Effect of rotation on vertical mixing and associated turbulence in stratified fluids

Combined effects of stratification and rotation on vertical mixing and the characteristics of associated small‐scale turbulence are explored using second‐moment closure methodology; the rotational terms in the equations for Reynolds stresses and turbulent heat fluxes are retained, not ignored as in earlier works. Semianalytical results valid for arbitrary values of rotation and stratification are derived by further invoking the local equilibrium limit of closure. Two cases are considered: nonzero vertical rotation and nonzero meridional rotation; the latter case is of more general interest in geophysics because of its potential application to equatorial mixed layers. In both cases the influence of rotation on mixing coefficients and Monin‐Obukhov constant flux layer similarity relations is investigated for arbitrary values of rotation and stratification. In both cases, turbulent mixing coefficients assume tensorial properties. However, meridional rotation appears to have a stronger influence on vertical mixing and turbulence characteristics than does vertical rotation. These results, along with perturbation expansions for weak rotation, suggest that for geophysical flows, in most cases, the direct effect of rotation on vertical turbulent mixing itself is but a small correction, a few tens of percent at best. It is seldom large, although it might not be negligible in some particular cases. Nevertheless, the study of rotational effects on small‐scale turbulence provides a fascinating insight into the direct impact of rotation on the characteristics of small‐scale turbulence and mixing in stratified fluids; the results are also of interest in other fields such as engineering.