On baroclinic instability over continental shelves: Testing the utility of Eady-type models

Shih-Nan Chen, Institute of Oceanography, National Taiwan University, Taipei, Taiwan, Chiou-Jiu Chen, Institute of Oceanography, National Taiwan University, Taiwan and James A Lerczak, Oregon State University, College of Earth, Ocean, and Atmospheric Sciences, Corvallis, OR, United States
This study examines the utility of Eady-type theories as applied to understanding the baroclinic instability in buoyant coastal flows. The focus is on the effects of ageostrophy, boundary dissipation, and bottom slope. The approach compares theoretically derived instability properties against numerical model calculations, for experiments designed to isolate individual effects and justified to have Eady-like basic states. For non-geostrophic effect, Stone’s (1966) theory is shown to give good 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: Wave phase locking and westward phase tilt allow waves to be mutually amplified. The analyses demonstrate that both 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 Eady-Ekman and Blumsack and Gierasch’s (1972; BG72) theories. 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. The 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. BG72 ignores slope-induced horizontal shear in mean flow that tilts the eddies to favor converting energy back to the mean, thus having limited utility over steep slopes.