Prediction of impact pressure induced by breaking waves on vertical cylinders in random seas

This paper presents a method to statistically predict the magnitude of impact pressure (including extreme values) produced by deep water waves breaking on a circular cylinder representing a column of an ocean structure. Breaking waves defined here are not those whose tops are blown off by the wind but those whose breaking is associated with steepness. The probability density function of wave period associated with breaking waves is derived for a specified wave spectrum, and then converted to the probability density function of impact pressure. Impacts caused by two different breaking conditions are considered; one is the impact associated with waves breaking in close proximity to the column, the other is an impact caused by waves approaching the column after they have broken. As an example of the application of the present method, numerical computations are carried out for a wave spectrum obtained from measured data in the North Atlantic.     

Wave run-up on slender circular cylindrical foundations for offshore wind turbines in nonlinear random waves

A practical method for estimating the wave run-up height on a slender circular cylindrical foundation for wind turbines in nonlinear random waves is provided. The approach is based on the velocity stagnation head theory and Stokes second order wave theory by assuming the basic harmonic wave motion to be a stationary Gaussian narrow-band random process. Comparisons are made with measurements by De Vos et al. (2007), and some of the highest wave run-up events that were predicted agree with those measured.     

Dynamic pressures on inclined cylinders due to freak waves

The dynamic pressure distribution around a cylinder tilted along and against the principal wave direction is measured. The cylinder was exposed to the action of random waves in the presence and absence of extreme waves. Six inclinations from the vertical plane, three along and three against the wave direction, were considered. The cylinder in upright position was also studied. The variation of dimensionless peak pressure (pressure maximum/average highest one-third wave height, H_1/3) with the relative wave height (maximum wave height/H_1/3) for locations facing the wave and at the rear of the cylinder for different angles of inclinations of the cylinder are reported for the two kinds of waves mentioned earlier. The statistical properties of the different asymmetries in the pressure traces are also discussed.     

In-line response of vertical cylinders in regular and random waves

The in-line response of a vertical flexibly mounted cylinder in regular and random waves is reported.Both theoretical analyses and experimental measurements have been performed.The theoretical predictions are based on the Morison equation which is solved by the incremental harmonic balance method.Experiments are then performed in a wave flume to determine the accuracy of the Morison equation in predicting the in-line response of the cylinder in regular and random waves.The interaction between waves and vibrating cylinders are investigated.     

Numerical modeling of wind waves generated by tropical cyclones using moving grids

A version of the WAVEWATCH III wave model featuring a continuously moving spatial grid is presented. The new model option/version is intended for research into wind waves generated by tropical cyclones in deep water away from the coast. The main advantage of such an approach is that the cyclones can be modeled with spatial grids that cover much smaller areas than conventional fixed grids, making model runs with high spatial resolution more economically feasible. The model modifications necessary are fairly trivial. Most complications occur due to the Garden Sprinkler effect (GSE) and methods used to mitigate it. The basic testing of the model is performed using idealized wind fields consisting of a Rankine vortex. The model is also applied to hurricane Lili in the Gulf of Mexico in October 2002. The latter application shows that the moving grid approach provides a natural way to deal with hurricane wind fields that have a high-resolution in space, but a low resolution in time. Although the new model version is originally intended for tropical cyclones, it is suitable for high-resolution modeling of waves due to any moving weather pattern.     

Interaction between waves and an array of floating porous circular cylinders

The present study theoretically as well as experimentally investigates the interaction between waves and an array of porous circular cylinders with or without an inner porous plate based on the linear wave theory.To design more effective floating breakwaters,the transmission rate of waves propagating through the array is evaluated.Each cylinder in the array is partly made of porous materials.Specifically,it possesses a porous sidewall and an impermeable bottom.In addition,an inner porous plate is horizontally fixed inside the cylinders.It dissipates the wave more effectively and eliminates the sloshing phenomenon.The approach suggested by Kagemoto and Yue(1986) is adopted to solve the multiple-scatter problem,while a hierarchical interaction theory is adopted to deal with hydrodynamic interactions among a great number of bodies,which efficiently saves computation time.Meanwhile,a series of model tests with an array of porous cylinders is performed in a wave basin to validate the theoretical work and the calculated results.The draft of the cylinders,the location of the inner porous plate,and the spacing between adjacent cylinders are also adjusted to investigate their effects on wave dissipation.     

Directional energy distribution of wind waves

Two-dimensional ocean wave spectrum developing under the atmospheric surface pressure fluctuations is linearly correlated with that of wind pressure itself, so that angular distribution of energy of ocean surface waves can be determined by directional properties of surface pressure fluctuations with the same frequency to the surface wave.From empirically determined spectral formula of the atmospheric surface pressure fluctuations the coefficients of Fourier series expanded around mean direction of wind are analytically integrated, from which r.m.s. angular distribution, spectral peakedness and long-crestedness are calculated, compared with previously proposed empirical formulae and observations carried out by ultrasonic current meter.     

Inelastic instability of circular corrugated cylinders under external hydrostatic pressure

The paper presents an experimental study on six circular corrugated cylinders which were tested to destruction under external hydrostatic pressure. The results obtained from these vessels, together with the results obtained from elsewhere, were used to provide a design chart. The design chart appears to be suitable for designing these vessels to guard against inelastic instability.     

