Nonlinear, multiscale systems such as turbulence are widely regarded as one of the most challenging problems in the physical sciences; the circulation of the ocean and atmosphere are examples of such systems which have tremendous societal importance. One of the most crucial functions of a climate model is to accurately represent the temporal and spatial distribution of scalar fields such as salt, heat, phytoplankton, nutrients and carbon within the ocean. However, the circulation of the ocean is dominated by waves and turbulence that operate on many scales which interact with each other due to the nonlinear nature of the fluid. These systems have a large number of degrees of freedom which can not be adequately represented in computational models. Thus, the effect of "small" scales of motion, (10's of kilometers and less) are typically parameterized so that models have many fewer degrees of freedom than the real system In this study, mathematicians with backgrounds in geophysical fluid dynamics, plan a fresh approach to how turbulence is represented in ocean general circulation models. They propose two approaches: multi-scale techniques and Lagrangian stochastic models. The first approach generalizes the current practice of using a constant eddy diffusivity and it will be developed through the mathematical theory of multiscale homogenization or random partial differential equations. The second approach provides a means of representing the anomalous diffusion that arises when coherent structures such as vortices and jets dominate the flow. A graduate student and postdoc will work on these interdisciplinary topics.
