1. Show that in a natural water body with characteristic horizontal dimension L and vertical dimension H, with H − L, the characteristic vertical velocity W should be much less than the characteristic...

1. Show that in a natural water body with characteristic horizontal dimension L and vertical dimension H, with H − L, the characteristic vertical velocity W should be much less than the characteristic horizontal velocity U.

2. Introduce the expression for the vorticity vector into Eq. (3.1.5), to obtain an equation of motion based on the velocity components.