Baroclinic instability of axially symmetric flow over sloping bathymetry

Abstract

Observations and models of deep ocean boundary currents show that they exhibit complex variability, instabilities and eddy shedding, particularly over continental slopes that curve horizontally, for example around coastal peninsulas. In this article the authors investigate the source of this variability by characterizing the properties of baroclinic instability in mean flows over horizontally curved bottom slopes. The classical 2-layer quasi-geostrophic solution for linear baroclinic instability over sloping bottom topography is extended to the case of azimuthal mean flow in an annular channel. To facilitate comparison with the classical straight channel instability problem of uniform mean flow, the authors focus on comparatively simple flows in an annulus, namely uniform azimuthal velocity and solid-body rotation. Baroclinic instability in solid-body rotation flow is analytically analogous to the instability in uniform straight channel flow due to several identical properties of the mean flow, including vanishing strain rate and vorticity gradient. The instability of uniform azimuthal flow is numerically similar to straight channel flow instability as long as the mean barotropic azimuthal velocity is zero. Nonzero barotropic flow generally suppresses the instability via horizontal curvatureinduced strain and Reynolds stresses work. An exception occurs when the ratio of the bathymetric to isopycnal slopes is close to (positive) one, as is often observed in the ocean, in which case the instability is enhanced. A non-vanishing mean barotropic flow component also results in a larger number of growing eigenmodes and in increased non-normal growth. The implications of these findings for variability in deep western boundary currents are discussed.

Biogeochemical Role of Subsurface Coherent Eddies in the Ocean: Tracer Cannonballs, Hypoxic Storms, and Microbial Stewpots?

“…Note that formation of Puddies in finer resolution models involves submesoscale adjustment processes after the detachment of the undercurrent from the shelf, and upscale organization into geostrophic or gradient wind balanced currents (Molemaker et al, ). In the mesoscale‐resolving model used for the present study, Puddies presumably form directly from boundary current instabilities as balanced flow (Combes et al, ; Hormazabal et al, ; Molemaker et al, ; Solodoch et al, ).…”

“…The formation of subsurface coherent eddies may arise from baroclinic instabilities, just as for surface ocean eddies. However, subsurface eddies can also form from convection, or boundary currents undergoing flow separation, centrifugal, and submesoscale instabilities that adjust into submesoscale or mesoscale balanced flows (Bosse et al, ; D'Asaro, ; Gula et al, ; McWilliams, ; Molemaker et al, ; Solodoch et al, ). Their physical and biogeochemical tracer characteristics, from salinity to oxygen, indicate an origin in water masses foreign to the locations where the eddies are found (e.g., Lukas & Santiago‐Mandujano, ; Riser & Owens, 1985).…”

Why Does the Deep Western Boundary Current “Leak” around Flemish Cap?

“…Given the separation of the mean flow from the DWBC into the interior, one might ask: how does the mean flow cross the dynamical barrier presented by the cross-bathymetry PV gradient? To address this, we now examine the TWA PV budget (Smith 1999;Young 2012). The TWA of a variable a, and its deviation from TWA, are defined byâ 5 (ha/h), and a 0 5 a 2â, respectively.…”

“…All averages are performed on a selected isopycnal. The TWA PVq, and its balance, are then respectively defined by Smith (1999),…”

On the nonlinear stability and the existence of selective decay states of 3D quasi‐geostrophic potential vorticity equation

“…Exact solutions to the QGPV equation without the dissipative term are constructed corresponding to Baroclinic Rossby waves in [15][16][17] and to Barotropic Rossby waves in [4,16]. The problems of baroclinic and barotropic instability is investigated in [13,18,19]; see [20][21][22] for the study of viscous instability associated with the QGPV equation. For the nonlinear stability of the QGPV equation, Majda and Wang in [1] constructed a family of exact solutions, including time-independent solutions such as simple shear flow, swirling eddies and Taylor vortices, and more general time-dependent solutions in presence of general Kolmogorov forcing and topography.…”