A note on the effects of a thin visco-elastic mud layer on small amplitude water-wave propagation

In this note we investigated the effects of a thin visco-elastic mud layer on wave propagation. Within the framework of linear water-wave theory, analytical solutions are obtained for damping rate, dispersion relation between wave frequency and wave number, and velocity components in the water column and mud layer. The wave attenuation rate reaches a maximum value when the mud layer thickness is about the same as the mud boundary layer thickness. Heavier mud has a weaker effect on the wave damping. However, the wave attenuation rate does not always decrease as the elastic shear modulus increases. In the range of small values for elastic shear modulus, the wave attenuation can be amplified quite significantly. The current solutions are compared with experimental data with different wave conditions and mud properties. In general, good agreements are observed.     

A linear Boltzmann equation to model wave scattering in the marginal ice zone

We present a linear Boltzmann equation to model wave scattering in the Marginal Ice Zone (the region of ocean which consists of broken ice floes). The equation is derived by two methods, the first based on Meylan et al. [Meylan, M.H., Squire, V.A., Fox, C., 1997. Towards realism in modeling ocean wave behavior in marginal ice zones. J. Geophys. Res. 102 (C10), 22981–22991] and second based on Masson and LeBlond [Masson, D., LeBlond, P., 1989. Spectral evolution of wind-generated surface gravity waves in a dispersed ice field. J. Fluid Mech. 202, 111–136]. This linear Boltzmann equation, we believe, is more suitable than the equation presented in Masson and LeBlond [Masson, D., LeBlond, P., 1989. Spectral evolution of wind-generated surface gravity waves in a dispersed ice field. J. Fluid Mech. 202, 111–136] because of its simpler form, because it is a differential rather than difference equation and because it does not depend on any assumptions about the ice floe geometry. However, the linear Boltzmann equation presented here is equivalent to the equation in Masson and LeBlond [Masson, D., LeBlond, P., 1989. Spectral evolution of wind-generated surface gravity waves in a dispersed ice field. J. Fluid Mech. 202, 111–136] since it is derived from their equation. Furthermore, the linear Boltzmann equation is also derived independently using the argument in Meylan et al. [Meylan, M.H., Squire, V.A., Fox, C., 1997. Towards realism in modeling ocean wave behavior in marginal ice zones. J. Geophys. Res. 102 (C10), 22981–22991]. We also present details of how the scattering kernel in the linear Boltzmann equation is found from the scattering by an individual ice floe and show how the linear Boltzmann equation can be solved straightforwardly in certain cases.     

A probability distribution for depth-limited extreme wave heights in a sea state

A model for the depth-limited distribution of the highest wave in a sea state is presented. The distribution for the extreme wave height is based on a probability density function (pdf) for depth-limited wave height distribution for individual waves [Méndez, F.J., Losada, I.J., Medina, R. 2004. Transformation model of wave height distribution. Coastal Eng, Vol. 50, 97:115.] and considers the correlation between consecutive waves. The model is validated using field data showing a good representation of the extreme wave heights in the surf zone. Some important statistical wave heights are parameterized obtaining useful expressions that can be used in further calculations.     

A comparison of several wave spectra for the random wave diffraction by a semi-infinite breakwater

A comparison of the diffraction of multidirectional random waves using several selected wave spectrum models is presented in this paper. Six wave spectrum models, Bretschneider, Pierson–Moskowitz, ISSC, ITTC, Mitsuyasu, and JONSWAP spectrum, are considered. A discrete form for each of the given spectrum models is used to specify the incident wave conditions. Analytical solutions based on both the Fresnel integrals and polynomial approximations of the Fresnel integrals and numerical solutions of a boundary integral approach have been used to obtain the two-dimensional wave diffraction by a semi-infinite breakwater at uniform water depth. The diffraction of random waves is based on the cumulative superposition of linear diffraction solution. The results of predicted random wave diffraction for each of the given spectrum models are compared with those of the published physical model presented by Briggs et al. [1995. Wave diffraction around breakwater. Journal of Waterway, Port, Coastal and Ocean Engineering—ASCE 121(1), 23–35]. Reasonable agreement is obtained in all cases. The effect of the directional spreading function is also examined from the results of the random wave diffraction. Based on these comparisons, the present model for the analysis of various wave spectra is found to be an accurate and efficient tool for predicting the random wave field around a semi-infinite breakwater or inside a harbor of arbitrary geometry in practical applications.     

Effect of free surface and strut on fins attached to a strut

An extensive experimental and computational investigation of the combined and separate effects of free surface and body on the lift characteristics of a pair of fins attached to a strut and fin alone is conducted. The results reveal that the free-surface effect becomes significant when the depth of submergence to chord ratio (H/c) is less than three. The effect of the strut is also realized for shallower depth of submergence of the fins through free-surface deformation leading to a significant change in the incidence angle of the flow to the fins. The numerical results based on the Higher Order Boundary Element Method with the linearized free-surface condition show good agreement with the experimental results for fin (foil) alone even at shallow submergence, but some discrepancies appear for the fin attached to the strut at higher speeds mostly due to the neglect of the nonlinear free-surface effect.     

Wave interaction with a submarine pipeline in clayey soil due to random waves

The wave pressure and uplift force due to random waves on a submarine pipeline (resting on bed, partially buried and fully buried) in clayey soil are measured. The influence of various parameters viz., wave period, wave height, water depth, burial depth and consistency index of the soil on wave pressures around and uplift force on the submarine pipeline was investigated. The wave pressures were measured at three locations around the submarine pipeline (each at 120° to the adjacent one). It is found that the wave pressure and uplift force spectrum at high consistency index of the soil is smaller compared to that of low consistency index. Just burying the pipeline (e/D=1.0) in clayey soil reduces the uplift force to less than 60% of the force experienced by a pipeline resting on the seabed (e/D=0.0) for I_c=0.33.     

一类典型模糊阵及其在传递闭包化简中的应用

本文研究模糊矩阵传递闭包的化简问题。通过定义 1类典型阵 ,给出传递闭包能够进一步化简的充要条件 ,为网络最大流分析提供了 1种新的模式。     

Distribution of nonlinear wave crests

The distribution of nonlinear wave crests is examined on the basis of a theoretical probability density previously given elsewhere (J. Eng. Mech. 120 (1994) 1009). Certain errors contained in the original theoretical density are corrected, and the corresponding exceedance distribution is derived. The resulting theoretical forms of the probability density and exceedance distribution are then slightly simplified and compared with nonlinear wave data gathered under hurricane conditions. The results indicate that the proposed theoretical forms describe the observed distributions of large wave crests better than the Rayleigh law. However, the quantitative accuracy of the predictions is somewhat poor, as is typical of approximate theories based on Gram–Charlier-type expansions.     

Wave runup on a concentric twin perforated circular cylinder

The regular wave interaction with a twin concentric porous circular cylinder system consisting of an inner impermeable cylinder and an outer perforated cylinder was studied through physical model and numerical model studies. The experiments were carried out on the twin concentric cylinder model in a wave flume to study the wave runup and rundown at the leading and trailing edges of the perforated cylinder. It was found that the maximum wave runup on the perforated cylinder is almost same as the incident wave height. The experimental results were used to develop the predictive formulae for the wave runup and rundown on the perforated cylinder, which can be easily used for design applications. The wave runup profiles around the perforated cylinder for different values of ka and porosities were studied numerically using Green's Identity Method. The results of the numerical study are presented and compared with the experimental measurements.