Topographically Forced Waves in a Thermally Driven Rotating Annulus of Fluid—Experiment and Linear Theory

Abstract

The amplitude and phase of a topographically forced wave in a baroclinic flow are studied both experimentally and theoretically. The experiments were conducted in a thermally driven fluid in a rotating annulus with two-wave bottom topography. Analysis of velocity data at a single level in seven different experiments at the same imposed temperature contrast and successively larger rotation rates (Ω) reveals that the forced wave is displaced upstream from the topography by an amount which increases with increasing Ω. The wave amplitude increases as we progress from low to moderate Ω, beyond Which it becomes smaller. Linear equivalent barotropic and baroclinic theory (the latter incorporating vertical density stratification) give an upstream phase displacement which increases with increasing Ω, in qualitative agreement with the experimental data. The phase lag in the theory is controlled by the ??-effect? (produced by the slope of the free surface) and by Ekman layer dissipation (measured by the ratio of the square root of the Ekman number to the Rossby number). The theoretical phase displacement increases with Ω more slowly at low Ω, and more rapidly at high Ω, than the experimentally determined displacement. The wave amplitude derived from the linear theory is too large and increases monotonically with Ω, peaking at resonance, which is found outside the range of rotation rates imposed in the experiments. The discrepancies between the theoretically and experimentally determined phase are attributed to variations in the vertical shear of the basic state velocity with Ω, which the present measurements were not designed to observe. The required variations are consistent with those observed in a related series of experiments without bottom topography. The discrepancies in the amplitude determinations are attributed to nonlinear wave-wave interactions that are not taken into account in the theory.