Showing papers in "Applied Ocean Research in 1999"

On the water impact of general two-dimensional sections

Abstract: We consider the analytic solution of the impact problem of a general two-dimensional body entering initially calm water. Of interest are the water splash-up height, the force history and the pressure distribution on the body. The potential-flow formulation of Wagner (Wagner, H. Math. Mech. 1932;12(4):193–215) is applied and extended to an arbitrary body section with the body boundary condition imposed on the exact wetted surface of the body. For wedges and circular cylinders, we derive closed-form solutions using conformal mapping for the boundary-value problem at any instant. These solutions reduce to those of Wagner in the small deadrise angle/shallow-body limit and are verified for the general case by the existing experiments and fully nonlinear numerical simulations. For ship-like sections, we develop a general scheme based on Lewis-form representations for which we also obtain analytic solutions. For illustration, the solution for a bow flare section is obtained which compares favorably with experiments. The present approach generalizes Wagner’s method to a wide class of body sections and is of immediate practical use in the study of ship slamming.

A note on finite depth second-order wave–wave interactions

Abstract: This note summarizes results which were obtained in an extension of existing deep-water wave–wave interaction theory to the second-order wave–wave interaction coefficients for finite depth.

Wave interactions with double slotted barriers

Abstract: The present article outlines the numerical calculation of wave interactions with a pair of thin vertical slotted barriers extending from the water surface to some distance above the seabed, and describes laboratory tests undertaken to assess the numerical model. The numerical model is based on an eigenfunction expansion method and utilizes a boundary condition at the surface of each barrier which accounts for energy dissipation within the barrier. Comparisons with experimental measurements of the transmission, reflection, and energy dissipation coefficients for partially submerged slotted barriers show excellent agreement and indicate that the numerical method is able to adequately account for the energy dissipation by the barriers.

On the estimation of Morison force coefficients and their predictive accuracy for very rough circular cylinders

Abstract: This paper makes an assessment of the various method that may be used to analyse experiment data on the force experienced by a circular cylinder in waves and combined wave and current flows to estimate drag and inertia coefficients for use in Morison's equation. Most of the widely used techniques are considered together with a weighted least squares approach for time domain analysis. A set of data obtained from experiments on heavily roughened circular cylinders of diameters 0.513 and 0.216 m in the Delta wave flume at De Voorst in Holland in waves and simulated current has been analysed in turn by all these techniques. The experiment data was split into two halves. The first was used for the analyses and the second was used to assess the predictive accuracy of Morison's equation. Using the force coefficients obtained from the different analysis techniques corresponding predicted force time series were constructed using the particle kinematics measured in the second parts of the data sets. These predicted time series were then compared with the corresponding measured force time histories. The root mean square error and the bias in the estimation of maximum force in each wave cycle are used as measures of predictive accuracy and as a basis for comparing the efficiency of the different analysis techniques. It was found that the weighted least square method generally gave the best predictive accuracy, but only by a small margin.

Deterministic wave model for short-crested ocean waves: Part I. Theory and numerical scheme

Abstract: A directional hybrid wave model (DHWM) has been developed for deterministic prediction of short-crested irregular ocean waves. In using the DHWM, a measured wave field is first decomposed into its free-wave components based on as few as three point measurements. Then the wave properties are predicted in the vicinity of the measurements based on the decomposed free-wave components. Effects of nonlinear interactions among the free-wave components up to second order in wave steepness are considered in both decomposition and prediction. While the prediction scheme is straightforward, the decomposition scheme is innovative and accomplished through an iterative process involving three major steps. The extended maximum likelihood method is employed to determine the directional wave spreading; the initial phases of directional free-wave components are determined using a least-square fitting scheme; and nonlinear effects are computed using both conventional and phase modulation methods to achieve fast convergence. The free-wave components are obtained after the nonlinear effects being decoupled from the measurements. Variety of numerical tests have been conducted, indicating that the DHWM is convergent and reliable.

A refined analytical analysis of submerged pipelines in seabed laying

Abstract: The paper analyzes the elastic deflection of submerged pipelines laid with a stinger by taking into account the overall effects of the ovalization of the cross section. The analysis is performed by means of a singular perturbation technique and the analytical solution obtained is shown to offer different advantages over the finite element method. Two examples demonstrate the effectiveness of the procedure by means of a comparison with results from other less refined analytical solutions and from the commercial finite element code Abaqus .

