Colloquium

This talk will be aimed at a general audience including graduate students in mathematics (and related areas that deal with fluids in motion). It is based on joint work with Nan Jiang, http://www.pitt.edu/~naj24/.

The problem of predicting fluids in motion is beset with difficulties. Inevitable small errors in data, geometry, parameterization and discretization grow exponentially in time with rate constant growing as the Reynolds number increases. (As an example, a 1 cm sphere creeping at 1cm/sec through water already has Re=100 and exp(+100t) rapidly becomes significant.) A standard method of increasing reliability of predictions, expanding the window of predictability and evaluating resulting uncertainty is through ensemble calculations. Unfortunately, computing flow ensembles immediately leads to the competition between high resolution single simulations and multiple ensemble runs. This is a boundary between what can be done and what cannot be done. It is also an area replete with high impact mathematics problems. This talk will describe the problem for fluids, present some methods of addressing it including some (simple but apparently new) ideas. For the fluids specialists, new ensemble turbulence models will be presented, leading to a new mixing length. A few simple (but not common in the mathematics literature) examples of how ensemble simulations can be used to interrogate flows will be shown.