral conditions, which generalize earlier work.

The peninsula also produces a zonal jet between the tip of the peninsula and the western boundary. The baroclinic transport of this current is related to the blocking of westward propagating Rossby waves from the basin's eastern boundary. The baroclinic structure of this current, as well as the interior flow and the western boundary currents, are determined in terms of the distribution of deep-water sources on the perimeter of the basin as well as by the spatial distribution of upwelling into the thermocline. For the zonal jet, boundary currants and interior the flow is strongly baroclinic. Especially in the interior, the baroclinic Stommel-Arons flow is only a small residual obtained by vertically averaging the motion.

The upper part of the water column responds strongly to the upwelling forcing, and the lower part of the water column is more strongly influenced by the structure and distribution of the sources. The strong recirculation, which is only weakly coupled to the structure of the sources, renders the total vertical structure of the predicted flow more complex than that of the sources.

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Joseph Pedlosky

Abstract

The finite-amplitude dynamics of an unstable baroclinic wave in an f-plane, two-layer model is examined in the case where the degree of Ekman friction is unequal in the two layers. In particular, the case is examined where one layer is free of frictional dissipation.

The method employed requires the calculations of the wave amplitude evolution on two long-time scales in order to describe the essential equilibration of the wave which at intermediate times is rendered unstable by asymmetric Ekman dissipation. The method of reconstitution is used to combine equations appropriate for each epoch of the wave's history to provide a single equation useful for calculation.

The main physical result is the emergence of a finite lifetime for the unstable wave. The wave grows, equilibrates and then decays, leaving a wave-free state and an altered zonal flow with reduced potential energy. The speculation is offered that this process will be repetitive with the addition of a weak dissipative process to restore the wave-free state to its initial configuration.

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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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