Turbulent Flow and Transport Modeling by Long Waves and Currents

Abstract

This dissertation presents models for turbulent flow and transport by currents and long waves in large domain. From the Navier-Stokes equations, a fully nonlinear depth-integrated equation model for weakly dispersive, turbulent and rotational flow is derived by a perturbation approach based on long wave scaling. The same perturbation approach is applied for the derivation of a depth-integrated transport equation. As the results, coherent structures generated by the turbulence induced by the bottom friction and topography can be predicted very reasonably. The three dimensional turbulence effects are incorporated into the flow model by employing a back scatter model. The back scatter model makes it possible to predict turbulent transport: It contributes to the energy transport and the lateral turbulent diffusion through relying on the turbulent intensity, not by relying on an empirical diffusion constant. The inherent limitation of the depth-integrated transport equation, that is, the limitation for the near field prediction is recognized in the derivation and the numerical simulation. To solve the derived equation set, a highly accurate and stable finite volume scheme numerical solver is developed. Thus, the numerical solver can predict dispersive and nonlinear wave propagation with minimal error. Also, good stability is achieved enough to be applied to the dam-break flows and undular tidal bores. In addition, a robust moving boundary scheme based on simple physical conditions is presented, which can extend the applicability area of the depth-integrated models. By the comparison study with experimental data, it is expected that the numerical model can provide high confidence results for the wave and current transformations including shocks and undular bores on complex bathymetry and topography. For the accurate near field transport prediction, a three dimensional transport model in ?-coordinate coupled with the depth-integrated flow model is developed. Like the other models, this model is also intended for large domain problems, and yet efficient and accurate in the far field and near field together.