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

对于海洋气候模式来说，上层海洋混合过程的适当参数化是很重要的。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坍塌的影响。垂直混合以朗缪尔湍流为主，风应力和面波Stokes漂移共同驱动上层海洋湍流边界层。横向混合以亚中尺度不稳定为主，Rossby数和Richardson数分别为O(1)和O(1)，横向密度和速度梯度驱动。这些现象在海洋前缘尤为突出。总而言之，这些过程跨越的尺度范围(米到几十公里)与涡旋分辨率气候模型(公里到几十兆米)的跨度相当。理解和参数化这一区域是对数学理论、模型和观测的巨大挑战。智力上的优点：这个项目将结合多尺度渐近理论、湍流大涡模拟(LES)和海洋观测的新方法，以解决上层海洋、三维、亚中尺度混合的难题。该理论方法使用渐近分析来产生简化的方程组。描述各向异性朗缪尔湍流的Craik-Leibovich方程的一个新的渐近简化版本将被用来模拟垂直风浪驱动。这项研究的目的是将类似的技术应用于竞争的侧向亚中尺度过程，以获得捕捉亚中尺度动力学及其与朗缪尔湍流的双向耦合的约化的粗尺度方程。为了检验简化模型的准确性和发展多尺度耦合系统的标度律，将进行一系列的数值实验，使用简化的方程和带有大涡湍流闭合的完整方程。这些理论工作的结果将通过与现有的使用拉格朗日浮子测量的上层海洋垂直动能、垂直热通量和浮力通量、能量和标量耗散率的比较来验证。这些数据将与部署在水平低梯度区域的朗缪尔湍流的预测进行比较，并与包括亚中尺度过程在内的部署在高梯度区域的浮标的预测进行比较。耦合过程的参数化将被嵌入到更粗分辨率的IPCC级OGCM中，并与现有混合参数化和全球气候数据集的结果进行比较。广泛影响：新的参数化可能导致IPCC级OGCM预测气候变化的能力显著提高。此外，PI发展的多尺度模拟方法很可能被推广到处理大气边界层，嵌入与朗缪尔环流相似的滚动涡旋结构。多尺度连续非线性动力系统，如本文所讨论的海洋表面混合层，在工程应用和应用科学中普遍存在，包括但不限于地球物理、海洋学、气象学和天体物理学。一个有希望的(也是唯一可靠的)途径是通过多学科团队的调查来洞察这些系统所表现出的复杂行为。这个项目将组成这样一个团队，跨学科、理论和观察之间以及三个不同的机构之间进行合作。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、流体力学、观测数据分析以及应用和计算数学等学科的高级培训和指导。这些下一代研究人员将获得一个绝佳的机会来学习这种现代的、真正的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.