The Effect of Curvature on Turbulence in Stratified Fluids

The influence of streamline curvature on small-scale turbulence and vertical mixing in stratified fluids is the subject of this study. The roles of curvature and stratification in enhancing and suppressing turbulent mixing are explored using second-moment closure for turbulence. Governing equations for second moments are expressed in generalized orthogonal curvilinear coordinates, from which, through a series of approximations, simplified expressions are derived for second moments in the limit of small streamline curvature. The governing equations are then used to obtain a quasi-equilibrium turbulence model suited for application to atmospheric and oceanic mixed layers. A typical model application is illustrated by simulation of stratified flows over two-dimensional, idealized mountains and valleys. The limit of local equilibrium is further invoked to derive semi-analytical results for the enhancement and suppression of vertical'turbulent mixing under the combined influence of stratification and curvature. It is shown that stabilizing curvature can drastically suppress turbulence even when the stratification is strongly destabilizing. Conversely, under strong stable stratification that would otherwise lead to total suppression of turbulence, destabilizing curvature can keep turbulence alive. Streamline curvature is also shown to significantly modify the Monin-Obukhov similarity laws for momentum and heat fluxes in the constant flux region of the atmospheric boundary layer. Finally, the need for observational data on curvature effects on mixing in stratified flows either in the laboratory or in flows over topography in the oceans and the atmosphere is highlighted.