Self-organized criticality of turbulence in strongly stratified mixing layers

We investigate the evolution of stratified shear flows for which the stratification is sufficiently 'strong' that the flow is primarily susceptible to Holmboe wave instability (HWI) and turbulent collapse at high Reynolds number. Our DNS-based findings demonstrate the emergence of self-organised criticality (SOC) that is manifest as an adjustment of the horizontally-averaged mean flow of the turbulence towards a critical state with a gradient Richardson number of Ri_g ~ 1/4. This self-organization occurs through a continuously reinforced localisation of turbulent 'avalanches' that are found to exhibit the expected scale invariant characteristics. From an energetics perspective, the emergence of SOC is expressed in the form of a long-lived turbulent flow that remains in a `quasi-equilibrium' state for an extended period of time, corroborating the original physical arguments of Turner (1973) associated with self-regulation of stratified turbulent flows as involving a 'kind of equilibrium'. Most importantly, the irreversible mixing that results from such self-organised behavior appears to be characterized generically by a universal cumulative turbulent flux coefficient of Γ_c ~ 0.2 only for turbulent flows engendered by HWI.