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Abstract This study examines the utility of Eady-type theories as applied to understanding baroclinic instability in coastal flows where depth variations and bottom drag are important. The focus is on the effects of nongeostrophy, boundary dissipation, and bottom slope. The approach compares theoretically derived instability properties against numerical model calculations, for experiments designed to isolate the individual effects and justified to have Eady-like basic states. For the nongeostrophic effect, the theory of Stone (1966) is shown to give reasonable predictions for the most unstable growth rate and wavelength. It is also shown that the growing instability in a fully nonlinear model can be interpreted as boundary-trapped Rossby wave interactions—that is, wave phase locking and westward phase tilt allow waves to be mutually amplified. The analyses demonstrate that both the boundary dissipative and bottom slope effects can be represented by vertical velocities at the lower boundary of the unstable interior, via inducing Ekman pumping and slope-parallel flow, respectively, as proposed by the theories of Williams and Robinson (1974; referred to as the Eady–Ekman problem) and Blumsack and Gierasch (1972). The vertical velocities, characterized by a friction parameter and a slope ratio, modify the bottom wave and thus the scale selection. However, the theories have inherent quantitative limitations. Eady–Ekman neglects boundary layer responses that limit the increase of bottom stress, thereby overestimating the Ekman pumping and growth rate reduction at large drag. Blumsack and Gierasch’s (1972) model ignores slope-induced horizontal shear in the mean flow that tilts the eddies to favor converting energy back to the mean, thus having limited utility over steep slopes.
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Rough Topography and Fast Baroclinic Rossby Waves
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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- Award ID(s):
- 2241625
- PAR ID:
- 10576558
- Publisher / Repository:
- DOI PREFIX: 10.1029
- Date Published:
- Journal Name:
- Geophysical Research Letters
- Volume:
- 52
- Issue:
- 2
- ISSN:
- 0094-8276
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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