The effects of different wind input and wave dissipation formulations on the steady Ekman current solution are described. Two formulations are considered: one from the wave modeling(WAM) program proposed by Hasselmann and Komen and the other provided by Tsagareli and Babanin. The solution adopted for our study was presented by Song for the wave-modifi ed Ekman current model that included the Stokes drift, wind input, and wave dissipation with eddy viscosity increasing linearly with depth. Using the Combi spectrum with tail effects, the solutions are calculated using two formulations for wind input and wave dissipation, and compared. Differences in the results are not negligible. Furthermore, the solution presented by Song and Xu for the eddy viscosity formulated using the K-Profi le Parameterization scheme under wind input and wave dissipation given by Tsagareli and Babanin is compared with that obtained for a depth-dependent eddy viscosity. The solutions are further compared with the available well-known observational data. The result indicates that the Tsagareli and Babanin scheme is more suitable for use in the model when capillary waves are included, and the solution calculated using the K-Profi le Parameterization scheme agrees best with observations.
Spacing characteristics of Langmuir circulation (LC) are computed by large eddy simulation (LES) model under modest wind. LC is an organized vertical motion, evidenced as buoyant materials forming lines nearly parallel to the wind direction. The horizontal distribution of velocity computed by LES shows clear lines formed by LC. These lines grow and parallel to each other for a while, which we call the stable state, before they finally form Y-junctions. We computed spacing between every two parallel lines by averaging them under the stable state. Statistically, spacing results of 154 tests (seven wind speed cases of 22 test runs each) show high correlations between spacing and wind speed, as well as mixed layer depth. The relationship of spacing and wind is important for future LC parameterization of upper-ocean mixing.
Numerical models based on the boundary element method and Boussinesq equation are used to simulate the wave transform over a submerged bar for regular waves.In the boundary-element-method model the linear element is used,and the integrals are computed by analytical formulas.The Boussinesq-equation model is the well-known FUNWAVE from the University of Delaware.We compare the numerical free surface displacements with the laboratory data on both gentle slope and steep slope,and find that both the models simulate the wave transform well.We further compute the agreement indexes between the numerical result and laboratory data,and the results support that the boundary-element-method model has a stable good performance,which is due to the fact that its governing equation has no restriction on nonlinearity and dispersion as compared with Boussinesq equation.
A numerical wave tank is used to investigate the onset and strength of unforced wave breaking, and the waves have three types of initial spectra: constant amplitude spectrum, constant steepness spectrum and Pierson-Moscowitz spectrum. Numerical tests are performed to validate the model results. Then, the onset of wave breaking is discussed with geometric, kinematic, and dynamic breaking criteria. The strength of wave breaking, which is always characterized by the fractional energy loss and breaking strength coefficient, is studied for different spectra. The results show how the energy growth rate is better than the initial wave steepness on estimating the fractional energy losses as well as breaking strength coefficient.
In this study, an analysis on the internal wave generation via the gravity collapse mechanism is carried out based on thetheoretical formulation and the numerical simulation. With the linear theoretical model, a rectangle shape wave is generated andpropagates back and forth in the domain, while a two-dimensional non-hydrostatic numerical model could reproduce all the observedphenomena in the laboratory experiments conducted by Chen et al. (2007), and the related process realistically. The model resultsfurther provide more quantitative information in the whole domain, thus allowing an in depth understanding of the correspondinginternal solitary wave generation and propagation. It is shown that the initial type of the internal wave is determined by the relativeheight between the perturbation and the environmental density interface, while the final wave type is related to the relative height ofthe upper and lower layers of the environmental fluid. The shape of the internal wave generated is consistent with that predicted bythe KdV and EKdV theories if its amplitude is small, as the amplitude becomes larger, the performance of the EKdV becomes betterafter the wave adjusts itself to the ambient stratification and reaches an equilibrium state between the nonlinear and dispersion effects.The evolution of the mechanical energy is also analyzed.
