WEAKLY NONLINEAR RESPONSE OF A STABLY STRATIFIED ATMOSPHERE TO DIABETIC FORCING IN A UNIFORM-FLOW

The weakly nonlinear response of a two-dimensional stably stratified a tmosphere to prescribed diabatic heating in a uniform flow is investig ated analytically using perturbation expansion in a small value of the nonlinearity factor for the thermally induced waves. The diabatic hea ting is assumed to have only a zeroth-order term specified to be verti cally homogeneous between the surface and a certain height and bell sh aped in the horizontal. The first-order (weakly nonlinear) solutions a re obtained using the FFT algorithm after solutions in wavenumber spac e are obtained analytically. The forcing (F) to the first-order pertur bation equation induced by the Jacobian of the zeroth-order (linear) s olutions always represents cooling in the lower layer regardless of sp ecified forcing type (cooling or heating). The vertical structure of F is related to the nondimensional heating depth (d) or the inverse Fro ude number. The first-order solutions are valid for relatively small v alues (<3) of d. The main nonlinear effect is to produce a strong conv ergence region near the surface associated with the zeroth-order pertu rbations regardless of the value of d. This convergence is responsible for producing upward motion in the center of the forcing region that extends upstream. As a result, the zeroth-order downward motion become s weaker according to a degree of nonlinearity. The relative magnitude of the zeroth-order downward motion and the first-order upward motion upstream of the forcing can be determined by d. The source of the fir st-order wave energy is found to come mainly from the horizontal advec tion of the zeroth-order total wave energy by the first-order perturba tion horizontal wind.