Structure and energetics of optimal Ekman layer perturbations

Abstract

The optimal non-modal perturbations for the neutrally stratified boundary layer in a rotating frame of reference (Ekman layer) are found for a Reynolds number characteristic of the planetary boundary layer (PBL). Two classes of non-modal instabilities are found: evanescent perturbations, with lifetimes up to about one hour, and growing instabilities. The important difference between these types of perturbations is whether or not the optimal non-modal perturbation projects onto an unstable normal mode. The evanescent instabilities are of smaller scale and are oriented at larger angles to the surface isobars compared to either the growing perturbations or normal-mode instabilities. The optimal perturbations take the form of vortices at an acute angle to the geostrophic flow that rapidly transform into streaks with associated overturning motion. The energetics of the optimal perturbations are investigated in detail to clarify the instability mechanism throughout its evolution.

Nonlinear stability analyses of the neutrally stratified Ekman layer have shown that the normal-mode instability will equilibrate with the mean flow to form boundary-layer-scale equilibrium roll eddies aligned closely with the geostrophic flow. However, numerical simulations do not generate these rolls in neutral stratification although they often realize small-scale near-surface streaks oriented at large angles to the geostrophic wind. The evanescent optimal perturbations bear a close resemblance to the simulated streaks. It is proposed that the non-model perturbation mechanism is associated with the streaks.