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In this paper, we propose a new numerical method for improving the mass conservation properties of the level set method when the interface is passively advected in a flow field. Our method uses Lagrangian marker particles to rebuild the level set in regions which are under-resolved. This is often the case for flows undergoing stretching and tearing. The overall method maintains a smooth geometrical description of the interface and the implementation simplicity characteristic of the level set method. Our method compares favorably with volume of fluid methods in the conservation of mass and purely Lagrangian schemes for interface resolution. The method is presented in three spatial dimensions.

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Laboratory experiments on stably stratified grid turbulence have suggested that turbulent diffusivity $\kappa_\rho$ can be expressed in terms of a turbulence activity parameter $\epsilon/\nu N^2$, with different power-law relations appropriate for different levels of $\epsilon/\nu N^2$. To further examine the applicability of these findings to both a wider range of the turbulence intensity parameter $\epsilon/\nu N^2$ and different forcing mechanisms, DNS data of homogeneous sheared stratified turbulence generated by Shih et al. (2000) and Venayagamoorthy et al. (2003) are analysed in this study. Both scalar eddy diffusivity $\kappa_\rho$ and eddy viscosity $\kappa_\nu$ are found to be well-correlated with $\epsilon/\nu N^2$, and three distinct regimes of behaviour depending on the value of $\epsilon/\nu N^2$ are apparent. In the diffusive regime $D$, corresponding to low values of $\epsilon/\nu N^2$ and decaying turbulence, the total diffusivity reverts to the molecular value; in the intermediate regime $I$, corresponding to $7 \,{<} \epsilon/\nu N^2 \,{<}\, 100$ and stationary turbulence, diffusivity exhibits a linear relationship with $\epsilon/\nu N^2$, as predicted by Osborn (1980); finally, in the energetic regime $E$, corresponding to higher values of $\epsilon/\nu N^2$ and growing turbulence, the diffusivity scales with $(\epsilon/\nu N^2)^{1/2}$. The dependence of the flux Richardson number $R_f$ on $\thing$ explains the shift in power law between regimes $I$ and $E$. Estimates for the overturning length scale and velocity scales are found for the various $\epsilon/\nu N^2$ regimes. It is noted that $\epsilon/\nu N^2 \,{\sim}\, \hbox{\it Re}/\hbox{\it Ri}\,{\sim}\,\hbox{\it ReFr}^2$, suggesting that such Reynolds–Richardson number or Reynolds–Froude number aggregates are more descriptive of stratified turbulent flow conditions than the conventional reliance on Richardson number alone.