Seabed shear stresses under irregular waves plus current from Monte Carlo simulations of parameterized models

Shear stresses on a rough seabed under irregular waves plus current are calculated. Parameterized models valid for regular waves plus current have been used in Monte Carlo simulations, assuming the wave amplitudes to be Rayleigh-distributed. Numerical estimates of the probability distribution functions are presented. For waves only, the shear stress maxima follow a Weibull distribution, while for waves plus current, both the maximum and time-averaged shear stresses are well represented by a three-parameter Weibull distribution. The behaviour of the maximum shear stresses under a wide range of wave-current conditions has been investigated, and it appears that under certain conditions, the current has a significant influence on the maximum shear stresses. Results of comparison between predictions and measurements of the maximum bottom shear stresses from laboratory and field experiments are presented.     

Probability distribution of random wave forces in weakly nonlinear random waves

Based on the second-order random wave theory, the joint statistical distribution of the horizontal velocity and acceleration 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 wave forces 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. It is found that the distribution of wave forces depends solely on the frequency spectrum of sea waves associated with the first order approximation and the second order wave–wave interaction.     

A semi-analytical solution for random wave-induced soil response and seabed liquefaction in marine sediments

In this study, unlike most previous investigations for wave-induced soil response, a simple semi-analytical model for the random wave-induced soil response is established for an unsaturated seabed of finite thickness. Two different wave spectra, the B-M and JONSWAP spectra, are considered in the new model. The influence of random wave loading on the soil response is investigated by comparing with the corresponding representative regular wave results through a parametric study, which includes the effect of the degree of saturation, soil permeability, wave height, wave period and seabed thickness. The maximum liquefaction depth under the random waves is also examined. The difference on the soil response under the two random wave types, B-M and JONSWAP frequency spectra, is also discussed in the present work.     

Mobile layer thickness in sheet flow beneath random waves

The erosion depth and the sheet flow layer thickness represent two characteristic parameters for transport processes in oscillatory sheet flow. Formulas for these parameters under regular waves have been applied to obtain characteristic statistical values under random waves. The applicability of the method for practical purposes is illustrated by two examples using data typical for field conditions at water depths of 70 m (Ekofisk location in the North Sea) and 15 m, respectively. Two fictive storms based on the Dohmen-Janssen and Hanes [Dohmen-Janssen, C.M., Hanes, D.M., 2005. Sheet flow and suspended sediment due to wave groups in a large wave flume. Cont. Shelf Res. 25, 333–347] data from large scale wave flume tests have also been utilized to demonstrate how the return period of the sheet flow layer thickness observed in their experiments can be estimated.     

A rational approach to seepage flow effects on bottom friction beneath random waves

The bottom friction beneath random waves is predicted taking into account the effect of seepage flow. This is achieved by using wave friction factors for rough turbulent, smooth turbulent and laminar flow valid for regular waves together with a modified Shields parameter which includes the effect of seepage flow. Examples using data typical to field conditions are included to illustrate the approach. The analytical results can be used to make assessment of seepage effects on the bottom friction based on available wave statistics. Generally, it is recommended that a stochastic approach should be used rather than using the rms values in an otherwise deterministic approach.     

Penetration depth of the dynamic response of seabed induced by internal solitary waves

We use flume experiments and numerical modeling to examine the penetration depth of internal solitary waves (ISWs) on partially saturated porous sandy silt and clayey silt seabed. The results of the experiment and model showed that the instantaneous excess pore water pressure in both the sandy silt and clayey silt seabed followed the same trend of decreasing with the seabed depth. In general, the excess pore water pressure generated by the sandy silt was bigger than that by clayey silt at the same depth. The ISW-induced excess pore water pressure greatly influenced the surface seabed and showed a linear relationship. The penetration depth was approximately one order of magnitude smaller than the half-wavelength of the ISWs, which might be larger than the penetration depth induced by surface waves. Our study results are helpful for understanding the damage that ISWs inflict upon the seabed and for informing future field experiments designed to directly measure the interaction between ISWs and seabed sediments.     

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.     

