Stability criterion for stably-stratified turbulent shear flows: Results of conditional averaging

Oceanic overflows, wind-driven thermocline layers and river estuaries are geophysical examples of stably-stratified shear flows. Our experimental realization of such flows consists of a turbulent wall-bounded shear flow with lighter fluid injected at initial downstream velocity between 4 and 8 cm/s over a quiescent heavier fluid. We measure planar velocity and density fields usingPIV and PLIF, respectively. We consider 4 cases with initial bulk Richardson Number $0.25 < Ri_b < 1$ and determine the fraction of unperturbed interface defined using a Thorpe length analysis. We explore different definitions of gradient Richardson Number $Ri_g$ evaluated and conditionally averaged over unperturbed interface. A conventional choice in linear stability theory is $Ri_{g_0}$ where the gradients are evaluated at the interface position. Another that we denote $Ri_{g_m}$ (consistent with Miles-Howard (MH) criterion) corresponds to the minimum value of $Ri_g$ as a function of vertical position. The second definition allows excellent comparison with linear stability theory and the MH criterion. For small Ri, there is robust Kelvin-Helmholtz instability (KHI) whereas for larger $Ri_g$ interfacial overturning is intermittent with infrequent KHI events and more frequent Holmboe instability.