Collaborative Research: Explorations of Salt Finger Convection in the Extreme Oceanic Parameter Regime: An Asymptotic Modeling Approach.

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This project is a theoretical and computational study of turbulent double diffusion in the ocean. Double diffusion processes arise from the different rates/scales of salinity and temperature diffusion in the ocean under thermohaline conditions that can lead to turbulent mixing. The project employs asymptotic scaling approaches to render the equations of motion more tractable, facilitating detailed examinations of double diffusion. The development of new asymptotic models provides a unique capability to perform simulations of the salt-finger convection in the extreme oceanic regime. The underlying scaling assumptions of the asymptotic theory also provide a new strategy for rescaling the oceanic equations of motion that allows for greater numerical stability in probing this regime. New theories will be developed to help improve our understanding of the saturated states of salt-finger turbulence. This project is a comprehensive study of salt-finger convection valid in the oceanic regime of small salinity to thermal diffusivity ratio. This is accomplished by utilizing: novel asymptotically reduced models that extrapolate to extreme parameter settings; a new reformulation of the Navier-Stokes fluid equations that extends the stability and computational capabilities of direct numerical simulations; and theoretical analysis that dissects the flow morphology, energetics and multiscale nature of turbulent salt fingers. At present, direct numerical simulations of turbulent double diffusion are limited by the diffusivity ratio. Asymptotic models which filter computationally prohibitive fast internal waves and maintain an inertia-free balance will be employed. The reformulated Navier-Stokes fluid equations retain internal gravity waves but utilize the asymptotic rescalings of the spatial and temporal derivatives and field magnitudes and allow for comparison with reduced models.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.