Constant vorticity atmospheric Ekman flows in the \( f\)-plane approximation. (English) Zbl 1498.35411
Summary: We study the geophysical fluid dynamical problem of the wind in the steady atmospheric Ekman layer with constant eddy viscosity. Three dimensional Ekman flows with constant vorticity is considered in the \( f\)-plane approximation. For non-equatorial \( f\)-plane approximation, we show that any bounded solution of the Ekman flow with a flat surface and constant vorticity vector is the stationary flow with vanishing velocity field, while for the equatorial \( f\)-plane approximation, we obtain that the pressure presents no variation in the northward direction and the meridional component is constant throughout the fluid domain.
MSC:
| 35Q31 | Euler equations |
| 35Q86 | PDEs in connection with geophysics |
| 86A10 | Meteorology and atmospheric physics |
| 76U60 | Geophysical flows |
| 35J60 | Nonlinear elliptic equations |
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