Development of Boundary Layer Rolls from Dynamic Instabilities

Abstract

The development of atmospheric boundary layer rolls from the inflection point and parallel instabilities is examined analytically using several three-dimensional linear models of flow in a neutral, rotational fluid. These models are formulated so that either arbitrary or observed background wind profiles can be examined easily to see which roll modes would likely occur. Necessary and sufficient conditions for the development of particular atmospheric modes are determined. These conditions are expressed as polynomials in the critical (eddy) Reynolds number Rec and depend on Fourier coefficients of a given height-dependent background wind profile. The preferred values of orientation angle ? and aspect ratio A, which describe the expected roll geometry, are assumed to be those that produce the smallest values of Rec. The ability of the models to successfully reproduce the modes arising from the inflection point and parallel instability mechanisms is tested by using idealized wind profiles to approximate the mean wind in the boundary layer. For the Ekman profile, the preferred values of ? and A are found to agree with those given by larger models, indicating that the simpler analytical models are incorporating the crucial information contained in the wind profile. Finally, a direct comparison with observations of atmospheric boundary layer rolls is given using a mean wind profile obtained during the 1981 West German KonTur experiment. For this case, the preferred values of ?, A and Rec, associated with the pure inflection point instability mechanism agree well with their observed values, It is this easy, direct comparison between the model results and observations that is the significant contribution of this analytical modeling approach.