Reflection of internal gravity waves at a bottom topography with near-critical slope

Direct numerical simulation is performed to study plane internal wave reflection at a sloping bottom at different values of Froude number, $Fr$. The slope angle is also varied in a range of near-critical values. At low $Fr$, the numerical results agree well with linear inviscid theory of near-critical internal wave reflection. With increasing Froude number, the reflection process becomes increasingly nonlinear with the formation of higher harmonics and subsequently fine scale turbulence. At a critical value of $Fr$, turbulence is initiated via convective instability. Also, turbulent intensities are more pronounced for somewhat off-critical reflection compared to exactly critical reflection. As the Froude number increases, the near wall shear plays a dominant role in critical reflection by enhancing turbulence compared to off-critical reflection. For a fixed slope angle, as the Froude number increases the fraction of the input energy converted into the turbulent kinetic energy increases and saturates at higher Froude numbers.