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.     

Rossby waves with linear topography in barotropic fluids

Rossby waves are the most important waves in the atmosphere and ocean, and are parts of a large-scale system in fluid. The theory and observation show that, they satisfy quasi-geostrophic and quasi-static equilibrium approximations. In this paper, solitary Rossby waves induced by linear topography in barotropic fluids with a shear flow are studied. In order to simplify the problem, the topography is taken as a linear function of latitude variable y, then employing a weakly nonlinear method and a perturbation method, a KdV （Korteweg-de Vries） equation describing evolution of the amplitude of solitary Rossby waves induced by linear topography is derived. The results show that the variation of linear topography can induce the solitary Rossby waves in barotropic fluids with a shear flow, and extend the classical geophysical theory of fluid dynamics.     

Numerical simulation of nearshore circulation on field topography under random wave environment

In order to investigate surf zone hydrodynamics through two-dimensional numerical simulations of nearshore circulation under random wave environment, a nearshore circulation model, SHORECIRC, and a random wave model, SWAN, were combined and utilized. Using this combined model, a numerical simulation of the October 2, 1997 SandyDuck field experiment was performed. For this simulation, field topography and an input offshore spectrum were constructed using observed data sets synchronized with the experiment. The wave-breaking model in SWAN was modified by using breaker parameters varied according to bottom slope. The simulation results were compared with the experimental data, which revealed a well-developed longshore current, as well as with results using other combinations which were SHORECIRC and its original monochromatic wave-driver, and SHORECIRC and the default of SWAN. The results from the novel combined model agreed well with the experimental data. The results of the present simulation also indicate that alongshore field topography influences shear fluctuation of longshore currents.     

乳山湾邻近海域波浪特征要素规律研究

基于高分辨率MASNUM第三代海浪模式并根据Yuan等(2009)提出的波浪破碎统计物理模型,对乳山湾外海2008年各个季节波浪特征要素(有效波高和跨零周期等)与波浪破碎参数(白冠覆盖率、卷入深度和破碎能量损耗率)进行了数值模拟。利用Janson-1卫星高度计观测资料对有效波高模拟结果进行了检验,平均误差在0.17m左右。模拟结果显示,该海域波浪参数具有明显的季节变化特征,在2008-08乳山湾邻近海域受大风天气过程影响期间,有效波高在1.0~1.8m,破碎参数变化显著,白冠覆盖率最大达4.5%,卷入深度在1.5m以上,相应的破碎能量损耗率量值在6~11kg/s3。结果表明,波浪破碎过程对该区域海洋动力环境有着重要影响,是造成乳山湾口表层高溶解氧的可能机制之一。