Mountain-induced lee waves and rotor circulations

Mountain-induced trapped lee waves can lead to rotor formation under certain conditions. The word 'rotor' is used in the literature to refer to many different phenomena involving flow reversal or overturning of some kind. In this work, a rotor is defined as a stationary closed circulation which forms underneath the crest of a trapped lee wave, whose axis of rotation is horizontal and parallel to the crest of a considered mountain ridge. The conditions under which rotors will form are not well known, but one pre-requisite is commonly understood to be a steep lee slope, giving rise to large amplitude lee waves. The separation and reattachment mechanism of the rotor is similar to that of a separation 'bubble' on the lee side of the mountain, except that it occurs further downstream, underneath the first lee wave crest. Whether the flow separates on the slope or downstream depends on the relative wavelengths of the mountain and the lee wave, and on the Froude number and steepness of the lee slope.

Regions of mountain-induced rotor formation near the ground, and mountain-induced wave breaking aloft, present a serious hazard for the aviation community. The dynamical mechanisms and height of upper level wave breaking are reasonably understood, whereas lee wave rotors are notoriously difficult to forecast. In most previous studies rotors have been postulated as steady features, linked to stationary, non-breaking, trapped lee waves. In reality, upstream flow conditions vary with time which, combined with potentially important non-linear effects, can give rise to unsteadiness in rotor size, strength and position. The present work assumes steady upstream conditions with the aim of simulating these rotors using a high resolution, non-hydrostatic numerical model, in order to better understand the flow patterns involved and the conditions conducive to their formation. In the long term, this knowledge will feed into the development of a more sophisticated local lee wave/rotor forecasting tool for aviation purposes.

Two-dimensional inviscid results from numerical model integrations of trapped lee waves have shown good agreement with analytical results for several idealised test cases. Following on from these studies, results will be presented from recent integrations attempting to simulate rotor formation both in an inviscid environment and in one with a neutral boundary layer included. A variety of upstream conditions (wind and stability profiles with height) are investigated, together with variations in mountain shape, height, width and slope, in order to find out which conditions lead to rotor formation. An overview of the current findings of this work will be given in the form of regime diagrams.