Scour below pipelines and around vertical piles in random waves

An approach by which the scour depth and scour width below a fixed pipeline and scour depth around a circular vertical pile in random waves can be derived is presented. Here, the scour depth formulas by Sumer and Fredsøe [ASCE J. Waterw., Port, Coastal Ocean Eng. 116 (1990) 307] for pipelines and Sumer et al. [ASCE J. Waterw., Port, Coastal Ocean Eng. 114 (1992) 599] for vertical piles as well as the scour width formula by Sumer and Fredsøe [The Mechanics of Scour in the Marine Environment, World Scientific, Singapore, 2002] for pipelines combined with describing the waves as a stationary Gaussian narrow-band random process are used to derive the cumulative distribution functions of the scour depths and width. Comparisons are made between the present approach and random wave scour data. Tentative approaches to related random wave scour cases are also suggested.     

Validation of the three-wave quasi-kinetic approximation for the spectral evolution in shallow water

This paper aims at validating the three-wave quasi-kinetic approximation for the spectral evolution of weakly nonlinear gravity waves in shallow water. The problem is investigated using a one-dimensional numerical wave propagation model, formulated in the spectral representation. This model includes both a nonlinear triad interactions term and a wave breaking dissipation term. Some numerical tests were carried out in order to show the importance of using the triad nonlinear term in wave propagation spectral models, particularly to describe both behavior of the spectral integral parameters and of the spectral shape evolution in shallow water depth. Furthermore; a comparison against different set of experimental observations was carried out. Comparing the numerical results with the experimental observations made it possible to show the modeling efficiency of the three-wave quasi-kinetic approximation.     

Wave forces on a seawater intake caisson

The wave force on a seawater intake structure consisting of a perforated square caisson of 400 mm×400 mm size encircling a vertical suction pipe of 160-mm diameter is investigated using physical model studies. The porosity of caisson was varied from 1.6 to 16.9%. Regular and random waves of wide range of heights and periods were used. It is found that the force ratio (ratio of the force on perforated caisson to the force on caisson with zero percent porosity) reduces to an extent of up to 60% with increase in porosity of the caisson from 1.6 to 16.9%. The force ratio was found to increase with increase in relative wave height and reduces with increase in relative width. Multiple regression analysis of the measured data points was carried out and predictive equations for wave force ratios are obtained both for regular and random waves. The results of this investigation can be used in the hydrodynamic design of perforated caissons, which are widely used as seawater intake structures.     

Calibration and verification of a spectral wind–wave model for Lake Okeechobee

A spectral wind wave model SWAN (Simulation WAves Nearshore) that represents the generation, propagation and dissipation of waves was applied to Lake Okeechobee. This model includes the effects of refraction, shoaling, and blocking in wave propagation. It accounts for wave dissipation by whitecapping, bottom friction, and depth-induced wave breaking. The wave–wave interaction effect also is included in this model. Measurements of wind and wave heights were made at different stations and different time periods in Lake Okeechobee. Significant wave height values were computed from the recorded data. The correlation between wind stress and significant wave height also was analyzed. A 6-day simulation using 1989 data was conducted for model calibration. Another 6-day simulation using 1996 data was conducted for model verification. The simulated significant wave heights were found to agree reasonably well with measured significant wave heights for calibration and verification periods. Agreement between observed and simulated values was based on graphical comparisons, mean, absolute and root mean square errors, and correlation coefficient. Comparisons showed that the model reproduced both general observed trends and short term fluctuations.     

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.     

Analysis of single and tandem cylinder data using an orthogonal Volterra model approach

The development of a definitive predictive model that accurately accounts for the nonlinear hydrodynamics and structural response behavior observed in arrays of closely spaced risers on deep water structures will require a more detailed understanding of this fluid–structure interaction. Through the analysis and interpretation of data from model basin tests on single and paired tandem cylinder configurations this study is directed at uncovering the nature of some aspects of this nonlinear response behavior using an orthogonal third-order Volterra technique that can delineate between linear, quadratic and cubic nonlinear frequency dependent behavior. As part of the analysis procedure the data was organized in input–output pairs that would provide logical groupings of the measured quantities. The data pairs presented in this study include wave excitation and inline cylinder displacement, wave excitation and transverse cylinder displacement, wave excitation and inline reaction force, and, upstream cylinder and downstream cylinder response. This information is presented in terms of spectral and coherence plots. The single cylinder data is presented as a means to contrast the behavior of the tandem cylinders. Both configurations were analyzed at two different pretensions adding another dimension to this investigation. It is shown that although a primary variable such as displacement may be more easily measured, pretension and force measurements provide an important key to our understanding of this difficult problem.     

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 tinite 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 detemained by the water depth and the wavenumber 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.     

On vertical velocity fluctuations and internal tides in an upwelling region off the west coast of India

Hourly fluctuations of vertical velocity in relation to components of flow and wind and temperature oscillations at a morring site in the shelf waters off the west coast of India are discussed. The vertical velocities were computed from a time series of vertical temperature profiles assuming that horizontal advection of temperature is negligible. The computed values at a depth of 40 m during the 72-h period of observation were of the order of 10⁻¹ to 10⁻²cm s⁻¹, with a mean value of −2·77 × 10⁻² cm s⁻¹ indicating a net upward movement of water. The computed vertical velocity showed fluctuations of about 2–3 h, in addition to weaker signals of about 12 h. Based on the spectral estimates, we speculate that these fluctuations of 2–3 h in the vertical velocity may be caused by the fluctuations in the along-shore wind. The oscillations of isotherms found in the temperaturedepth time series and the spectral estimates of temperature and cross-shore flow component showed a periodicity of about 12 h, which indicated the presence of semi-diurnal internal waves. The fact that these internal wave troughs were associated with the measured onshore flow suggested that the waves were propagating offshore. The computed stability parameters showed little evidence of instability or mixing. It was found that the isotherm troughs in the temperaturedepth time series at about 12-h period coincided with high vertical shear in the cross-shore direction and low values of Brunt Vaisälä frequency.