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

本项目是对海洋中湍流双扩散的理论和计算研究。在可能导致湍流混合的温盐条件下，海洋中盐度和温度的不同扩散速率/尺度引起了双重扩散过程。该项目使用渐近缩放方法使运动方程更容易处理，便于对双重扩散的详细检查。新的渐近模式的发展为模拟极端海洋环境中的盐指对流提供了独特的能力。渐近理论的基本标度假设也为重新标度海洋运动方程提供了一种新的策略，允许在探索这一区域时有更大的数值稳定性。将发展新的理论来帮助我们更好地理解盐指湍流的饱和状态。本项目是对盐度与热扩散率比较小的海洋区域盐指对流的综合研究。这是通过以下方式实现的：外推到极端参数设置的新的渐近简化模型；扩展了直接数值模拟的稳定性和计算能力的新的Navier-Stokes流体方程；以及剖析湍流盐指的流动形态、能量和多尺度性质的理论分析。目前，湍流双扩散的直接数值模拟受到扩散系数的限制。将采用渐近模型，过滤计算上禁止的快速内波，并保持无惯性平衡。重新制定的Navier-Stokes流体方程保留了内部重力波，但利用了空间和时间导数以及场大小的渐近重新定标，并允许与简化的模型进行比较。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

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.