Wave Exchange between the Ground Surface and a Boundary-Layer Critical Level

Abstract

Gravity waves induced by two- and three-dimensional terrain features are examined theoretically in the planetary boundary layer (PBL) using a linear wave model that includes reabsorption at a critical level. The PBL structure is characterized by a constant Brunt-Väisälä frequency and a hyperbolic tangent wind speed profile, which can be adjusted to produce critical levels. It is found that for typical values of wind speed and thermal stratification in the stable PBL and for even mild terrain disturbances, the Reynolds stress and surface drag caused by surface-generated waves can be at least as large as those conventionally associated with surface friction. The wave drag will act on the PBL flow where wave dissipation occurs, for example, at a critical level or in regions of wave breaking. The drag over a given crosswind section of a two-dimensional ridge is about twice as great as that over a three-dimensional of approximately the same horizontal area. An entirely new result is the prediction that over a three-dimensional hill the wave stresses may generate a horizontal layer of counterrotating vortices immediately below a critical level.