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.
