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.
