On the influence of the horizontal component of the earth's rotation on long period waves

Abstract

Abstract A general linearized wave equation for a stratified rotating fluid is derived and applied to obtain a dispersion relation for waves of short latitudinal extent in a thin shell of fluid. Long period wave solutions in three ocean models are compared: (1) for a stratified ocean with both components of the rotation vector; (2) for a stratified ocean without the horizontal component of rotation, and finally, (3) for a homogeneous ocean without horizontal rotation. The inclusion of the horizontal component of the Earth's rotation is found to have no noticeable effect on the dispersion relation of long period waves; its only influence is the introduction of a vertical phase shift in the motions. The origin of this phase shift is found in the tendency of the motions to satisfy the Taylor-Proudman theorem. The phase shift is of possible oceanographic relevance only for bottom-trapped buoyancy waves in a relatively weak stratification. The differences between the three ocean models are also discussed with ...