Comparison Study on Wind Input and Whitecapping Dissipation Expressions in Numerical Simulation of Typhoon Generated Waves

In order to investigate the effect of wind input and whitecapping dissipation on the simulation of typhoon-waves, three experiments are conducted with the latest version of SWAN （Simulating WAves Nearshore） model. The three experiments adopt the Komen, Janssens, and Westhuysen expressions for wind input and whitecapping dissipation, respectively. Besides the above-mentioned source tems, other parameterization schemes in these experiments are the same. It shows that the experiment with the Westhuysen expression result in the least simulation errors while that with the Janssens expression has the most. The results from the experiments with Komen and Westhuysen expressions show that the differenees in significant wave height （SWH） have a good correlation with the differences in dissipation energy caused by whiteeapping. This indicates that the whitecapping dissipation source term plays an important role in the resultant differences of the simulated SWH between the two experiments.     

An approximated method for the solution of elliptic problems in thin domains: Application to nonlinear internal waves

Realistic numerical simulations of nonlinear internal waves (NLIWs) have been hampered by the need to use computationally expensive nonhydrostatic models. In this paper, we show that the solution to the elliptic problem arising from the incompressibility condition can be successfully approximated by a few terms (three at most) of an expansion in powers of the ratio (horizontal grid spacing)/(total depth). For an n dimensional problem, each term in the expansion is the sum of a function that satisfies a one-dimensional second-order ODE in the vertical direction plus, depending on the surface boundary condition, the solution to an n-1 dimension elliptic problem, an evident saving over having to solve the original n-dimensional elliptic problem. This approximation provides the physically correct amount of dispersion necessary to counteract the nonlinear steepening tendency of NLIWs. Experiments with different types of NLIWs validate the approach. Unlike other methods, no ad hoc artificial dispersion needs to be introduced.     

A global wave parameter database for geophysical applications. Part 1: Wave-current–turbulence interaction parameters for the open ocean based on traditional parameterizations

Ocean surface mixing and drift are influenced by the mixed layer depth, buoyancy fluxes and currents below the mixed layer. Drift and mixing are also functions of the surface Stokes drift U_ss, volume Stokes transport T_S, a wave breaking height scale H_swg, and the flux of energy from waves to ocean turbulence Φ_oc. Here we describe a global database of these parameters, estimated from a well-validated numerical wave model, that uses traditional forms of the wave generation and dissipation parameterizations, and covers the years 2003–2007. Compared to previous studies, the present work has the advantage of being consistent with the known physical processes that regulate the wave field and the air–sea fluxes, and also consistent with a very large number of in situ and satellite observations of wave parameters. Consequently, some of our estimates differ significantly from previous estimates. In particular, we find that the mean global integral of Φ_oc is 68 TW, and the yearly mean value of T_S is typically 10–30% of the Ekman transport, except in well-defined regions where it can reach 60%. We also have refined our previous estimates of U_ss by using a better treatment of the high frequency part of the wave spectrum. In the open ocean, U_ss  0.013U₁₀, where U₁₀ is the wind speed at 10 m height.     

Characteristics of developing waves as a function of atmospheric conditions,water properties,fetch and duration

For any specific wind speed, waves grow in period, height and length as a function of the wind duration and fetch until maximum values are reached, at which point the waves are considered to be fully developed. Although equations and nomograms exist to predict the parameters of developing waves for shorter fetch or duration conditions at different wind speeds, these either do not incorporate important variables such as the air and water temperature, or do not consider the combined effect of fetch and duration. Here, the wind conditions required for a fully developed sea are calculated from maximum wave heights as determined from the wind speed, together with a published growth law based on the friction velocity. This allows the parameters of developing waves to be estimated for any combination of wind velocity, fetch and duration, while also taking account of atmospheric conditions and water properties.     

