Significance of Length Scale Models and Realizability in Free Surface Flows for NWTs Application

Numerical Wave Tanks (NWTs) necessitate a turbulent model that meets specific criteria: in regions of breaking waves and wave structure interactions that have very high shear rates, it must accurately compute the eddy viscosity to capture turbulent dynamics effectively. Conversely, in areas of regular non-breaking waves which has very low levels of turbulence, the model should preserve wave energy without unnecessary dissipation. This delicate balance ensures the numerical wave tank's capability to simulate both breaking and non-breaking wave phenomena with precision and fidelity. High shear rates are handled by the constitutive relationship, whereas the transport length scale equation deals with low Reynolds number effects. In this study, we will combine various constitutive relations and transport models to thoroughly understand and explain the physics underlying realizability and length scale model. A numerical study focuses on regular waves interacting with a fixed cylinder in a deep wave tank, with results validated against implemented DNS simulations and available experimental data. Results underscore the crucial rule of selecting an appropriate length scale model in conserving wave energy in low-turbulence regions and accurately capturing turbulent dynamics during wave-structure interactions, such as the secondary load cycle phenomenon. Moreover, the study indicates that non-breaking waves, characterized by high strain rates, cause turbulence to behave more like an elastic medium than a viscous one, rendering conventional Boussinesq constitutive relations physically inaccurate. Realizability conditions play a pivotal role in ensuring physically consistent Reynolds stresses in NWTs, thereby enhancing the fidelity of turbulence modeling.