Refraction and diffraction of random waves through breakwater

A physical model study of combined refraction and diffraction of waves through a breakwater gap at different incident angles was conducted. Both regular and random waves with narrow and broad frequency and direction spreading were studied. Besides the presence of a mild bottom slope in the lee of the breakwater, the distribution of wave heights across the width of a navigation channel inside the model harbor was also simulated. In addition to contributing to an understanding of the phenomenon of refraction and diffraction of random waves, the relatively complete set of data obtained can serve as a benchmark for testing of numerical models.     

Bottom friction caused by boundary layer streaming beneath random waves for laminar and smooth turbulent flow

The effect of boundary layer streaming on the sea bed shear stresses, beneath random waves, is investigated for laminar flow as well as smooth turbulent flow. It is demonstrated how bottom friction formulas for regular waves can be used to obtain the bed shear stresses resulting from steady streaming under random waves. As a result, friction factors for steady streaming under random waves are provided, and the effect of streaming versus the effect of linear waves is discussed. For laminar flow the effect of second order Stokes waves is also included. Examples are included to illustrate the applicability of the present practical method, and results are obtained using data typical for field conditions.     

未破碎变浅随机海浪的波面高度概率分布

利用青岛海洋大学物理海洋实验室现代化的大型水槽,设计进行了多种海浪强度下,由深水传入近岸不同坡度水底上的变浅随机海浪的实验.依据实验资料分析结果表明,对变浅非正态海浪过程而言,其波面高度分布取Gram-Charlier级数前3项,所得结果与实验分布符合良好.该分布中σ、λ₃、λ₄3个参量是测点水深和波浪强度的函数,并获得了与无因次参量Hs/d之间的经验关系,为预测变浅随机海浪的波面高度分布提供了可能.     

Extended mild-slope equation for random waves

A time-dependent extended mild-slope equation is derived from the elliptic equation of Chamberlain and Porter [J. Fluid Mech. 291 (1995) 393] using the Taylor series technique. Numerical tests are made on a horizontally one-dimensional case for regular waves over sloping beds and for both regular and irregular waves over a ripple patch. Numerical results prove that the proposed model gives accurate results for both regular and irregular waves over rapidly varying topography.     

Diffraction of multidirectional random waves by multiple rectangular submarine pits

A numerical model is presented to predict the interaction of multidirectional random surface waves with one or more rectangular submarine pits. The water depth is assumed uniform and the method involves the superposition of diffraction solutions based on linearized shallow water wave theory obtained by a two-dimensional boundary integral approach. The incident wave conditions are specified using a discrete form of the Mitsuyasu directional spectrum. The present numerical model has been validated through comparisons with previous theoretical results for regular waves. Good agreement was obtained in all cases. Based on these comparisons it is concluded that the present numerical model is an accurate and efficient tool to predict the wave field around multiple submarine pits and navigation channels in many practical situations.     

剪切流中界面波的二阶Stokes波解

考虑了均匀剪切流场中强非线性界面波,建立了基于任意水深处速度而不是通常所用的平均速度为速度变量的模型,分析了其色散关系,并求得了各层速度的二阶渐近解和界面内波波面位移的二阶Stokes解,揭示了波流之间的非线性相互作用和界面波解之间的非线性相互作用。     

Seabed shear stress and bedload transport due to asymmetric and skewed waves

A simple conceptual formulation to compute seabed shear stress due to asymmetric and skewed waves is presented. This formulation generalizes the sinusoidal wave case and uses a variable friction factor to describe the physics of the boundary layer and to parameterize the effects of wave shape. Predictions of bed shear stresses agree with numerical computations using a standard boundary layer model with a k–ε turbulence closure. The bed shear stress formulation is combined with a Meyer-Peter and Müller-type formula to predict sheet flow bedload transport under asymmetric and skewed waves for a horizontal or sloping bed. The predictions agree with oscillatory water tunnel measurements from the literature.     

Probability distribution of surface slope for nonlinear random sea waves and calculation of whitecap coverage

Based on the nonlinear model of two-dimensional random sea waves, a statistical distribution of wave surface slope exact to the third order is derived by using the expansion of the characteristic function and direct calculations of each order moment. Based on the distribution of wave surface slope derived in this paper, a whitecap coverage is proposed by using the limit surface slope as a criterion of wave breaking. The whitecap coverage expressed by the model depends on three parameters which can be determined in principle by the linear wave spectrum and three kinds of wave-wave interaction.     

