Abstract
This paper presents an exact solution for nonlinear shallow-water waves on an f plane. It is a long wave satisfying the hydrostatic balance. It is also a solitary wave maintained by the balance of a dispersion effect of Coriolis force and the nonlinear effect of advection and finite wave amplitude. It satisfies the conservation of potential vorticity. It has a negative wave height, a negative (positive) relative vorticity in the Northern (Southern) Hemisphere, and a propagation speed smaller than that of the shallow-water wave. It propagates upstream, as a consequence of the conservation of potential vorticity, with a speed of
Corresponding author address: C. Li, Skidaway Institute of Oceanography, 10 Ocean Science Circle, Savannah, GA 31411. Email: chunyan@skio.peachnet.edu