CMG Collaborative Research: Multiscale Modeling of the Coupling between Langmuir Turbulence and Submesoscale Variability in the Oceanic Mixed Layer

海洋上层混合过程的适当参数化对海洋气候模式是重要的。这是一个特别困难的问题，因为它既包括倾向于使边界层分层的垂直湍流混合的影响，也包括倾向于使边界层分层的亚中尺度横向混合和滑塌的影响。垂直混合以朗缪尔湍流为主，其中风应力和表面波斯托克斯漂移共同驱动上层海洋湍流边界层。横向混合主要由次中尺度不稳定性控制，Rossby和Richardson数为O（1），由横向密度和速度梯度驱动。这些在海洋前沿尤为突出。总的来说，这些过程跨越的尺度范围（从米到几十公里）与涡动分辨气候模式的尺度范围（从公里到几十兆米）相等。理解和参数化这一制度是一个巨大的挑战，数学理论，建模和observation.Intellectual优点：该项目将汇集在多尺度渐近理论，湍流的大涡模拟（LES）和海洋观测的新方法，以解决海洋上层，三维，亚中尺度混合的难题。理论方法使用渐近分析产生减少方程组。一个新的渐近减少版本的克雷克？描述各向异性朗缪尔湍流的Leibovich方程将用于模拟垂直风浪驱动。本研究的目的是应用类似的技术竞争的横向亚中尺度过程，以获得减少，粗尺度方程，捕获的亚中尺度动力学和他们的双向耦合与朗缪尔湍流。为了检验简化模式的准确性和发展耦合多尺度系统的标度律，将进行一系列的数值试验，这些理论工作的结果将通过与现有的上层海洋垂直动能、垂直热通量和浮力通量的测量结果进行比较来验证。和能量和标量耗散率使用拉格朗日浮体。这些数据将进行比较，朗缪尔湍流的预测，部署在低水平梯度的地区，和预测，包括亚中尺度过程，部署在较高梯度的地区的浮子。耦合过程的参数化将被嵌入到粗分辨率IPCC级OGCM和现有的混合参数化和全球气候数据sets.Broader影响的结果进行比较：新的参数化可能会导致显着提高IPCC级OGCM预测气候变化的能力。此外，它是可能的，由PI开发的多尺度模拟方法可以推广到处理大气边界层，嵌入式滚涡结构与朗缪尔环流没有什么不同。多尺度连续非线性动力系统，如海洋表面混合层在这个建议中解决，是无处不在的工程应用和应用科学，包括，但不限于，地球物理学，海洋学，气象学和天体物理学。深入了解这些系统所表现出的复杂行为的一个有前途的（也可以说是唯一可靠的）途径是通过多学科团队进行的调查。这个项目将形成这样一个团队，跨学科，理论和观察之间，以及三个不同的机构之间的合作。最后，该项目将使博士后学者和一名研究生能够接受物理海洋学、流体动力学、观测数据分析以及应用数学和计算数学等学科的高级培训和指导。这些下一代的研究人员将获得一个极好的机会来学习这种现代和真正跨学科的科学探究方法。

A proper parameterization of upper ocean mixing processes is important for ocean climate models. This is a particularly difficult problem because it includes both the effects of vertical turbulent mixing, tending to destratify the boundary layer, and submesoscale lateral mixing and slumping, tending to stratify the boundary layer. The vertical mixing is dominated by Langmuir turbulence, in which both wind stress and surface wave Stokes drift drive an upper ocean turbulent boundary layer. The lateral mixing is dominated by submesoscale instabilities, with O(1) Rossby and Richardson numbers, driven by lateral density and velocity gradients. These are particularly prominent at ocean fronts. Taken together, these processes span a range of scales (meters to tens of kilometers) equal to that spanned by eddy-resolving climate models (kilometers to tens of megameters). Understanding and parameterizing this regime is a grand challenge to mathematical theory, modeling and observation.Intellectual Merit: This project will bring together new approaches in multiscale asymptotic theory, large eddy simulations (LES) of turbulence, and ocean observations to tackle the difficult problem of upper ocean, three-dimensional, submesoscale mixing. The theoretical approach uses asymptotic analysis to produce reduced equation sets. A new asymptotically reduced version of the Craik?Leibovich equations describing anisotropic Langmuir turbulence will be used to model vertical wind-wave driven. This study aims to apply similar techniques to the competing lateral submesoscale processes to obtain reduced, coarse-scale equations which capture the submesoscale dynamics and their two-way coupling with Langmuir turbulence. A series of numerical experiments using both the reduced equations and the full equations with LES turbulence closures will be conducted to test the accuracy of the reduced models and to develop scaling laws for the coupled multi-scale system.Results emerging from these theoretical efforts will be verified by comparison with existing measurements of upper ocean vertical kinetic energy, vertical heat and buoyancy fluxes, and energy and scalar dissipation rates made using Lagrangian floats. These data will be compared to predictions of Langmuir turbulence, for floats deployed in regions of low horizontal gradients, and to predictions including submesoscale processes, for floats deployed in regions of higher gradients. Parameterizations of the coupled processes will be embedded in coarser resolution IPCC-class OGCMs and the results compared with those of existing mixing parameterizations and global climatological data sets.Broader Impacts: The new parameterizations may result in significant improvements in the ability of IPCC-class OGCMs to predict climate change. Moreover, it is likely that the multiscale modeling methodology developed by the PIs can be generalized to treat the atmospheric boundary layer, with embedded roll vortical structures not dissimilar to Langmuir circulation. Multiscale continuum nonlinear dynamical systems, such as the ocean surface mixed layer addressed in this proposal, are ubiquitous in engineering applications and applied sciences including, but hardly limited to, geophysics, oceanography, meteorology, and astrophysics. A promising (and arguably the sole robust) route for gaining insight into the complex behavior exhibited by these systems is through investigations made by multidisciplinary teams. This project will form such a team, collaborating across disciplines, between theory and observation, and among three different institutions. Finally, the project will enable postdoctoral scholars and a graduate student to receive advanced training and mentoring in the disciplines of physical oceanography, fluid dynamics, observational data analysis and applied and computational mathematics. These next generation researchers will be given an excellent opportunity to learn this modern and truly interdisciplinary approach to scientific inquiry.