Correlation between fluid deformation and density distortions in stably stratified shear layers

Understanding the interplay between buoyancy and fluid motions within stably stratified shear layers is crucial for unravelling the contribution of flow structures to turbulent mixing. In this study, we examine statistically the local relationship between stratification and fluid deformation rate in wave and turbulent regimes, using experimental datasets obtained from a stratified inclined duct (SID) containing fluids of different densities that form an exchange flow. We introduce rotational and shear components of varying strength within the vorticity and a family of coherent gradient Richardson numbers ( $Ri_C$ ), ratios related to the buoyancy frequency and the strength of either the rotational or shearing motion. Conditional statistical analysis reveals that both shear and stratification intensity affect the probability distribution of the $Ri_C$ , with extreme events occurring more frequently in areas of weak stratification. In the wave regime, we identify the persistence of fast-spin vortices within the strongly stratified density interface. However, scouring of the density interface is primarily driven by shearing motions, with baroclinic torque making a notable contribution to enstrophy transport. In the turbulent regime, rigid-body rotations occur at significantly shorter time scales than that associated with the local buoyancy frequency, making them more disruptive to stratification than shear. Additionally, correlation analysis reveals that irrotational strain distorts stable stratification similarly to shearing motions, but is weaker than both shearing and rotational motions and less likely to have a time scale longer than that related to the buoyancy frequency. Moreover, we observed that the interplay between rotational and shearing motions intensifies as stratification increases. Finally, a comparison of length scales along the shear layers highlights the $Ri_C$ as a valuable measure of the relative sizes of different motions compared with the Ozmidov scale and shows that stratification can influence sub-Ozmidov scales through baroclinic torque. This study highlights the critical impact of the type, strength and location of fluid deformations on localised mixing, providing new insights into the role of rotational motions in shear-driven stratified flows.