On the baroclinic instability of cold-core coupled density fronts on a sloping continental shelf

Abstract

A theory is presented to describe the linear baroclinic instability of coupled density fronts on a sloping continental shelf. The new baroclinic model equations used to study the instability process correspond to an ‘intermediate lengthscale’ dynamical balance. Specifically, the frontal dynamics, while geostrophic, is not quasigeostrophic because frontal height deflections are not small in comparison with the frontal scale height. The evolution of the frontal height is strongly coupled to the geostrophic pressure in the surrounding slope water through the hydrostatic balance which expresses the continuity of the dynamic pressures across the frontal interface. The deeper surrounding slope water evolves quasi-geostrophically and is coupled to the front by baroclinic vortex-tube stretching/compression associated with the perturbed density front (allowing the release of mean frontal potential energy) and the topographic vorticity gradient associated with the sloping bottom. It is shown that the baroclinic stability characteristics are principally determined by a so-called non-dimensional interaction parameter (denoted μ) which physically measures the ratio of the destabilizing baroclinic vortex-tube stretching/compression to the stabilizing topographic vorticity gradient. For a given along-front mode wavenumber it is shown that a minimum μ is required for instability. Several other general stability results are presented: necessary conditions for instability, growth rate and phase speed bounds, the existence of a high wavenumber cutoff, and a semicircle theorem for the unstable modes. The linear stability equations are solved exactly for a parabolic coupled density front and a detailed description of the spatial and temporal characteristics of the instabilities is given. For physically realistic parameter values the instabilities are manifested as amplifying topographic Rossby waves in the slope water, and on the density front the unstable perturbations take the form of amplifying anticyclones which have maximum amplitude on the offshore side.

Faroe Bank Channel Overflow: Mesoscale Variability*

“…Their generation is generally suggested to be due to vortex stretching (Lane-Serff and Baines 1998; Spall and Price 1998), baroclinic instability (Smith 1976;Swaters 1991), or changes in topography (Nof et al 2002;Pratt et al 2008). These mechanisms are discussed below.…”

“…Unfortunately, it is not possible, using the present dataset, to identify an upper-isotherm boundary or the lateral gradients needed to calculate the divergence of the temperature flux following Voet and Quadfasel (2010). Swaters (1991) describes a type of baroclinic instability for the downslope side of the plume where the isopycnals tend to slope steeper than the bottom. This mechanism is expected to generate the strongest variability on the deep side of the overflow and within the dense layer.…”

“…A number of generation mechanisms has been suggested, often related to baroclinic instabilities (Smith 1976;Swaters 1991), vortex stretching (Lane-Serff and Baines 1998; Spall and Price 1998), or the bathymetry (Nof et al 2002;Pratt et al 2008), but as of today no consensus or clear understanding of the origin and nature of these oscillations exist. In the following, we loosely refer to the oscillations as eddies.…”

Meridional flow of grounded abyssal currents on a sloping bottom in spherical geometry

“…The formation of such a shock could result in mixing on the up slope flank of the abyssal water mass as it propagates equatorward. This would be a decidedly different "instability mechanism" than baroclinic destabilization, which preferentially occurs on the down slope or offshore side of grounded abyssal currents [7,8,10].…”

“…These currents form an important component in the deep "leg" of the meridional overturning circulation in the oceans. The mesoscale dynamics of these currents has been described in a series of papers [1][2][3][4][5][6][7][8][9][10][11]. All of these studies have implicitly assumed either an f or β-plane approximation in which the dynamics is modelled in a Cartesian coordinate system with the implicit assumption that the horizontal length scales are not too much larger than the internal deformation radius (on the order of about 10-100 km in the ocean).…”