Linear Surface Waves over Rotating Fluids

Abstract

Assuming that fluids are incompressible, inviscid, and homogeneous, natural linear surface waves in a rotating system can be decomposed into different frequency components. For each frequency component, solutions can be further decomposed into modes of an infinite series in the vertical direction. A depth‐integrated two‐dimensional model equation is derived to include Coriolis effects for waves of each mode propagating over variable depth topography in rotating fluids. The model equation reduces to the mild‐slope equation for waves in irro‐tational flows when Coriolis effects are ignored. It also reduces to an equation for waves in a rotating fluid of constant water depth. With respect to the Coriolis factor, propagating and evanescent modes of frequency components are distinguished. Analytical solutions for waves of the zeroth‐mode around a circular island on a paraboloidal water depth are obtained. Effects of the earth's rotation on wave response around a circular island are also discussed.