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Chinese Academy of Sciences (ISCAS)

The effects of random surface waves on the steady Ekman current solutions

The response of near-surface current profiles to wind and random surface waves are studied based on the approach of Jenkins [1989. The use of a wave prediction model for driving a near surface current model. Dtsch. Hydrogr. Z. 42,134-149] and Tang et al. [2007. Observation and modeling of surface currents on the Grand Banks: a study of the wave effects on surface currents. J. Geophys. Res. 112, C10025, doi:10.1029/2006JC004028]. Analytic steady solutions are presented for wave-modified Ekman equations resulting from Stokes drift, wind input and wave dissipation for a depth-independent constant eddy viscosity coefficient and one that varies linearly with depth. The parameters involved in the solutions can be determined by the two-dimensional wavenumber spectrum of ocean waves, wind speed, the Coriolis parameter and the densities of air and water, and the solutions reduce to those of Lewis and Belcher [2004. Time-dependent, coupled, Ekman boundary layer solutions incorporating Stokes drift. Dyn. Atmos. Oceans. 37, 313-351] when only the effects of Stokes drift are included. As illustrative examples, for a fully developed wind-generated sea with different wind speeds, wave-modified current profiles are calculated and compared with the classical Ekman theory and Lewis and Belcher's [2004. Time-dependent, coupled, Ekman boundary layer solutions incorporating Stokes drift. Dyn. Atmos. Oceans 37, 313-351] modification by using the Donelan and Pierson [1987. Radar scattering and equilibrium ranges in wind-generated waves with application to scatterometry. J. Geophys. Res. 92, 4971-5029] wavenumber spectrum, the WAM wave model formulation for wind input energy to waves, and wave energy dissipation converted to currents. Illustrative examples for a fully developed sea and the comparisons between observations and the theoretical predictions demonstrate that the effects of the random surface waves on the classical Ekman current are important, as they change qualitatively the nature of the Ekman layer. But the effects of the wind input and wave dissipation on surface current are small, relative to the impact of the Stokes drift. (C) 2008 Elsevier Ltd. All rights reserved.

Joint statistical distribution of two-point sea surface elevations in finite water depth

Based on the second-order random wave solutions of water wave equations in finite water depth, a joint statistical distribution of two-point sea surface elevations is derived by using the characteristic function expansion method. It is found that the joint distribution depends on five parameters. These five parameters can all be determined by the water depth, the relative position of two points and the wave-number spectrum of ocean waves. As an illustrative example, for fully developed wind-generated sea, the parameters that appeared in the joint distribution are calculated for various wind speeds, water depths and relative positions of two points by using the Donelan and Pierson spectrum and the nonlinear effects of sea waves on the joint distribution are studied. (C) 2003 Elsevier B.V. All rights reserved.

Statistical distribution of depth-integrated local horizontal momentum for second-order random ocean waves in finite water depth

Based on the second-order random wave solutions of water wave equations in finite water depth, statistical distributions of the depth- integrated local horizontal momentum components are derived by use of the characteristic function expansion method. The parameters involved in the distributions can be all determined by the water depth and the wave-number spectrum of ocean waves. As an illustrative example, a fully developed wind-generated sea is considered and the parameters are calculated for typical wind speeds and water depths by means of the Donelan and Pierson spectrum. The effects of nonlinearity and water depth on the distributions are also investigated.

Statistical distribution of wave-surface elevation for second-order random directional ocean waves in finite water depth

Based on the second-order random wave solutions of water wave equations in finite water depth, a statistical distribution of the wave-surface elevation is derived by using the characteristic function expansion method. It is found that the distribution, after normalization of the wave-surface elevation, depends only on two parameters. One parameter describes the small mean bias of the surface produced by the second-order wave-wave interactions. Another one is approximately proportional to the skewness of the distribution. Both of these two parameters can be determined by the water depth and the wave-number spectrum of ocean waves. As an illustrative example, we consider a fully developed wind-generated sea and the parameters are calculated for various wind speeds and water depths by using Donelan and Pierson spectrum. It is also found that, for deep water, the dimensionless distribution reduces to the third-order Gram-Charlier series obtained by Longuet-Higgins [J. Fluid Mech. 17 (1963) 459]. The newly proposed distribution is compared with the data of Bitner [Appl. Ocean Res. 2 (1980) 63], Gaussian distribution and the fourth-order Gram-Charlier series, and found our distribution gives a more reasonable fit to the data. (C) 2002 Elsevier Science B.V. All rights reserved.

Probability distribution of random wave-current forces

Based on the second-order solutions obtained for the three-dimensional weakly nonlinear random waves propagating over a steady uniform current in finite water depth, the joint statistical distribution of the velocity and acceleration of the fluid particle in the current direction is derived using the characteristic function expansion method. From the joint distribution and the Morison equation, the theoretical distributions of drag forces, inertia forces and total random forces caused by waves propagating over a steady uniform current are determined. The distribution of inertia forces is Gaussian as that derived using the linear wave model, whereas the distributions of drag forces and total random forces deviate slightly from those derived utilizing the linear wave model. The distributions presented can be determined by the wave number spectrum of ocean waves, current speed and the second order wave-wave and wave-current interactions. As an illustrative example, for fully developed deep ocean waves, the parameters appeared in the distributions near still water level are calculated for various wind speeds and current speeds by using Donelan-Pierson-Banner spectrum and the effects of the current and the nonlinearity of ocean waves on the distribution are studied. (c) 2006 Elsevier Ltd. All rights reserved.

非线性数值波浪水槽及其应用

本文分别使用基于边界元方法和高阶Boussinesq-type方程的非线性数值波浪水槽，研究了波浪破碎判据，波浪破碎能量损失以及一些特殊的波浪生成机制。基于边界元方法的数值波浪水槽使用线性元，记为DAS，其第一个改进模型修正了DAS中的积分解析公式，简称MDAS，其第二个改进模型在自由表面使用三阶元取代线性元，简称MDAS2。 鉴于Song和Banner（2002，2004）使用DAS模型提出了一个基于无量纲局部能量密度极大值平均增长率参数的破碎阈值dth，本文首先验证了dth对于MDAS和MDAS2的适用性；其次，本文考虑了海底坡度对dth的影响，结果表明dth对于中等水深下坡度小于1:100的缓坡仍然适用；再次，本文讨论了破碎阈值dth对于汇聚波的适用性，这些汇聚波具有常振幅谱，常波陡谱和PM谱，结果表明dth对这三种谱形的汇聚波都是适用的。 本文计算了常振幅谱情形时破碎能量损失对于最大能量增长率dmax的依赖性，结果表明，破碎能量损失随dmax几乎线性增长。同Banner和Pierson（2007）实验数据比对说明不同谱形的破碎能量损失随dmax的变化关系大致相同。相反，破碎能量损失随初始波陡(ak)0的变化曲线对于谱形有着显著的依赖性。此外，本文使用基于高阶Boussinesq-type方程的数值波浪水槽研究了近岸梯形潜坝上的破碎能量损失。结果指出，相对于潜坝的坡度和宽度，入射波的非线性参数和色散性参数以及潜坝的高度对于破碎能量损失具有更重要的影响。 MDAS还被用于模拟水槽中底部抬升、底部塌陷以及水中岩石坠落激发的表面波生成过程。对于底部抬升激发表面波这一过程，研究表明非线性效应对于表面波生成具有重要影响。对于底部塌陷和水中岩石坠落激发表面波过程，数值模拟结果与实验室水槽实验结果比较表明：MDAS能够有效地模拟这些生成过程。