Linearized shallow water equations
= Linearized shallow water equations
For a homogeneous layer of mean depth $H_0$ on an f-plane, linearization about rest gives
$$
u_t-fv=-g\eta_x,\qquad
v_t+fu=-g\eta_y,\qquad
\eta_t+H_0(u_x+v_y)=0.
$$
= Linearized shallow water equations
For a homogeneous layer of mean depth $H_0$ on an f-plane, linearization about rest gives
$$
u_t-fv=-g\eta_x,\qquad
v_t+fu=-g\eta_y,\qquad
\eta_t+H_0(u_x+v_y)=0.
$$