Flow–topography interactions in shallow-water turbulence

Abstract

Topography and external time-varying flows such as tides can have a profound influence on atmospheric and oceanic fluid motion. The effects of topography on turbulence have been little studied, and until recently those of tides have been overlooked. Our lack of understanding of these effects is a serious impediment to predicting flows both in the atmosphere and in the oceans. As a first step toward modelling realistic tidal oscillations, this study focuses on how an initially balanced flow containing a distribution of potential vorticity anomalies develops and becomes unbalanced (by emitting gravity waves) as a result of interactions with topography in the presence of an oscillating flow, here in the form of pure inertial oscillations (at the Coriolis frequency). We investigate a large parameter space spanned by the Burger number, the maximum amplitude of topography, and the amplitude of the flow oscillations. Comparisons are made with a time-independent and spatially-homogeneous steady flow in order to better understand the role played by flow oscillations. The most persistent large-amplitude gravity wave activity occurs for large-amplitude flow oscillations and for large topography. The latter produces large potential vorticity and depth anomalies which remain locked to the topography, thereby allowing gravity waves to be continually generated. By contrast, for a steady flow, large potential vorticity and depth anomalies are advected away from topographic features and so gravity waves are only generated at early times.

Keywords:

• Inertial oscillations
• Topography
• Tides
• Potential vorticity
• Balance

Notes

†When “low” or “high” values of correlation are referred to, absolute values are meant. “Low” implies a weak correlation, while “high” implies a strong one.