A new hybrid mass-flux/ high-order turbulence closure for ocean vertical mixing

TL;DR

This paper introduces a novel hybrid turbulence closure model for ocean vertical mixing, extending the atmospheric ADC framework to improve accuracy and energetic consistency over existing parameterizations.

Contribution

The paper develops a new ADC-based turbulence closure for the ocean surface boundary layer, incorporating non-local fluxes and energetic constraints, and demonstrates its robustness and accuracy.

Findings

ADC scheme compares well with LES results

Robust across different vertical resolutions

Addresses limitations of existing models

Abstract

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 $k-\epsilon$ directly solve an equation for the turbulent kinetic energy but do not account for non-local fluxes, and high-order closures that include the non-local transport terms are computationally expensive. To address these, here 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 (OSBL). 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, the ADC parameterization scheme has full energetic constraints. We have tested the ADC scheme against a combination of large eddy simulation (LES), KPP, and $k-\epsilon$ 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.