Discussion on “phenomenological modeling: Present and future”

This afternoon all of the models that we have heard fall in the same class; namely, local closures. First-order local closure (K-theory or eddy diffusivity) models the momentum fluxes as down-gradient of the mean momentum. The second-order local closure models the third moments as down-gradient of the local second moments, or local mean variables. There is another completely different class of modeling or class of closure, and that is non-local turbulence closure. I mentioned before about the transilient matrix that describes the mixing between different points separated a finite distance in space. One can parameterize this matrix in terms of mean flow state or mean flow instability. When you do that, you can then make forecasts of the mean field in a turbulent flow that takes into account this nonlocal mixing. That has been done. For the ocean, we found results as good as third-order local closure. For the atmosphere, results were as good as second-order local closure. We've used it in three-dimensional weather forecast models covering the whole United States. This is a new concept of non-local closure, which is different from all the other local closures. When would you want to consider using a non-local kind of closure? Well, if any of you are dealing with turbulent flow that has a spectrum of eddy sizes where your greatest energy is in the largest wavelengths, or if you are dealing with turbulent flow that has large structures in it that are causing non-local mixing, then you might want to consider a non-local turbulence closure