On topographic generation and coupling of internal waves

Abstract

For a two-dimensional geometry the internal wave eigenfunctions are constructed as combinations of non-uniform wave trains to satisfy variable boundary conditions. All the notable features of the wave-topography interaction problem can be derived from the form of in homogeneous phase function; hence its construction is the central theme of this paper. It is shown that the general solution can be expanded in many (perhaps an infinite number) complete sets of eigenfunctions, but that the application of physical constraints (if available) narrows the choice to at most two sets, in terms of which the general topographic generation and coupling problem can be solved. The general method is illustrated by several special cases, which indicate that coupling is relatively weak for sub-critical slopes but strong for critical and also for supercritical slopes.