Wake behind a three-dimensional dry transom stern. Part 2. Analysis and modelling of incompressible highly variable density turbulence

We analyse the turbulence characteristics and consider the closure modelling of the air entraining flow in the wake of three-dimensional, rectangular dry transom sterns obtained using high-resolution implicit large eddy simulations (iLES) (Hendrickson et al., J. Fluid Mech., vol. 875, 2019, pp. 854–883). Our focus is the incompressible highly variable density turbulence (IHVDT) in the near surface mixed-phase region ${\mathcal{R}}$ behind the stern. We characterize the turbulence statistics in ${\mathcal{R}}$ and determine it to be highly anisotropic due to quasi-steady wave breaking. Using unconditioned Reynolds decomposition for our analysis, we show that the turbulent mass flux (TMF) is important in IHVDT for the production of turbulent kinetic energy and is as relevant to the mean momentum equations as the Reynolds stresses. We develop a simple, regional explicit algebraic closure model for the TMF based on a functional relationship between the fluxes and tensor flow quantities. A priori tests of the model show mean density gradients and buoyancy effects are the main driving parameters for predicting the turbulent mass flux and the model is capable of capturing the highly localized nature of the TMF in ${\mathcal{R}}$ .