Onset of large-scale convection in wall-bounded turbulent shear flows

Large-scale coherent rolls are observed frequently in unstably stratified turbulent wall-bounded flows where they influence strongly the transport and mean flow properties. Here we address question of their genesis by means a linear stability analysis model Reynolds stresses is embedded operator. We use channel as testbed for analysis. show that onset large-scale convection associated to instability streamwise-uniform aspect ratio $A \approx 3\unicode{x2013}3.3$ when friction Richardson number exceeds $|Ri_{\tau,c}|=0.86$ . This corresponds critical Rayleigh numbers increase with approximately $Ra_c 0.04\,Re_b^{1.8}$ These results consistent those obtained recent direct numerical simulations performed same setting. It also found if not modelled operator used analysis, then predictions results.