A Secondary Flow Model for the Planetary Boundary Layer

TLDR: In this article, the secondary flow is considered to be a finite perturbation on a mean large-scale flow, and approximate equations are obtained for the secondary flows and the modified mean flow an functions of the large scale parameters.

Abstract: The equations of motion for a neutrally buoyant fluid are solved to produce an equilibrium flow consisting of a modified Ekman spiral mean flow plus a helical secondary flow. By considering the secondary flow to be a finite perturbation on a mean large-scale flow, approximate equations are obtained for the secondary flow and the modified mean flow an functions of the large-scale parameters. When the energetics of this system are considered, an equilibrium magnitude for the secondary flow can be obtained. The finite perturbations are assumed to preserve the structure of the infinitesimal perturbation solutions for the dynamic instability of the Ekman boundary layer. In particular, helical rolls occur as finite perturbation solutions. These finite disturbances are found to alter the mean Ekman velocity profile such that it becomes stable. The rolls, with characteristic depths of 5–7 times the Ekman characteristic length and corresponding wavelengths of 4π times this parameter, may be frequent occur...