Effects of Topography and Orientation on the Nonlinear Equilibration of Baroclinic Instability

Abstract

This study attempts to identify the equilibration mechanisms of baroclinic instability and investigate the effects of the orientation of the background flow and topography on eddy-induced transport. The analysis is based on growth rate balance theory, which assumes that nonlinear equilibration occurs when the growth rate of the primary baroclinic instability becomes comparable to that of the secondary instabilities of amplifying modes. Two-layer quasi-geostrophic numerical simulations are performed and compared to growth rate balance theory in order to analytically predict the cross-stream fluxes of potential vorticity. The model performs remarkably well in predicting the effects of variation in zonal topographic slope and background flow orientation. We find that meridional topographic slopes affect the baroclinic instability in an inherently nonlinear way. A predictive model based on conservation of potential vorticity is developed for the optimal slope that maximizes the transport characteristics of the baroclinic instability. Plain Language SummaryThe ocean is full of vortices on the scale of 10-100 km which play a major role in dispersing heat, salt, nutrients, and pollutants. However, the precise equilibration mechanisms controlling the production of these vortices remain a mystery. Physically, this process begins with the creation of north-south oriented streams which themselves result in a secondary stream formation oriented in an east-west direction. A new theory has found that when the north-south streams balance the east-west streams, the system achieves an equilibrium that allows us to characterize the heat transport by vortices through this system, which is critical to understanding global climate. Some key parts of this mystery are the effects of the ocean floor topography and the direction of the current on the production of these vortices. The proposed theory predicts the fluxes of heat as a function of ocean floor slopes and current direction. Key Points:• A semianalytical theory predicts eddy-induced transport in baroclinically unstable ocean regions • Effects of zonal topographic slope and orientation of the basic flow compare well to growth rate balance theory • We present a predictive model that determines the meridional slope that maximizes cross-stream flux of potential vorticity Supporting Information:• Supporting Information S1

Topographic Stabilization of Ocean Rings

“…(2018), and Brown et al. (2019). Promising attempts have also been made to parameterize the effects of topography using statistical circulation models (Alvarez et al., 1994; Chavanis & Sommeria, 2002; Frederiksen & O’Kane, 2005; Merryfield & Holloway, 2002; Okane & Frederiksen, 2004; Polyakov, 2001).…”

“…In fact, some of the longest-lived coherent structures are situated over prominent topographic features (Dewar, 1998;de Miranda et al, 1999), which can be attributed to the mechanisms originally advocated by Bretherton and Haidvogel (1976) and Verron and Le Provost (1985). Topographic influences on baroclinic instability have been explored by Hart (1975), Benilov (2005), Rabinovich et al (2018), andBrown et al (2019). Promising attempts have also been made to parameterize the effects of topography using statistical circulation models (Alvarez et al, 1994;Chavanis & Sommeria, 2002;Frederiksen & O'Kane, 2005;Merryfield & Holloway, 2002;Okane & Frederiksen, 2004;Polyakov, 2001).…”

Spin-down of a barotropic vortex by irregular small-scale topography

“…Arbic et al 2019;Klymak et al 2021) and the topographic control of the flow stability (e.g. Chen, Kamenkovich & Berloff 2015;Brown, Gulliver & Radko 2019). A distinct group of studies explored configurations where bathymetry affects transient eddies that, in turn, modulate time-mean flows (e.g.…”

Spin-down of a baroclinic vortex by irregular small-scale topography

“…Bathymetry can also control large-scale flows by affecting their stability and associated mixing characteristics (e.g. Chen, Kamenkovich & Berloff 2015; Brown, Gulliver & Radko 2019; LaCasce et al. 2019; Radko 2020).…”