Topographic effects in stratified flows resolved by a spectral method

Abstract

The aim of the paper is to validate a particular model formulation in the study of wind-induced response in a wide, rotating channel with varying bottom topography. The model consists of a continuous stratified upper layer joined to a homogeneous lower layer. For this density profile, standard normal mode solution techniques can be extended to forced models with sloping bottoms in order to separate the vertical dependency. The governing equations are then reduced to a time dependent problem by expanding across channel variations in Fourier series and applying periodic boundary conditions along the channel. An initial-value problem is solved numerically, using an eigenmode solution technique starting from a state of rest, where a constant wind stress is suddenly imposed and then switched off after a certain period of time. The eigenmode solution technique is found to be applicable in the examination of the coupling between vertical modes and the analysis has resulted in a simplified coupling pattern for this specific two layer model. Modified baroclinic eigenmodes are introduced in a superposition of each baroclinic and the barotropic mode, according to the eigenvalue problem. For these modes the interaction amongst baroclinic modes is found to be insignificant while the barotropic eigenmodes are not found to be affected by the stratification. For varying bottom topography these modified baroclinic modes will reflect both stratification and topography. Model simulations show that the flow pattern is dominated by long period barotropic oscillations as topographic Rossby waves. The waves show a dominance in the second lateral mode, and they are less affected by the stratification. The barotropic response to the wind is mirrored in internal displacements and shows long periodic oscillations corresponding to the topographic waves. The use of a bottom Ekman layer has shown that bottom friction mainly influences on long-period barotropic modes. The baroclinic modes are damped by internal friction.