internal waves
Internal tides
The problem of internal-tide generation can be formulated as a coupled-mode system of the form [See paper]
\[\begin{aligned} \phi_{m,xx}+\frac{m^2\pi^2}{\mu^2h^2}\phi_m+\sum\limits_{n=1}^{\infty}\left[\frac{b_{mn}h_x}{h}\phi_{n,x} + \left(\frac{c_{mn}h_x^2}{h^2}+\frac{d_{mn}h_{xx}}{h}\right)\phi_n\right]= 2 g_m h\left(\frac{1}{h}\right)_{xx} \end{aligned}\]The horizontal barocilinic velocity of an internal tide corresponding to the \(M_2\) tidal constituent with constant stratification \(N=0.0015\) (1/s), Coriolis frequency \(f = 0.0001\) (1/s). The amplitude of the horizontal barotropic current at infinity is \(U_0 = 0.04\) (m/s). The depth at infinity is \(3000\) m and the Gaussian ridge has a criticality \(0.8\) and relative height \(0.5\).