It is shown that the general nonlinear potential vorticity equation for viscous and conductive fluid in a rotating system can be expressed in terms of the geostrophic stream function for the horizontal velocity alone, provided that the motions are hydrostatic and quasi-geostrophic and the Richardson number is much larger than unity. The form of this equation is identical with that obtained from an asymptotic expansion for a small Rossby number.
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Kuo, H.L. On a generalized potential vorticity equation for quasi-geostrophic flow. PAGEOPH 96, 171–175 (1972). https://doi.org/10.1007/BF00875640
- Asymptotic Expansion
- Stream Function
- Horizontal Velocity
- Potential Vorticity