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

该项目是对海洋中湍流双扩散的理论和计算研究。双扩散过程是由于在温盐条件下海洋中盐度和温度扩散的速率/尺度不同而产生的，这种扩散可能导致湍流混合。该项目采用渐近缩放的方法，使运动方程更容易处理，便于详细检查双扩散。新的渐近模型的发展提供了一个独特的能力，在极端的海洋制度进行模拟的盐指对流。渐近理论的基本尺度假设也提供了一个新的策略，重新调整海洋运动方程，允许更大的数值稳定性，在探测这一制度。新的理论将有助于提高我们的盐指湍流的饱和状态的理解。该项目是一个综合性的研究盐指对流有效的海洋制度的小盐度热扩散率比。这是通过利用：新的渐近减少模型，外推到极端的参数设置;一个新的重新制定的Navier-Stokes流体方程，扩展了直接数值模拟的稳定性和计算能力;和理论分析，解剖的流动形态，能量和多尺度性质的湍流盐手指。目前，湍流双扩散的直接数值模拟受到扩散率比的限制。渐近模型过滤计算禁止快速内波和保持惯性自由的平衡将被采用。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幅度的渐近重新缩放，并允许与简化模型进行比较。该奖项反映了NSF的法定使命，并被认为值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估来支持。

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.