Abstract
Weakly non-linear theory of steady hydrostatic mountain waves in 2-layered stratified Boussinesq fluid of infinite depth is presented. Weakly non-linear effects (second-order correction) on drag, downslope wind and the steepening or flattening of the streamline are examined, and are found to be very sensitive to the depth of the lower layer, D, ι2/l1 (ι1≡N1/U and ι1≡N1/U; N1 and N2: BruntVaisala frequencies of the lower layer and upper layer, respectively; U: horizontal wind) and terrain shape. Drag obtained from linear theory is invariant under the change of π in ι1D, while that obtained from weakly non-linear theory is no more invariant under the change of π in ι1D. The theory gives an estimate of the applicability range of linear theory. The theory is found to be in good agreement at least in a qualitative sense with non-linear numerical solutions for some cases.