Interaction of regular waves with a group of dual porous circular cylinders

Diffraction of linear waves around a group of dual porous cylinders consisting of a thin and porous outer cylinder with an impermeable inner cylinder is investigated analytically based on the eigenfunction expansion method proposed by Spring and Monkmeyer [Spring BH, Monkmeyer PL. Interaction of plane waves with vertical cylinders. In: Proceedings 14th international coastal engineering conference. 1974. p. 1828–47] and further modified by Linton and Evans [Linton CM, Evans DV. The interaction of waves with arrays of vertical circular cylinders. Journal of Fluid Mechanics 1990;215:549–69]. The present formulation is an extension of the work of Wang and Ren [Wang KH, Ren X. Wave interaction with a concentric porous cylinder system. Ocean Engineering 1994;21(4):343–60], wherein; the interaction of linear waves with a single concentric porous cylinder system was studied. This paper aims at investigating the influence of multiple interactions between the cylinders in the group on the hydrodynamic wave forces, wave run-up and free-surface elevation in their vicinity. Further, the study focuses on the variation of the forces and run-up on the individual cylinders within the group compared to that on isolated cylinders.     

Radiation and scattering of surface waves by a group of submerged,horizontal, circular cylinders

One of the major methods available for investigating the interaction of water waves with arbitrarily shaped structures is based on the classical theory of Green's functions. For multiple bodies, however, this technique can become expensive in terms of both computer storage and execution time and it is desirable for special geometrics where possible, to seek simpler methods. In this paper, the radiation and scattering of surface waves by a group of parallel, horizontal, circular cylinders, submerged in deep water is studied using a method involving multipole potentials. The method is developed for any number of submerged, parallel, horizontal cylinders with arbitrary positions and radii. In particular, hydrodynamic coefficients are determined for various configurations of two and three cylinders and a comparison is made with results obtained for a cylinder in isolation.     

Inelastic shell instability of thin-walled circular cylinders under external hydrostatic pressure

This paper reports on experimental work carried out on nine thin-walled circular cylinders which were tested to destruction under external hydrostatic pressure. Seven of the cylinders failed through non-symmetric bifurcation buckling and two failed through axisymmetric collapse. The results were used from these tests, together with the results from other experiments, to produce a design chart which could be used for designing against the occurence of elastic and inelastic shell instability.     

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.     

Scattering of surface waves by submerged cylinders

A train of surface waves is normally incident upon a cylinder that is totally submerged in a body of deep water. Details are given for the cases of circular or elliptic cross-sections, with estimates for the transmission and reflection constants when the cylinder is many wavelengths below the surface. Corresponding results are suggested for arbitrary smooth cylinders.     

Reflection of surface waves by submerged cylinders

Reflection from submerged cylinders are studied by means of integral equations. By expressing the solution as a distribution of vortices, the integral equations become non-singular for closed contours. It is shown that the method gives a short and easy proof for the classical result that no reflection occurs for the circular cylinder. The reflection power for the elliptic contour and the flat plate are studied when the bodies are situated deeply below the surface.     

Edge waves generated by atmospheric pressure disturbances moving along a shoreline on a sloping beach

Edge waves generated by moving atmospheric disturbances parallel to the shoreline are investigated. Following a standard transformation method, an analytical expression of the surface elevation is derived, which consists of an infinite number of modes. Each mode is expressed as the sum of three singular integrals. Using the contour integration method, these singular integrals are converted to regular integrals, which are evaluated by numerical integration methods. The numerical results of two atmospheric pressure distributions studied by Greenspan (1956) are presented, and the resonance conditions are discussed.     

Dynamic pressures and run-up on semicircular breakwaters due to random waves

The dynamic pressures due to random waves of predefined spectral characteristics exerted on a semicircular breakwater model at five different elevations along the depth are measured. In addition, the wave run-up on the model and its reflection characteristics are measured. The results on the variation of the frequency pressure spectra along the depth and the run-up spectra are reported in this paper. The average spectral characteristics as well as statistical properties of the above two parameters are presented. The average reflection coefficient is reported as a function of the wave steepness, described as the ratio of the significant wave height to the square of the peak period.     

Long internal waves in the Tropical Atlantic ocean generated by periodic air pressure fluctuations

Taking into consideration stratification, the mean current velocity, and the tangential wind stress expressed in terms of air pressure fluctuations, we have derived iteration formulae and have performed computations of the amplitudinal characteristics of oceanic internal waves generated by air pressure waves of semi-diurnal and 4-day long periodicity propagating over the Tropical Atlantic Ocean. It has been demonstrated that such periodicity and wavelengths may contribute to the generation of long-amplitude internal waves, whose intensity is largely dependent on the direction of atmospheric wave propagation.Translated by Vladimir A. Puchkin.     

Long-term distribution of seabed shear stresses beneath random waves

The long-term distribution of seabed shear stresses under random waves is presented. The approach combines short-term distribution of maximum bottom shear stresses with a joint frequency table of significant wave height and peak period. An example of application is given where the long-term probability of exceeding a given level of the maximum bottom shear stress in the central North Sea is presented. The example includes estimation of the return period of the critical shear stress for sheet flow conditions, as well as the bottom shear stresses associated with the 1, 10 and 100 years return periods.