Turbulence Modeling of Wave Boundary Layers

Different turbulence models of variable complexity based on the user’s requirements are used to analyze turbulence boundary layers. The governing (Navier- Stokes) equation is a nonlinear, time-dependent, 3D partial differential equation. The actual solutions of this equation are few and only applicable to laminar flow. At high Reynolds numbers, which is the case for most of the practical applications, the laminar flow undergoes instabilities, generally referred as turbulence. Since these instabilities generate three-dimensional features, no satisfactory 2D approximations for turbulent phenomena are available. In addition, turbulence being random process in time, the deterministic approach is not fully applicable. The turbulent flows contain small fluctuations, which can be resolved by choosing very fine grids and time steps, such that a direct simulation is not feasible for high Reynolds numbers. Using Reynolds Averaged Navier-Stokes (RANS) models, the computational costs are significantly reduced, however, it requires closure assumptions for the higher moments. Large Eddy Simulation (LES) aims to reduce the dependence on the turbulence model by simulating the major portion of the flow without any models, resolving by the grid. Only the scales smaller than the resolution of the grid are simulated by a model. Such a computational strategy makes LES approach computationally more demanding than RANS. It is estimated that RANS models have a computing time of about 5% of the LES whereas, LES has a computing time of about 10% of DNS [1]. Owing to the computational economy and reasonable accuracy of RANS models, various practical flow phenomena have been simulated using different types of models. In this paper, a brief review of some of the applications of two-equation turbulence models in different types of wave boundary layers is presented. Such a review may be helpful in selecting an appropriate turbulence model for relevant field applications.