Asymptotic behavior of internal Rossby waves with a sharp density interface

An asymptotic analysis of a quasi-geostrophic model is presented to investigate the vertically propagating internal Rossby wave structure in the presence of a sharp density interface. For the case of a nonconstant density gradient, the pattern of the vertical structure is nontrivial and depends on the parameter of varying strati. cation, denoted by delta. As this parameter approaches a critical value from above (i.e., delta approximate to delta(cri)), the internal wave amplitudes increase continually until wave breaking occurs. When delta < delta(cri), two cases are considered. For the case without a turning-point, the requirement of appropriate interfacial conditions provides a general matching solution, available only for a certain range of delta. In the presence of a turning-point, which describes the solution transition from monotonic to oscillatory behavior or vice versa, three asymptotic forms of the solutions are derived, even for small values of delta.