Splitting of subinertial coastal Kelvin waves at a gap

The splitting of Kelvin waves at a gap in a shoreline has received renewed interest in studies of the Indonesian Throughflow (ITF) variability. Remotely generated Kelvin waves traveling down the Indonesian coast have been shown to modulate the ITF in the Lombok Strait, the first deep water gap encountered. The question remains as to how much of the Kelvin wave bridges the gap and continues down the archipelago to similarly affect the other ITF straits. The problem may also be of interest in relation to basin-scale adjustment, where Kelvin waves associated with the adjustment encounter inland seas, gaps in island chains, etc.

Analytical solutions of the linear, inviscid, shallow water equations on an f-plane exist for the limit of gap widths that are small compared to the Rossby radius, but this condition is not often met with the baroclinic waves of interest. This work seeks solutions to these equations valid for all gap widths, primarily for the case of a finite-length channel connecting two semi-infinite seas. The semi-infinite channel case is visited along the way. Only subinertial waves are considered, and the solution sought is the fraction of the incident energy transmitted through the gap.

In Part A, a combination of numerical solutions, symmetry arguments and physical approximations are used to obtain a simple expression for the energy transmission coefficient in the classical case of a uniform-width channel with square-corner mouths. Numerical solutions are used to verify the validity of the expression over a wide range of realistic parameter values. The expression shows considerable sensitivity not only to channel width, but also to channel length and wave frequency.

In Part B, the techniques used in Part A are extended to the more realistic cases of channels and channel mouths of arbitrary geometry. Some general conclusions will be presented - not all of them intuitively obvious, and an iterative solution is being developed which exhibits moderate success at predicting the effects of arbitrary geometries.