A New Hybrid Mass-Flux/High-Order Turbulence Closure for Ocean Vertical Mixing

While various parameterizations of vertical turbulent fluxes at different levels of complexity have been proposed, each has its own limitations. For example, simple first-order closure schemes such as the K-Profile Parameterization (KPP) lack energetic constraints; two-equation models like k-e $k-\varepsilon $ directly solve an equation for the turbulent kinetic energy but do not account for non-diffusive fluxes, and high-order closures that include the high-order transport terms are computationally expensive. To address these, we extend the Assumed-Distribution Higher-Order Closure (ADC) framework originally proposed for the atmospheric boundary layer and apply it to the ocean surface boundary layer. By assuming a probability distribution function relationship between the vertical velocity and tracers, all second-order and higher-order moments are exactly constructed and turbulence closure is achieved in the ADC scheme. In addition, this ADC parameterization has full energetic constraints and includes non-diffusive fluxes without the computational cost of a full higher-order closure scheme. We have tested the ADC scheme against a combination of large eddy simulation (LES), KPP, and k-e $k-\varepsilon $ for surface buoyancy-driven convective mixing and found that the ADC scheme is robust with different vertical resolutions and compares well to the LES results. The upper ocean (order of few tens of meters depth from the surface) has a substantial influence on our climate and weather systems. Specifically, upper ocean mixing processes play a key role in modulating global heat budget in the ocean and atmosphere by mixing heat deeper into the ocean or warming the atmosphere above. Accurate representation of the effects of these mixing processes on the global climate and in ocean models is crucial for understanding our current and changing climate. However, current mixing schemes used in these models have shown significant biases. We present a new physically-motivated mixing scheme for the upper ocean inspired by atmospheric mixing schemes. Results show that the proposed mixing scheme can simulate upper ocean mixing efficiently, suggesting its potential use in climate and ocean models to help reduce model biases. A new physically-motivated, PDF-based parameterization of ocean surface boundary layer turbulence is presentedThe non-diffusive fluxes are included naturally and the scheme provides a closed set of equations with realizable closure assumptionsThe mixing scheme accurately predicts the effects of convective turbulence across different vertical resolutions