Development of boundary layer rolls from dynamic instabilities

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 conditions are expressed as polynomials in the critical (eddy) Reynolds number Re_c and depend on Fourier coefficients of a given height-dependent background wind profile. The preferred values of orientation angle θ and aspect ratio A, which describe the expected roll geometry, are assumed to be those that produce the smallest values of Re_c. For the Ekman profile, the preferred values of θ 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. For this case, the preferred values of θ, A and Re_c associated with the pure inflection point instability mechanism agree well with their observed values. -from Authors