An integrated three-dimensional model of wave-induced pore pressure and effective stresses in a porous seabed: II. Breaking waves

The evaluation of the wave-induced liquefaction potential is particularly important for coastal engineers involved in the design of marine structures. Most previous investigations of the wave-induced liquefaction have been limited to two-dimensional non-breaking waves. In this paper, the integrated three-dimensional poro-elastic model for the wave-seabed interaction proposed by [Zhang, H., Jeng, D.-S., 2005. An integrated three-dimensional model of wave-induced pore pressure and effective stresses in a porous seabed: I. A sloping seabed. Ocean Engineering 32(5/6), 701–729.] is further extended to simulate the seabed liquefaction potential with breaking wave loading. Based on the parametric study, we conclude: (1) the liquefaction depth due to breaking waves is smaller than that of due to non-breaking waves; (2) the degree of saturation significantly affects the wave-induced liquefaction depth, and no liquefaction occurs in full saturated seabed, and (3) soil permeability does not only significantly affect the pore pressure, but also the shear stresses distribution.     

磨刀门拦门沙区域枯季波流共同作用近底切应力和泥沙运动研究

On the basis of the measurement data pertaining to waves, current, and sediment in February 2012 in the mouth bar of the Modaomen Estuary, the Soulsby formulae with an iterative method are applied to calculating bottom shear stresses （BSS） and their effect on a sediment resuspension. Swell induced BSS have been found to be the most important part of the BSS. In this study, the correlation coefficient between a wavecurrent shear stress and SSC is 0.86, and that between current shear stresses and SSC is only 0.40. The peaks of the SSC are consistent with the height and the BSS of the swell. The swell is the main mechanism for the sediment re-suspension, and the tidal current effect on sediment re-suspension is small. The peaks of the SSC are centered on the high tidal level, and the flood tide enhances the wave shear stresses and the SSC near the bottom. The critical shear stress for sediment re-suspension at the observation station is between 0.20 and 0.30 N/m2. Tidal currents are too weak to stir up the bottom sediment into the flow, but a WCI （wave-current interaction） is strong enough to re-suspend the coarse sediment.     

The retrieval of the nonlinear random waves from the non-Gaussian characteristics of the sea surface elevation distribution

In this paper, without recourse to the nonlinear dynamical equations of the waves, the nonlinear random waves are retrieved from the non-Gaussian characteristic of the sea surface elevation distribution. The question of coincidence of the nonlinear wave profile, spectrum and its distributions of maximum (or minimum) values of the sea surface elevation with results derived from some existing nonlinear theories is expounded under the narrow-band spectrum condition. Taking the shoaling sea wave as an example, the nonlinear random wave process and its spectrum in shallow water are retrieved from both the non-Gaussian characteristics of the sea surface elevation distribution in shallow water and the normal sea waves in deep water and compared with the values actually measured. Results show that they can coincide with the actually measured values quite well, thus, this can confirm that the method proposed in this paper is feasible.     

Scour below marine pipelines in shoaling conditions for random waves

This paper provides an approach by which the scour depth below pipelines in shoaling conditions beneath non-breaking and breaking random waves can be derived. Here the scour depth formula in shoaling conditions for regular non-breaking and breaking waves with normal incidence to the pipeline presented by Cevik and Yüksel [Cevik, E. and Yüksel, Y., (1999). Scour under submarine pipelines in waves in shoaling conditions. ASCE J. Waterw., Port, Coast. Ocean Eng., 125 (1), 9–19.] combined with the wave height distribution including shoaling and breaking waves presented by Mendez et al. [Mendez, F.J., Losada, I.J. and Medina, R., (2004). Transformation model of wave height distribution on planar beaches. Coast. Eng. 50 (3), 97–115.] are used. Moreover, the approach is based on describing the wave motion as a stationary Gaussian narrow-band random process. An example of calculation is also presented.