Effects of three-dimensionality on instability and turbulence in a frontal zone

Abstract

Linear stability analysis and direct numerical simulation are used to investigate the evolution of a symmetrically unstable uniform frontal zone. Simulations in a three-dimensional computational domain capable of resolving near-symmetric currents develop strong nonlinearities without the emergence of pure symmetric instability. Linear stability analysis demonstrates that for $ft>1$ ( $f$ is the Coriolis parameter and $t$ denotes time) the flow generates strongly asymmetric structures which become nearly symmetric when $ft\gg 1$. Unlike the currents generated during pure symmetric instability, near-symmetric instability generates currents that do not align with isopycnals. This greatly modifies their energetics and evolution, leading to regions of the flow that are unstable to gravitational instability and energized by the reservoir of available potential energy. A high-resolution simulation demonstrates the flow evolution from near-symmetric currents to secondary shear-convective instabilities and finally, through tertiary instabilities, to fully three-dimensional turbulence. The effect of this sequence of instabilities is quantified through velocity and vorticity statistics as well as budgets for turbulent kinetic and potential energy. It is not until $ft\sim 10$ that the energy source for fluctuations is primarily shear, in contrast to the purely symmetric instability which draws its energy exclusively from shear production.