Velocity potential formulations of highly accurate Boussinesq-type models

The highly accurate Boussinesq-type equations of Madsen et al. (Madsen, P.A., Bingham, H.B., Schäffer, H.A., 2003. Boussinesq-type formulations for fully nonlinear and extremely dispersive water waves: Derivation and analysis. Proc. R. Soc. Lond. A 459, 1075–1104; Madsen, P.A., Fuhrman, D.R., Wang, B., 2006. A Boussinesq-type method for fully nonlinear waves interacting with a rapidly varying bathymetry. Coast. Eng. 53, 487–504); Jamois et al. (Jamois, E., Fuhrman, D.R., Bingham, H.B., Molin, B., 2006. Wave-structure interactions and nonlinear wave processes on the weather side of reflective structures. Coast. Eng. 53, 929–945) are re-derived in a more general framework which establishes the correct relationship between the model in a velocity formulation and a velocity potential formulation. Although most work with this model has used the velocity formulation, the potential formulation is of interest because it reduces the computational effort by approximately a factor of two and facilitates a coupling to other potential flow solvers. A new shoaling enhancement operator is introduced to derive new models (in both formulations) with a velocity profile which is always consistent with the kinematic bottom boundary condition. The true behaviour of the velocity potential formulation with respect to linear shoaling is given for the first time, correcting errors made by Jamois et al. (Jamois, E., Fuhrman, D.R., Bingham, H.B., Molin, B., 2006. Wave-structure interactions and nonlinear wave processes on the weather side of reflective structures. Coast. Eng. 53, 929–945). An exact infinite series solution for the potential is obtained via a Taylor expansion about an arbitrary vertical position z = zˆ. For practical implementation however, the solution is expanded based on a slow variation of zˆ and terms are retained to first-order. With shoaling enhancement, the new models obtain a comparable accuracy in linear shoaling to the original velocity formulation. General consistency relations are also derived which are convenient for verifying that the differential operators satisfy a potential flow and/or conserve mass up to the order of truncation of the model. The performance of the new formulation is validated using computations of linear and nonlinear shoaling problems. The behaviour on a rapidly varying bathymetry is also checked using linear wave reflection from a shelf and Bragg scattering from an undulating bottom. Although the new models perform equally well for Bragg scattering they fail earlier than the existing model for reflection/transmission problems in very deep water.     

Nonlinear random wave-induced drag force on a vegetation field

This paper provides a practical method by which the drag force on a vegetation field beneath nonlinear random waves can be estimated. This is achieved by using a simple drag formula together with an empirical drag coefficient given by Mendez et al. (Mendez, F.J., Losada, I.J., Losada, M.A., 1999. Hydrodynamics induced by wind waves in a vegetation field. J. Geophys. Res. 104 (C8), 18383–18396). Effects of nonlinear waves are included by using Stokes second order wave theory where the basic harmonic motion is assumed to be a stationary Gaussian narrow–band random process. An example of calculation is also presented.     

Partially standing wave measurement in the presence of steady current by use of coincident velocity and/or pressure data

In recent years, instrumentation for field flow measurements has become more and more sophisticated. In particular, local pressure and velocity are measured at frequency rates up to at least 2 Hz, which gives information on wave energy. The present work describes the methods for partially standing wave measurement in the presence of current by use of coincident measurements of both horizontal velocity and pressure, or vertical velocity. Reflection calculated from either coincident horizontal and vertical velocities or three-gauge methods are compared. They are based on existing experiments carried out in an ocean wave basin for both regular and irregular waves in the presence of current. Applications to field measurements, out of and in the breaking zones are then presented. In the nearshore, coincident horizontal and vertical velocities far from the bottom, and coincident horizontal velocity and pressure close to the bottom give relevant information concerning partially standing waves.     

Theoretical Analysis of A Buoyant Jet Interacting with Small Amplitude Waves

A new theoretical solution is presented here for the dynamic characteristics of a buoyant jet due to opposing small amplitude waves.The conservation equations of mass,tangential momentum and vertical momentum are solved by the integral method which encompasses the Gaussian profiles of velocity and density.The action of waves is incorporated into the equations of motion as an external force and a new exact solution is obtained to predict the trajectory,velocity distribution and boundary thickness of the buoyant jet over an arbitrary lateral cross section.It is found that the velocity along the centerline is inversely proportional to the ratio of the momentum of the wave to the buoyant jet.The averaged boundary width varies with the fluctuation of the boundary width,the distance from the orifice and the velocity correction function.Owing to the motion d waves,the fluctuation of the boundary width is proportional to the wave steepness.     

Large-scale laboratory measurements of solitary wave inundation on a 1:20 slope

The run-up flow and related pressure of solitary waves breaking on a 1:20 plane beach were investigated experimentally in a super tank (300 m × 5 m × 5.2 m). Swash flow measurements of flow velocities are compared with an existing analytical solution. By incorporating an analytical solution, the hydrodynamic pressure for a quasi-steady flow state is determined and compared with laboratory data. Concerning the evident extra pressure exerted by the impact of swash flow, an empirical drag coefficient for a circular plate is also suggested in the present study.