A general turbulence velocity scale for transport of buoyant materials in the oceanic mixed layer

In this work we introduce an approach to predict the mixing and transport of passive buoyant materials in the Oceanic Mixed Layer (OML). The main goal of our approach is that it should be general enough to work with a broad spectrum of forcing conditions acting on the OML (namely surface wind shear, surface cooling, and nonbreaking wave effects with different wind-alignment angles), while still maintaining simplicity. We begin by introducing a turbulence scale for the velocity field that is based on the Turbulent Kinetic Energy equation. This scale is used to define a floatability parameter for the material, which represents how much the material's buoyancy opposes turbulent downwelling. Using the floatability parameter, we were able to derive analytical predictions for the material concentration as a function of depth. These predictions are shown to work for several different combinations of forcing conditions despite their simplicity. Building on this result, we derive analytical solutions that predict important characteristics of plumes of buoyant material such as the depth of the plume’s center of mass and the characteristics of their horizontal transport. We test our model against LES simulations from our work and from previous works and obtain good results.