The Modification of Long Planetary Waves by Homogeneous Potential Vorticity Layers

Abstract

A mechanism by which long planetary waves in the ocean may propagate significantly faster than the classical long baroclinic Rossby waves is investigated. The mechanism depends on the poleward thickening of intermediate density layers and the concomitant thinning of near-surface and deep layers. These features of the mass distribution are associated with the well-known homogenization of potential vorticity in intermediate density layers and with significantly elevated meridional potential vorticity gradients near the surface and somewhat at depth. The mechanism is explored in a simple three-layer model, in which the middle layer has zero potential vorticity gradient and is sandwiched between a surface layer with large potential vorticity gradient and a bottom layer with modest potential vorticity gradient. The effective phase speed of the planetary waves is merely the sum of the phase speeds of virtual baroclinic Rossby waves propagating on the individual layer interfaces as though the other interface were not there and as though there were no mean vertical shear. The mechanism is also examined for a continuous model with zero potential vorticity gradient throughout the interior and large virtual potential vorticity gradients near the surface and bottom. Planetary waves in these models can propagate westward up to twice as fast as baroclinic Rossby waves would through an ocean with the same vertical stratification, but no mean vertical shear. This explanation of the Rossby wave speedup complements a recent detailed theoretical calculation of planetary-wave phase speeds based on geostrophic velocity profiles from archived hydrographic data.

The Interaction of a Baroclinic Mean Flow with Long Rossby Waves

“…Although the mean pv gradient has been found so important for the instabilities (i.e., the imaginary parts of the phase speed), it does not appear to control the real part of the phase speed, and it is instead the meridional gradient of the quantity N 2 /f, which appears when the second and third term in (20) are summed up. Suppose now (R. S. Schopp 2004, personal communication) that the mean flow is such that the gradient of potential vorticity vanishes, then the gradient of N 2 /f doubles, leading to an increase in westward first-mode phase speeds, which is to be compared with the 56% increase calculated by de Szoeke and Chelton (1999) when discussing the case of a vanishing pv mean flow. These comments, which are of a qualitative nature, are not meant to say that the first Doppler shift term is unimportant but that it does not govern the sign of the corrections to the first-mode phase speed for the family of mean flows profiles considered herein.…”

“…There remains the possibility that c be complex. Such possibilities were raised by Colin de Verdière (1986), Cavallini et al 1988, andde Szoeke (1999). Colin de Verdière and Huck (1999) have argued that such instabilities are important in the western regimes of numerical ocean models forced by fixed fluxes of buoyancy at the surface.…”

“…He attributed the sign of this peculiar effect to the vertical shear distribution of his steady flow and emphasized that three layers were the minimum to show this effect. A similar model was used by de Szoeke and Chelton (1999) to study the effect of a vanishing mean potential vorticity gradient in the middle layer, an assumption supported on several theoretical and observational grounds. They were able to demonstrate that their mean flow configuration led to an increase of the westward phase speeds in agreement with the Killworth et al (1997) remark about the importance of secondmode structure in the mean flow.…”

Extratropical Rossby Waves in the Presence of Buoyancy Mixing

“…However, the westward propagation of SSH anomalies outside the band 108S-108N appeared systematically faster than predicted (Chelton and Schlax 1996). A wealth of studies that attempted to interpret the reported disagreement in terms of effects absent from the standard linear theory of Rossby waves followed (e.g., Killworth et al 1997;Qiu et al 1997;Dewar 1998;de Szoeke and Chelton 1999;Killworth and Blundell 1999;Tailleux and McWilliams 2001;LaCasce and Pedlosky 2004;Killworth and Blundell 2005). Zhang and Wunsch (1999) revisited the analysis of North Pacific data by Chelton and Schlax (1996) by using a different processing method and contended that a significant fraction of the data is actually consistent with linear theory.…”

“…Whereas the representation of mixing as Fickian diffusion is almost universal in dissipative theories, there still appears to be no fundamental justification for it. Other limitations include the omissions of a background flow (e.g., Killworth et al 1997;Dewar 1998;de Szoeke and Chelton 1999) and bottom topography (e.g., Killworth and Blundell 1999). It is felt that the influences of mixing on Rossby waves should first be considered in isolation of these yet important aspects of the general circulation.…”