Relating surface signatures to modeled turbulence dynamics in open channel flow

In open channel flow (OCF), expressions and patterns at the water surface may represent underwater turbulent phenomena. In this study, we seek to connect the surface signatures with the turbulence beneath it through the prediction of the time and length scales of turbulent structures in second moment closure (SMC) models. In the simplest scenario, the unforced free surface OCF is driven by a uniform horizontal pressure gradient and the only source of turbulence is the bottom shear. Working with Neumann surface boundary conditions for turbulence quantities, the traditional ‘return-to-isotropy’ for turbulent kinetic energy (TKE) components is modified to decay – in the absence of local TKE production – to a specified anisotropy profile as a function of depth below the surface, rather than to isotropy. This gives rise to distinct vertical and horizontal length scales, formed from the TKE components and the turbulence decay timescale. It also results, through changes in the algebraic closure solution, in a modification of vertical diffusivity consistent with more ad-hoc proposals in other studies to address excessive flux predictions using depth-dependent damping functions. An examination of results from these model changes is presented for weak equilibrium k - ε SMC models. The weak equilibrium k - ε SMC model solves for turbulent second moments by combining prognostic equations for TKE (k) and dissipation (ε) with an algebraic model to obtain eddy viscosity and diffusivity. SMC predictions for TKE components, dissipation, and horizontal turbulent length scales at the free surface are compared with observations obtained in a tidally modulated river, as well as with published results from OCF lab experiments and direct numerical simulations.