Random Waves and Vortices: Flow Decomposition and Energy Fluxes

New York University, New York NY

Investigators

Abstract

This project is a theoretical fluid dynamics study aimed at improving our understanding of turbulent atmosphere ocean processes at small scales, which are unresolvable in today's global-scale computer models. Key components of the project are the improved understanding of turbulent energy transfers from large to small scales in the fluid, and the effect of turbulent advection on passive floating devices in the ocean, which is aimed at extracting maximal information from costly oceanographic measurements. Overall, the proposed work has broad impacts within fluid mechanics, physical oceanography, and dynamical meteorology, and its training aspects include both graduate and undergraduate students. The fluid dynamics of these complex systems is characterized by a nonlinear jigsaw puzzle of intermingling turbulent waves and vortices, especially at small scales, such as those relevant to submesoscale oceanography, for instance. Here classical wave-mean interaction theory fails, direct numerical simulation of the fluid motion with global computational models is not possible, and theoretical innovations for diagnostic and predictive models are needed. In this connection the project seeks to break new ground with a multi-pronged approach that combines theory and numerical modelling in three problem areas. First, a fundamental study of third-order structure functions in rotating stratified turbulence is proposed, with the aim of better diagnosing spectral, scale-to-scale energy fluxes from sparse observational data. Second, a recent diagnostic wave- vortex decomposition method is to be extended to the increasingly important case of data acquisition following a set of random Lagrangian tracers. Third, a predictive model for interactions between waves and vortices is to be improved by generalizing a certain asymptotic conservation law for slowly varying waves to more general wave fields. The proposed research calls for non-trivial mathematical investigations that involves various systems of multi-dimensional PDEs, asymptotic analysis, stochastic modelling, and numerical computation, all with an eye towards ultimate applications in the real world that are relevant to atmosphere and ocean dynamics. This is a non-trivial technology transfer between different branches of applied mathematics as well as of several physical sciences. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.