High-drag states and lee vortices in stratified flow over topography

Abstract

Stratified flow with uniform basic wind and stability past long three-dimensional (3d) ridges is studied in the absence of surface friction and planetary rotation. The dominant control parameters for this problem are the nondimensional mountain height e=Nh0U0 and the horizontal aspect ratio beta (i.e., ratio of cross-stream to streamwise length scales).A weakly nonlinear semi-analytic model for steady inviscid flow past 3d obstacles is developed in Chapter 2. The model is based on a perturbation expansion for small e carried out through Oe2 and is implemented using numerical Fourier transforms. Comparison of the semi-analytic results with fully nonlinear numerical simulations reveals excellent agreement for small but finite e .Chapter 3 compares nonlinear numerical simulations of high-drag state flow over long three-dimensional ridges (beta ∼ O(10)) to the corresponding two-dimensional (2d) limit. It is found that the onset of wave-breaking and the transition to the high-drag state is accompanied in three dimensions by an abrupt increase in deflection of the low-level flow around the ridge. The increased flow deflection is effected in part by upstream propagating columnar disturbances forced by the transition to the high-drag state. The deflection of the incident flow reduces the amplitude of the mountain wave aloft relative to 2d and acts as a negative feedback on the surface drag.Chapter 4 explores the formation of lee wakes and vortices in flow over moderately long ridges (beta ∼ O(5)). Results of the semi-analytic model show that weakly nonlinear inviscid theory predicts the generation of vertical vorticity above the lee slope but fails to give an indication of flow reversal and eddy formation. Comparison of the weakly nonlinear results with fully nonlinear numerical simulations reveals the importance of a nonlinear stratified jump downstream of the obstacle. The dynamics leading to vortex formation in the nonlinear simulations is clarified through an analysis based on a Lagrangian decomposition of the vorticity according to source. It is found that weak vertical vorticity originating in the mountain wave upstream of the jump is strongly amplified by vertical stretching in the jump to produce the pronounced vertical vorticity anomalies of the wake.