Mixed Convective–Dynamic Roll Vortices and Their Effects on Initial Wind and Temperature Profiles

Abstract

The onset and development of both dynamically and convectively forced boundary-layer rolls are studied with linear and nonlinear analyses of a truncated spectral model of shallow Boussinesq flow. Emphasis is given here on the energetics of the dominant roll modes, on the magnitudes of the roll-induced modifications of the initial basic-state wind and temperature profiles, and on the sensitivity of the linear stability results to the use of modified profiles as basic states. It is demonstrated that the roll circulations can produce substantial changes to the cross-roll component of the initial wind profile and that significant changes in orientation angle estimates can result from use of a roll-modified profile in the stability analysis. These results demonstrate that roll contributions must be removed from observed background wind profiles before using them to investigate the mechanisms underlying actual secondary flows in the boundary layer. The model is developed quite generally to accept arbitrary basic-state wind profiles as dynamic forcing. An Ekman profile is chosen here merely to provide a means for easy comparison with other theoretical boundary-layer studies; the ultimate application of the model is to study observed boundary-layer profiles. Results of the analytic stability analysis are validated by comparing them with results from a larger linear model. For an appropriate Ekman depth, a complete set of transition curves is given in forcing parameter space for roll modes driven both thermally and dynamically. Preferred orientation angles, horizontal wavelengths, and propagation frequencies, as well as energetics and wind profile modifications, are all shown to agree rather well with results from studies on Ekman layers as well as with studies on near-neutral and convective atmospheric boundary layers.