Tide-topography interactions: the influence of an along-shelf current on the internal wave spectrum

We investigate the influence of a barotropic geostrophic current on
the internal wave (IW) generation over a shelf slope.
It is well known that most of the energy in the tide-topography
generated waves lies in waves with tidal frequency $\sigma_T$. 
Here we restrict our attention on the frequencies other than the dominant frequency $\sigma_T$. 
The current $V_g(x)$ is modeled as an idealized Gaussian function centered at
$x_0$ with width $x_r$ and maximum velocity $V_{max}$.
The bathymetry is modelled as a linear slope with smoothed corners.
Since the center of the current lies on the slope, there will always
be a region on the slope where the effective frequency $f_{eff}$ is
greater than the Coriolis parameter $f$ and another region where
$f_{eff} < f$. Parametric subharmonic instability (PSI) occurs where
waves with approximately half of the primary wave frequency, in this
case $\sigma_T/2$, are generated. In the presence of a large current,
PSI can occur where $f_{eff} < \sigma_T/2 < f$. This could not
happen without a current, i.e. $f_{eff} = f > \sigma_T/2$. Other interesting
interactions, including interharmonics and strong tidal harmonics, are also observed.