Instability of a Surface Jet over Rough Topography

Abstract

The instability of a surface-trapped jet over rough bottom topography is examined using a linearized quasigeostrophic model. The jet is laterally-sheared and thus susceptible to both barotropic and baroclinic instability. The relative magnitude of the two depends on the jet width and on the spectral characteristics and amplitude of the bathymetry. The most unstable eddies in the upper layer are typically smaller over bathymetry than with a flat bottom. Topography also alters momentum flux convergence in the upper layer and causes the perturbations to resemble eddies in a 1.5 layer flow. But as long as the jet is wider than the deformation radius, baroclinic instability is present, yielding deep eddies which are phase-locked to those at the surface. In addition, topography facilitates scattering of energy at depth to other scales. So instability over rough topography could be an efficient, and largely overlooked, means of transferring mesoscale energy to the dissipative scales.

Prevalence of Deformation‐Scale Surface Currents

“…The jet half-widths were linked to the L d on either side and the upper layer PV, that is, that above the 1,027 kg/m 3 isopycnal, was nearly constant on the jet flanks. The results are also in line with linear baroclinic models which predict neutral momentum fluxes when the jet half-width is deformation scale (Held & Andrews, 1983;Palóczy & LaCasce, 2022), and with nonlinear models which assume PV homogenization on the jet flanks (Nakamura, 1999;Esler, 2008, DM08). Geostrophic adjustment models, like those considered here, are perhaps the simplest to exhibit the relevant characteristics.…”

“…Eddy momentum fluxes tend to sharpen jets which are too broad and to widen jets which are too narrow (e.g., Held & Andrews, 1983). In a study of topographic effects on jet stability, Palóczy and LaCasce (2022) found that the momentum fluxes were near zero when the jet half‐width was roughly 1.1–2 times the deformation radius ( L d ). A similar prediction follows from the argument that eddies tend to homogenize potential vorticity (PV) on the jet flanks.…”

The sandpaper theory of flow–topography interaction for homogeneous shallow-water systems

“…LaCasce et al. 2019; Radko 2020; Palóczy & LaCasce 2022). Rough bathymetry can stabilize coherent vortices (Gulliver & Radko 2022), extending their lifespan and enhancing their ability to transport heat, salt and nutrients.…”

“…For instance, small-scale variability in the bottom relief regulates the pattern and intensity of baroclinic instability in vertically sheared currents (e.g. LaCasce et al 2019;Radko 2020;Palóczy & LaCasce 2022). Rough bathymetry can stabilize coherent vortices (Gulliver & Radko 2022), extending their lifespan and enhancing their ability to transport heat, salt and nutrients.…”

The sandpaper theory of flow–topography interaction for multilayer shallow-water systems

“…Several studies (e.g. LaCasce et al 2019;Radko 2020;Palóczy and LaCasce 2022) underscore the adverse impact of seafloor roughness on baroclinic instability and associated mesoscale variability. LaCasce et al (2019) note that the sinusoidal topography with a 1 km wavelength and amplitude of only 10 m can stabilize surface-intensified flows with strength and dimensions commensurate to those of the main western boundary currents.…”