Effects of Wave–Current Interactions on Bay–Shelf Exchange

Bay–shelf exchange is critical to coastal systems because it promotes self-purification or pollution dilution of the systems. In this study, the effects of wave–current interactions on bay–shelf exchange are explored in a micromesotidal system—Daya Bay in southern China. Waves can enlarge the shear-induced seaward transport and reduce the residual-current-induced landward transport, which benefits the bay–shelf exchange; however, tides work oppositely and slow the wave-induced bay–shelf exchange through vertical mixing and reduced shear-induced exchange. Five wave–current interactions are compared, and it is found that the depth-dependent wave radiation stress (WRS) contributes most to the bay–shelf exchange, followed by the wave dissipation as a source term in the turbulence kinetic energy equation, and the mean current advection and refraction of wave energy (CARWE). The vertical transfer of wave-generated pressure to the mean momentum equation (also known as the form drag) and the combined wave–current bottom stress (CWCBS) play minor roles in the bay–shelf exchange. The bay–shelf exchange is faster under southerly wind than under northerly wind because the bay is facing southeast; synoptic events such as storms enhance the bay–shelf exchange. The CARWE terms are dominant in both seasonal and synoptic variations of the bay–shelf exchange because they can considerably change the distribution of significant wave height. The WRS changes the bay–shelf exchange mainly through altering the flow velocity, whereas the wave dissipation on turbulence alters the vertical mixing. The form drag and the CWCBS have little impact on the bay–shelf exchange or its seasonal and synoptic variations.

On Surf Zone Fluid Dynamics

There have been several numerical models developed to represent the phase-averaged flow in the surf zone, which is characterized by kD less than unity, where k is wavenumber and D is the water column depth. The classic scenario is that of surface gravity waves progressing onto a shore that create an offshore undertow current. In fact, in some models, flow velocities are parameterized assuming the existence of an undertow. The present approach uses the full vertically dependent continuity and momentum equations and the vertically dependent wave radiation stress in addition to turbulence equations. The model is applied to data that feature measurements of wave properties and also cross-shore velocities. In this paper, both the data and the model application are unidirectional and the surface stress is nil, representing the simplest surf zone application. Breaking waves are described empirically. Special to the surf zone, it is found that a simple empirical adjustment of the radiation stress enables a favorable comparison with data. Otherwise, the model applies to the open ocean with no further empiricism. A new bottom friction algorithm had been derived and is introduced in this paper. In the context of the turbulence transport model, the algorithm is relatively simple.

Marginal Ice Zone Thickness and Extent due to Wave Radiation Stress

Ocean surface wave radiation stress represents the flux of momentum due to the waves. When waves are dissipated or reflected by sea ice, that momentum is absorbed or reflected, resulting in a horizontal forcing that frequently compresses the ice. In this work, wave radiation stress is used to estimate the compressive force applied by waves to the marginal ice zone (MIZ). It is balanced by an ice internal compressive stress based on Mohr–Coulomb granular materials theory. The ice internal stress can be related to ice thickness, allowing this force balance to be used as a model for the estimation of MIZ ice thickness. The model was validated and tested using data collected during two field campaigns in the St. Lawrence estuary in 2016 and 2017. Modeled ice thickness was found to be consistent with the mean measured ice thickness over the conditions available. The range of validity of the model is discussed, and a definition of MIZ extent, based on the relative strength of wind and wave forcing, is proposed.

Effects of Wave–Current Interactions on Suspended-Sediment Dynamics during Strong Wave Events in Jiaozhou Bay, Qingdao, China

Wave–current interactions are crucial to suspended-sediment dynamics, but the roles of the associated physical mechanisms, the depth-dependent wave radiation stress, Stokes drift velocity, vertical transfer of wave-generated pressure transfer to the mean momentum equation (form drag), wave dissipation as a source term in the turbulence kinetic energy equation, and mean current advection and refraction of wave energy, have not yet been fully understood. Therefore, in this study, a computationally fast wave model developed by Mellor et al., a Finite Volume Coastal Ocean Model (FVCOM) hydrodynamics model, and the sediment model developed by the University of New South Wales are two-way coupled to study the effect of each wave–current interaction mechanism on suspended-sediment dynamics near shore during strong wave events in a tidally dominated and semiclosed bay, Jiaozhou Bay, as a case study. Comparison of Geostationary Ocean Color Imager data and model results demonstrates that the inclusion of just the combined wave–current bottom stress in the model, as done in most previous studies, is clearly far from adequate to model accurately the suspended-sediment dynamics. The effect of each mechanism in the wave–current coupled processes is also investigated separately through numerical simulations. It is found that, even though the combined wave–current bottom stress has the largest effect, the combined effect of the other wave–current interactions, mean current advection and refraction of wave energy, wave radiation stress, and form drag (from largest to smallest effect), are comparable. These mechanisms can cause significant variation in the current velocities, vertical mixing, and even the bottom stress, and should obviously be paid more attention when modeling suspended-sediment dynamics during strong wave events.

Numerical Modeling of Wave-Current Flow around Cylinders Using an Enhanced Equilibrium Bhatnagar-Gross-Krook Scheme

Flow around cylinders is a classic issue of fluid mechanics and it has great significance in engineering fields. In this study, a two-dimensional hydrodynamic lattice Boltzmann numerical model is proposed, coupling wave radiation stress, bed shear stress, and wind shear stress, which is able to simulate wave propagation of flow around cylinders. It is based on shallow water equations and a weight factor is applied for the force term. An enhanced equilibrium Bhatnagar-Gross-Krook (BGK) scheme is developed to treat the wave radiation stress term in collision step. This model is tested and verified by two cases: the first case is the flow around a single circular cylinder, where the flow is driven by current, wave, or both wave and current, respectively, and the second case is the solitary waves moving around cylinders. The results illustrate the correctness of this model, which could be used to analyze the detailed flow pattern around a cylinder.

A Coupled Circulation–Wave Model for Numerical Simulation of Storm Tides and Waves

The Stevens Institute of Technology Estuarine and Coastal Ocean Model (sECOM) is coupled here with the Mellor–Donelan–Oey (MDO) wave model to simulate coastal flooding due to storm tides and waves. sECOM is the three-dimensional (3D) circulation model used in the New York Harbor Observing and Prediction System (NYHOPS). The MDO wave model is a computationally cost-effective spectral wave model suitable for coupling with 3D circulation models. The coupled sECOM–MDO model takes into account wave–current interactions through wave-enhanced water surface roughness and wind stress, wave–current bottom stress, and depth-dependent wave radiation stress. The model results are compared with existing laboratory measurements and the field data collected in New York–New Jersey (NY–NJ) harbor during Hurricane Sandy. Comparisons between the model results and laboratory measurements demonstrate the capabilities of the model to accurately simulate wave characteristics, wave-induced water elevation, and undertow current. The model results for Hurricane Sandy reveal the successful performance of sECOM–MDO in situations where high waves and storm tides coexist. The results indicate that the temporal maximum wave setup in NY–NJ harbor was 0.26 m. On the other hand, the contribution of wave setup to the peak storm tide was 0.13 m, a contribution of only 3.8%. It is found that the inclusion of wave radiation stress and wave-enhanced bottom friction in the circulation model can reduce the errors in the calculated storm tides. At the Battery (New York), for example, the root-mean-square error reduced from 0.17 to 0.12 m.