DOI: 10.25549/usctheses-c40-373879
title: Highly resolved simulations of large scale wave driven processes

description: Nearshore hydrodynamics are driven by a wide spectrum of motions/scales with length-scale varying on the order of O (10) m to O (100) km and time-scale varying on the order of seconds to hours. Capturing the various effects of these different scales is essential in accurately modeling the nearshore processes such as mixing, pollutant transport, wave damping, and sediment re-suspension and transport. In this study, a multiple-scale perturbation approach is implemented to solve Navier-Stokes equations to include bottom boundary layer effects under one and/or two wave motions. In this approach, fluid velocities and pressure field are decomposed into two components: potential component and rotational component. Contrary to other approaches in the literature, the two components are allowed to exist throughout the whole water column through scaling each component with its appropriate length and time scales. A one-way coupling between the two components is implemented in which the potential component is assumed to be known analytically or numerically, and then, it is passed to the rotational/viscous model. A numerical model using σ-coordinate transformation in the vertical direction is developed to solve the resulting governing equations for the rotational component. Through order of magnitude analysis, it is found that coupling of the two components occurs through the convective inertia terms. It is shown that the vertical convective acceleration plays an important role in the bottom boundary layer behavior. The effect of this coupling term is discussed for different wave-forcing conditions: purely harmonic forcing and impurely harmonic forcing. Results from the numerical model agree very well with the available experimental and numerical data for laminar boundary layers. The approach is then applied to derive the governing equations for bottom boundary layer developed under two wave motions interaction: shorter and longer motions. Both motions—the shorter and the longer waves—are decomposed into two components, potential and rotational, as in single wave motion. A test case is presented wherein two different wave forcings are simulated: 1) two periodic oscillatory motions and 2) short waves interacting with a solitary wave. Analysis of the two periodic motions indicates that nonlinear effects in the rotational solution may be significant even though nonlinear effects are negligible in the potential forcing. For the cases simulated, with maximum wave nonlinearities in a range typically considered to be very weak, local differences in the rotational solution due to nonlinear vertical convection were found to be on the order of 30 % of the maximum boundary layer velocity. This difference increases with increase in the wave nonlinearity. Another commonly encountered situation in coastal areas is the interaction of waves and tidal-current. The time and length scales of the current are much larger than those of the waves. Tidal currents often have time scale of hours and length scale of kilometers, and waves often have time scale of seconds and length scale of hundreds of meters. Thus simulating this interaction using a single numerical model requires large numerical domain simulations while using huge computations resources. An alternative, optimum solution can be via coupling two numerical models, such that the current is simulated in a circulation model and then exported to the second numerical model where waves are simulated with the background current forcings. In the literature, spectral wave models have been widely used and coupled with various circulation models to study wave-current interaction. They give accurate predictions for wave height, but they do not provide accurate results for the bottom velocity moments which is a key parameter in sediment transport models. On the other hand, phase-resolving wave models are capable of providing such accurate results. In time domain models, the free surface evolves in time and space, while in frequency models, the free surface is assumed to be periodic in time in steady simulations. Thus, we anticipate that the use of a time domain Boussinesq model improves the prediction of the combined velocity profile under external forcings as in: tidal currents. Moreover, time domain wave models provide the nonlinear wave statistics, i.e. wave skewness, which is an important parameter in estimating wave-induced sediment transport. Such an application will fulfill the community needs for a “spot application tool” where we simulate wave-driven processes in a large domain with fine-resolution. The numerical results show that the use of the Boussinesq time domain model coupled with Delft3d-Flow better predicts the vertical velocity profile compared with the field data.