The influence of a geostrophic current on the internal tide generation

We investigate the influence of a barotropic geostrophic current on
internal tide (IT) generation over a shelf slope.
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.
We calculate the total barotropic-to-baroclinic energy conversion $C =
\int \overbar{C} \,dx = \int \int \rho' g W \,dx\, dz$. 
$\overbar{C}(x,t)$ can be either positive or negative. Positive (negative) conversion means energy is
converted from barotropic to baroclinic (baroclinic to barotropic)
waves. 
The main conclusions are: 1) $V_g(x)$ changes the effective
frequency $f_{eff}$. This has a direct impact on the slope of the IT
characteristics and the slope criticality, which affects the total
conversion rate;
2) Since $(V_g)_x$ is not a constant value, $f_{eff}$ varies along the
slope. This has a significant effect on the IT beam generation
location and its propagation path. If the current is strong enough so
that $f_{eff}$ is greater than the barotropic tidal frequency $\sigma_T$, a blocking
region is formed where the conversion vanishes and IT propagation is blocked;
3) Changes of sign in $\bar{C}(x,t)$ correspond to the locations where
IT beams reflect from the boundaries. As a result, the total conversion rate $C$ is
also strongly affected by the IT beam pattern.
In conclusion, the total conversion rate $C$ is affected by a
combination of three factors: slope criticality, size and location of the blocking
region and the IT beam patterm, all of which can be varied by changing
the strength, width and location of the geostrophic current $V_g(x)$.