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. Ocean mixing ultimatelydetermines the sea--surface temperature, which, in turn, affectsatmospheric winds, temperature and humidity. Mixing by upward propagatingbreaking waves is known to play a significant role in the exchange ofmomentum between the lower and the upper layers of the atmosphere. In theocean, turbulent wave action is responsible for the transfer of energy fromthe very large scales of storms to the small scales at whichdissipation takes place. It is expected that the research proposedhere will contribute to the understanding of fundamental physicalmechanisms behind these important phenomena, and hence improveour capability to predict and quantify climate changes.This proposal will also have a strong educational impact, throughthe training of graduate students, the development of a research seminarfor undergraduate students, the teaching of challenging undergraduate classes,and by having undergraduate students participate in summer projects focused onthe research.