Beta-plane turbulence above monoscale topography

TL;DR

This paper investigates how monoscale topography influences beta-plane turbulence using a one-layer QG model, revealing flow regimes, eddy saturation phenomena, and the role of transient eddies in energy and momentum transfer.

Contribution

It introduces a detailed analysis of flow regimes and the conditions for eddy saturation in beta-plane turbulence over monoscale topography, highlighting the role of PV diffusion.

Findings

Flow regimes depend on the relation between beta and topographic PV gradient.

Eddy saturation occurs when transient eddies act as PV diffusion, making flow insensitive to wind stress.

Flow transitions from form stress balance to large transport as wind stress increases.

Abstract

Using a one-layer QG model, we study the effect of random monoscale topography on forced beta-plane turbulence. The forcing is a uniform steady wind stress that produces both a uniform large-scale zonal flow $U(t)$ and smaller-scale macroturbulence (both standing and transient eddies). The flow $U(t)$ is retarded by Ekman drag and by the domain-averaged topographic form stress produced by the eddies. The topographic form stress typically balances most of the applied wind stress, while the Ekman drag provides all of the energy dissipation required to balance the wind work. A collection of statistically equilibrated solutions delineates the main flow regimes and the dependence of the time-mean $U$ on the problem parameters and the statistical properties of the topography. If $\beta$ is smaller than the topographic PV gradient then the flow consists of stagnant pools attached to pockets of closed geostrophic contours. The stagnant dead zones are bordered by jets and the flow through the domain is concentrated into a narrow channel of open geostrophic contours. If $\beta$ is comparable to, or larger than, the topographic PV gradient then all geostrophic contours are open and the flow is uniformly distributed throughout the domain. In this case there is an "eddy saturation" regime in which $U$ is insensitive to changes in the wind stress. We show that eddy saturation requires strong transient eddies that act as PV diffusion. This PV diffusion does not alter the energy of the standing eddies, but it does increase the topographic form stress by enhancing the correlation between topographic slope and the standing-eddy pressure field. Last, using bounds based on the energy and enstrophy we show that as the wind stress increases the flow transitions from a regime in which form stress balances the wind stress to a regime in which the form stress is very small and large transport ensues.