Instability of coastal currents

We have been studying the stability of shallow, density-driven boundary currents. Basic flow shown below has a depth of 20 m, maximal along-shore velocity = 0.3 m/s, M² ~ 1.5e-6 (1/s²), N² ~ 0.0015 (1/s²). Its geometry is similar to that of river-fed coastal currents like Adriatic Coastal Current, China Coastal Current, Soya warm current, etc.

It can be seen that the flow becomes baroclinically unstable, with alternating onshore/offshore flows, in a few days. Our goal is to understand the factors that influence the growth rate, length and velocity scales.