Depth independence of hydrostatic shallow-water flow
= Depth independence of hydrostatic shallow-water flow
In a homogeneous layer under the <hydrostatic approximation>, the horizontal <pressure gradient> is independent of depth. The depth derivatives of velocity obey $(u_z)_t-fv_z=0$, $(v_z)_t+fu_z=0$. If the motion starts without shear, these derivatives remain zero. Hydrostatic pressure alone does not eliminate a pre-existing freely oscillating shear.