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Abstract Oceanographic observations have revealed that basin‐scale Rossby waves can travel at speeds systematically exceeding values predicted by linear theory based on the flat‐bottom approximation. Using the recently developed parametric “sandpaper” theory of seafloor roughness, we construct a set of analytical solutions for the vertical structure and dispersion relationship of Rossby waves. We then use simulations to confirm these results and show that baroclinic Rossby waves can be accelerated by irregular small‐scale rough topography by up to a factor of 1.6 relative to their flat‐bottom counterparts. This acceleration is most extreme at high latitudes and wavelengths of approximately 600 km. Our investigation demonstrates the importance of relatively small‐scale processes for the large‐scale flow dynamics in general and baroclinic Rossby waves in particular.
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A series of recent studies has indicated that the component of the bottom drag caused by irregular small-scale topography in the ocean varies non-monotonically with the flow speed. The roughness-induced forcing increases with the speed of relatively slow abyssal currents but, somewhat counterintuitively, starts to decrease when flows are sufficiently swift. This reduction in drag at high speeds leads to the instability of laterally uniform currents, and the resulting evolutionary patterns are explored using numerical and analytical methods. The drag-law instability manifests in the spontaneous emergence of parallel jets, aligned in the direction of the basic flow and separated by relatively quiescent regions. We hypothesize that the mechanisms identified in this investigation could play a role in the dynamics of zonal striations commonly observed in the ocean.more » « less
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Seafloor roughness profoundly influences the pattern and dynamics of large-scale oceanic flows. However, these kilometre-scale topographic patterns are unresolved by global numerical Earth system models and will remain subgrid for the foreseeable future. To properly represent the effects of small-scale bathymetry in analytical and coarse-resolution numerical models, we develop the stratified ‘sandpaper’ theory of flow–topography interaction. This model, which is based on the multilayer shallow-water framework, extends its barotropic antecedent to stratified flows. The proposed theory is successfully tested on the configuration representing the interaction of a zonal current with a corrugated cross-flow ridge.more » « less
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Recent studies reveal the dramatic impact of seafloor roughness on the dynamics and stability of broad oceanic flows. These findings motivate the development of parameterizations that concisely represent the effects of small-scale bathymetric patterns in theoretical and coarse-resolution numerical circulation models. The previously reported quasi-geostrophic ‘sandpaper’ theory of flow–topography interactiona prioriassumes gentle topographic slopes and weak flows with low Rossby numbers. Since such conditions are often violated in the ocean, we now proceed to formulate a more general model based on shallow-water equations. The new version of the sandpaper model is validated by comparing roughness-resolving and parametric simulations of the flow over a corrugated seamount.more » « less
