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Vertical Motions Driven by Geostrophic Stress in Surface Boundary Layer Under a Finite Ekman Number Regime


Geostrophic stress caused by strong horizontal density gradient embedded in the surface boundary layer plays an important role in generating vertical motion and associated tracer transport. However, dependence of this frictionally driven vertical velocity on the Ekman number (Ek), a key dimensionless parameter for frictional flows in a rotating reference frame, has not been systematically analyzed, especially for a finite Ek. In this study, we theoretically demonstrate that the geostrophic stress always induces an ageostrophic stress acting to offset itself, and such an offsetting effect becomes more evident with increasing Ek. When Ek approaches unity or larger, vertical motion driven by geostrophic stress is much weaker than that derived by Garrett and Loder (GL81) who neglect effects of ageostrophic stress and predict a vertical velocity magnitude scaled with curl of geostrophic stress. Although the cancellation tendency between geostrophic and ageostrophic stress is universal, its underlying dynamics depends on vertical structures of turbulent viscosity and geostrophic flows.
A realistic simulation in the winter Kuroshio extension is conducted to validate the theoretical results and examine which regime, a small vs. finite Ek, is more relevant in this region. It is found that the characteristic vertical scale involved in the definition of Ek is primarily determined by the vertical structure of turbulent viscosity and evidently smaller than that of geostrophic flow. The value of Ek in the winter Kuroshio extension is generally larger than unity. Correspondingly, the GL81 model results in severe overestimation of the geostrophic stress-driven vertical velocity and tracer transport.