The Effects of Surface Wind Stress and Buoyancy Flux on the Evolution of a Front in a Turbulent Thermal Wind Balance

Matthew N. Crowe,John R. Taylor

doi:10.3390/fluids5020087

Abstract

Here we consider the effects of surface buoyancy flux and wind stress on a front in turbulent thermal wind (TTW) balance using the framework of Crowe and Taylor (2018). The changes in the velocity and density profiles induced by the wind stress and buoyancy flux interact with the TTW and can qualitatively change the evolution of the front. In the absence of surface-forcing, Crowe and Taylor (2018) found that shear dispersion associated with the TTW circulation causes the frontal width to increase. In many cases, the flow induced by the surface-forcing enhances the spreading rate. However, if the wind stress drives a cross-front flow which opposes the frontal buoyancy gradient or the buoyancy flux drives an unstable stratification, it is possible to obtain an up-gradient cross-front buoyancy flux, which can act to sharpen the front. In certain conditions, an equilibrium state develops where the tendency for the TTW circulation to spread the front is balanced by the frontogenetic tendency of the surface forces. We use numerical solutions to a nonlinear diffusion equation in order to test these predictions. Finally, we describe the connection between surface-forcing and vertical mixing and discuss typical parameters for mid-ocean fronts.

Highlights

Fronts, or regions of large horizontal density gradient are important features of the upper ocean and atmosphere where they play an important role in the exchange of heat, carbon, and other important tracers
Fronts can be characterised by their cross-front width which can range from tens of kilometers for large fronts including the Gulf Stream, Kuroshio, and fronts associated with the Antarctic Circumpolar Current (ACC), to scales of meters for fronts associated with freshwater plumes and gravity currents
We extend the model of Crowe and Taylor [1], where turbulence is represented by vertical mixing, to include a surface wind stress and buoyancy flux imposed as boundary conditions

Summary

Introduction

Regions of large horizontal density gradient are important features of the upper ocean and atmosphere where they play an important role in the exchange of heat, carbon, and other important tracers. An answer to this question could provide a basis for improving parametrisations of submesoscale processes where the horizontal buoyancy gradient is an important input parameter that is often under-resolved in ocean models (e.g., [18,19]) To address these questions, we extend the model of Crowe and Taylor [1], where turbulence is represented by vertical mixing, to include a surface wind stress and buoyancy flux imposed as boundary conditions. We extend the model of Crowe and Taylor [1], where turbulence is represented by vertical mixing, to include a surface wind stress and buoyancy flux imposed as boundary conditions This system is solved analytically in the limit of small Rossby number in Section 3 in terms of a background buoyancy field.

Governing Equations

Analytic Solution

The Evolution of the Depth-Averaged Buoyancy

The y Independent Case

Frontal Evolution

Weak Surface Heat Flux

Weak Wind Stress

Numerical Simulations

A Spreading Front—Indefinite Spreading

A Spreading Front—Equilibrium Width

Sharpening Front

Wind Stress and Buoyancy Flux Driven Turbulence