Wave Turbulence and Mixing

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This collaborative effort addresses two closure problems arisingin fluid systems: the description of turbulent energy transferthrough a large number of wave modes, and the determination of theamount of mixing at internal breaking waves in a stratifiedenvironment. The methodology proposed includes the asymptoticreduction of complex partial differential equations to simplersystems, the numerical simulation of dynamic equations, thecritical analysis of physical principles, and the comparison oftheory and computations with physical laboratory experiments. Weanticipate that the work will yield both physical insights andinteresting new mathematics.Turbulent energy transfer, dissipation and mixing are keyprocesses in fluid dynamical problems ranging from the windgeneration of water waves to climate dynamics. In the ocean, forexample, wind driven ocean waves leads to ocean mixing, ultimatelydetermining the sea--surface temperature, which, in turn, affectsatmospheric winds, temperature and humidity. Turbulent wave actionis responsible for the transfer of energy between the very largescales of storms and the small scales of wind ripples at whichdissipation takes place. In an atmospheric example, mixing byupward propagating breaking waves plays a significant role in thedynamical coupling between the lower and the upper layers of theatmosphere. The research proposed here will contribute to theunderstanding of fundamental physical mechanisms behind theseimportant phenomena, and hence improve our capability to predictand quantify climate changes. The proposal will also have a strongeducational impact, through the training of graduate students, thedevelopment of a research seminar for undergraduate students, theteaching of challenging undergraduate classes, and by havingundergraduate students participate in summer projects focused onthe research.