Models are developed for the turbulent mixing and growth at a batch interface. These models depend crucially on the choice of diffusion coefficient $D$. The model where $D$ is the harmonic average of the mixing coefficients of the two pure fluids is analysed in detail, since this is likely to be a good approximation when the density difference between the two fluids is small. When the density difference is large, the laminar flow regime fingering will occur and there will be a relatively sharp interface between the fluids. However, in the turbulent case, as gravity drives the denser fluid into the less dense one the invading fluid is immediately mixed by turbulent diffusion. This means that sharp interfaces do not exist. Instead there will be a finite mixing region where the volume fraction of each fluid changes from $0$ to $1$. In this case $D$ will depend upon the relative concentration of the fluids. This approach leads to a degenerate diffusion problem
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