Surface Drag Instabilities in the Atmospheric Boundary Layer

Abstract

Jefferys' analysis of wavelike instabilities observed in turbulent water running down an incline is extended to wavelike instabilities in the wind over level ground. In the lowest part of the atmosphere the wind experiences an aerodynamic surface drag that balances part of the horizontal pressure gradient, and this balance is shown to be unstable against wave-associated modulation of the drag, the mechanism presented by Jeffreys. Model computations for the statistically stable atmospheric boundary layer evaluate this instability for several classes of ducted waves. Linearized theory predicts very small growth rates for the Fundamental modes (those with the simplest vertical structure) and much larger growth rates for the higher modes. The drag mechanism allows synoptic conditions to maintain turbulence in the stably gratified boundary layer waves grow until overturning cascades energy into the small-scale turbulence, and in this way the waves process available potential energy from the larger scales into boundary-layer mixing. Field experiments are needed to verify the mechanism and provide better parameterizations of the turbulent Reynolds stresses associated with wave activity.