Wave Turbulence and Mixing

This collaborative effort addresses two closure problems arising

in fluid systems: the description of turbulent energy transfer

through a large number of wave modes, and the determination of the

amount of mixing at internal breaking waves in a stratified

environment. The methodology proposed includes the asymptotic

reduction of complex partial differential equations to simpler

systems, the numerical simulation of dynamic equations, the

critical analysis of physical principles, and the comparison of

theory and computations with physical laboratory experiments. We

anticipate that the work will yield both physical insights and

interesting new mathematics.

Turbulent energy transfer, dissipation and mixing are key

processes in fluid dynamical problems ranging from the wind

generation of water waves to climate dynamics. In the ocean, for

example, wind driven ocean waves leads to ocean mixing, ultimately

determining the sea--surface temperature, which, in turn, affects

atmospheric winds, temperature and humidity. Turbulent wave action

is responsible for the transfer of energy between the very large

scales of storms and the small scales of wind ripples at which

dissipation takes place. In an atmospheric example, mixing by

upward propagating breaking waves plays a significant role in the

dynamical coupling between the lower and the upper layers of the

atmosphere. The research proposed here will contribute to the

understanding of fundamental physical mechanisms behind these

important phenomena, and hence improve our capability to predict

and quantify climate changes. The proposal will also have a strong

educational impact, through the training of graduate students, the

development of a research seminar for undergraduate students, the

teaching of challenging undergraduate classes, and by having

undergraduate students participate in summer projects focused on

the research.