FINITE-AMPLITUDE EFFECTS ON STEADY LEE-WAVE PATTERNS IN SUBCRITICAL STRATIFIED FLOW OVER TOPOGRAPHY

The flow of a continuously stratified fluid over a smooth bottom bump in a channel of finite depth is considered. In the weakly nonlinear-we akly dispersive regime epsilon = alpha/h much less than 1, mu = h/l mu ch less than 1 (where h is the channel depth and alpha,l are the peak amplitude and the width of the obstacle respectively), the parameter A = epsilon/mu(p) (where p > 0 depends on the obstacle shape) controls the effect of nonlinearity on the steady lee wavetrain that forms down stream of the obstacle for subcritical flow speeds. For A = 0(1), when nonlinear and dispersive effects are equally important, the interacti on of the long-wave disturbance over the obstacle with the lee wave is fully nonlinear, and techniques of asymptotics 'beyond all orders' ar e used to determine the (exponentially small as mu --> 0) lee-wave amp litude. Comparison with numerical results indicates that the asymptoti c theory often remains reasonably accurate even for moderately small v alues of mu and epsilon in which case the (formally exponentially smal l) lee-wave amplitude is greatly enhanced by nonlinearity and can be q uite substantial. Moreover, these findings reveal that the range of va lidity of the classical linear lee-wave theory (A much less than 1) is rather limited.