Continental shelf wave scattering by a semi-infinite coastline

Abstract

In seeking to determine how the energy in a continental shelf wave that has travelled across the Great Australian Bight can reach the east Australian coast, the reflection/ transmission process at the southern tip of Tasmania is modelled by using a doublesided continental shelf of exponential/constant depth profile on which the coastline is semi-infinite.

The Wiener-Hopf technique provides a suitable method for solution but the factorization is non-trivial because |k | enters to ensure exponential decay in the ocean and the newly required “ridge” modes are determined by a more complicated transcendental equation than that for the shelf wave modes. The number of modes is usually the same on the shelf or ridge but in the latter case, the longest mode has such a large wavelength that it essentially represents a “swell”, with dissipation into the ocean. Practically all the reflected and transmitted energy is contained in the modes having the longer wavelength with preference towards those corresponding to the incident shelf wave mode.

Key Words:

• Coastal trapped waves
• scattering