Experimental and theoretical study of a stratified boundary layer above a tilted undulated plate

Stratification plays a key role in the dynamics of geophysical flows. Stratified fluids support waves, called internal gravity waves (IGW), which can lead by their interactions to instabilities, turbulence, and ultimately mixing. Understanding these processes is a main concern for geophysicists who try to describe how energy is distributed and transported in these flows.

Critical layers are well-known regions of interaction between a shear flow and IGW, preventing them from propagating further. However, Passaggia et al. 2014 numerically and analytically pointed out the existence of a new kind of critical layer, occurring in a stratified boundary layer above an inclined undulated wall. This critical layer consists in the divergence of transverse velocity and density at a critical level, due to the stretching of the IGW by the shear.

In our study, we have observed for the first time this critical layer experimentally thanks to Particle Image Velocimetry measurements. Moreover, further theoretical analysis has been performed to upgrade the one presented in Passaggia et al. 2014, by expressing the basic stratified boundary layer flow developing above a flat inclined plate and imposing the no-slip boundary condition thanks to the introduction of a viscous sub-layer.