Rectangular standing surface-gravity mode
= Rectangular standing surface-gravity mode
In a rectangular box with Neumann side walls, a horizontal mode
$$
\cos\frac{m\pi x}{L_x}\cos\frac{n\pi y}{L_y}
$$
has horizontal wavenumber $k=[(m\pi/L_x)^2+(n\pi/L_y)^2]^{1/2}$, depth dependence $e^{kz}$ in infinitely deep fluid, and natural frequency $\Omega=\sqrt{gk}$.