Kinematic simulation for stably stratified and rotating turbulence

Abstract

The properties of one-particle and particle-pair diffusion in rotating and stratified turbulence are studied by applying the Rapid Distortion Theory to a Kinematic Simulation of the Boussinesq equation with a Coriolis term.Scalings for one-and two-particle horizontal and vertical diffusions in purely rotating turbulence are proposed for small Rossby numbers.Particular attention is given to the locality-in-scale hypothesis for two-particle diffusion in purely rotating turbulence both in the horizontal and the vertical directions. It is observed that both rotation and stratification decrease the pair diffusivity and improve the validity of the locality-in-scale hypothesis. In the case of stratification the range of scales over which the locality-in-scale hypothesis is observed is increased.It is found that rotation decreases the diffusion in the horizontal direction as well as, though to a much lesser extent, in the vertical direction.

Effective diffusivity of passive scalars in rotating turbulence

“…Within error bars, and for small enough Rossby number and large enough Schmidt number, our results are consistent with theoretical results based on single-particle dispersion that predict that vertical diffusion is twice larger than horizontal diffusion in the presence of pure rotation [19,22]. For small Schmidt and Pèclet numbers, the turbulent diffusion decreases as molecular diffusion becomes more important, while for large enough Pèclet numbers the effective diffusion becomes independent of the Pèclet number, resulting in a turbulent Schmidt number of order one.…”

“…This indicates horizontal diffusion decreases in the presence of rotation, in comparison with the isotropic and homogeneous cases. This is in good agreement with predicted reductions of the horizontal passive scalar transport in the presence of rotation [22,23], and also with previous measurements of turbulent transport coefficients in numerical simulations using a different method (the test field model, see [8]). …”

“…This is in good agreement with theoretical arguments in [22] for single-particle dispersion, where it was found that vertical diffusion is twice larger than horizontal diffusion in the presence of pure rotation. Within error bars, our results are consistent with this finding.…”

“…This could be associated with the fact that in the presence of rotation the turbulent diffusivity is already reduced, and that therefore larger molecular diffusivities are needed to decrease it further. Also, note that in the runs with large enough P e and small enough R o , the vertical turbulent diffusion reaches a value that is approximately twice the horizontal, in good agreement with predictions in [19,22].…”

“…These studies are related with the transport of passive scalars, as the average concentration of a passive scalar is related to single-particle dispersion in a fluid. Theoretical and numerical studies [18,19] (see also [20][21][22], and simulations in [23]) indicate one-particle dispersion is suppressed along the direction of stratification in stably stratified turbulence with and without rotation. Moreover, results in [19] and [22] show that the anisotropy introduced by stratification also reduces horizontal diffusion, although to a much lesser extent than vertical diffusion.…”