The perturbed structure of the neutral atmospheric boundary layer over irregular terrain

The differential equations for first-order (linear) response of the planetary boundary layer are formulated for flow over periodic terrain, for variations in both surface roughness and terrain elevation. A simple second-order closure model of the turbulence is used, and Coriolis forces are neglected. Flow over a periodic terrain produces corresponding periodic structure in all meteorological fields above the surface. The periodic structure consists of two components. The first is very nearly evanescent with height. It corresponds to the motion that would be observed were the atmosphere inviscid. The second component, introduced by turbulent viscosity, exhibits a phase variation with height in addition to a decay in amplitude. W.K.B. Wentzel-Kramers-Brillouin] approximations for the two components are developed, and the coupling between the components is discussed. The formulation for calculating solutions by numerical integration is developed, including specification of appropriate boundary conditions. Calculations are presented in a companion paper.Wave Propagation Laboratory.Environmental Science Group.