Dynamics of sand ripples and burial/scouring of cobbles in oscillatory flow

Abstract: The purpose of this paper is to present the results of a series of laboratory experiments aimed at better understanding (i) the dynamics of sand ripples formed in a wave-induced oscillatory flow and (ii) the influence of sand ripples on the behavior of solid objects (which are free to move) in steady oscillatory flow. This problem is closely related to the migration and burial/scouring of isolated cobbles/mines on a sandy floor by an oscillatory flow such as that occurs in coastal waters beyond the region of wave breaking. The aims of the study were (i) to mimic this process in laboratory experiments and (ii) to develop a physical understanding of the processes involved in the water motion and cobble and sandy surface interaction. The oscillatory flow was created in a long tank of rectangular cross-section using standing waves (first mode) of large amplitudes. Model cobbles (mostly disks) were placed on the sandy bottom and their subsequent behavior, the temporal evolution of the sandy bottom profile and the velocity field in water were observed. The main findings include (i) the demonstration that long-time changes of the bottom topography occur and this may lead to the periodic burial/unburial of cobbles and (ii) the scouring of the bedform surrounding the cobbles is relatively unimportant in the burial/unburial process.

Uncertainty in the estimation of the slope of the high frequency tail of wave spectra

Abstract: The uncertainty of the high frequency tail slope of wave spectra, as a result of the intrinsically random variability of wind generated waves and the estimation procedures of the wave spectra, is examined by using simulated and field measured wave records. It is shown that considerable uncertainty on the ‘true’ value of the slope exists due to the statistical variability of the spectral estimates. Furthermore, significant uncertainties are introduced both by the choice of the method of spectral estimation and by varying the number of degrees of freedom. The identification of these different sources of uncertainty and the quantification of their values in some representative cases are important for the correct interpretation of results from measurements programs aiming at establishing the correct slope of the high frequency tail of wave spectra.

On providing a reaction for efficient wave energy absorption by floating devices

Abstract: This paper investigates possible use of a heave/surge compensated on-board platform (block) to enable and optimize energy absorption by deep-water floating wave energy devices. The block forms one of the masses in a system of coupled, controlled oscillators. In the absence of control, favorable dynamic interaction leads to isolation of the block from hull heave or surge at one frequency, whereas control can extend this behavior to a range of frequencies. The paper presents a frequency-domain solution for an optimal power absorption problem of a single-mode floating device utilizing such a system. Results are used to address the more complicated problem of optimal power absorption by floating oscillating water column devices. Calculations based on published results for one such device are carried out in the frequency domain for four different situations representing various degrees of compromises to optimality. Conclusions on the effectiveness of the proposed system are drawn based on comparisons, and areas needing further work are pointed out.

A criterion for the automatic identification of multimodal sea wave spectra

Abstract: A simple and efficient procedure to automatically distinguish between uni-modal and multi-modal scalar spectra, which is consistent with the random nature of the spectral density estimations, is proposed. The suggested methodology is based on the logarithmic transformation of the spectral estimations. Examples that demonstrate the procedure are presented.

Task-related wave groups for seakeeping tests or simulation of design storm waves

Abstract: The chaotic wave field of a natural seaway can be decomposed into an infinite number of independent harmonic waves, and its spectrum follows from the associated wave amplitudes and frequencies. If superimposed with random phase we register the well-known irregular sea, which is characterized by its significant wave height and zero-up-crossing period. As rare events very high waves are observed accidentally. Since RAOs of wave/structure interactions are independent of the random phase shift between superimposing component waves this parameter can be selected arbitrarily to compose an optimum and short-duration transient wave train which allows the precise determination of all response amplitude operators within the relevant spectral range. Applications of the wave group technique are presented for: (i) standard seakeeping tests of stationary or moving (self-propelled) marine structures; (ii) simulation of design storm waves for the investigation of coastal and offshore structures. The paper illustrates the generation of task-related wave packets, the determination of the associated acceleration, velocity and pressure fields, as well as the related energy flux. Based on the dispersion relation the propagation behavior is exactly predictable. Consequently, the kinematics and dynamics of the wave field can be determined at any position and time. If the converging wave group approaches its concentration point the associated particle motions are analyzed by a nonlinear procedure using coupled Lagrangian expansion equations. The efficiency and the limitations of the transient wave technique are demonstrated by presenting typical test examples. These include the determination of the RAOs of stationary offshore structures and towed or self-propelled ships as well as the investigation of coastal structures in 100-year waves. As the entire process is deterministic, the action/reaction chains can be evaluated in detail. The paper demonstrates that the wave group technique is a reliable and efficient tool for all standard investigations related to wave/structure interactions, and opens a new area for the analysis of transient processes in the sea, e.g. dynamic stability of floating vessels or design wave impacts on coastal or offshore structures.

The effect of internal pipes on the fundamental frequency of liquid sloshing in a circular tank

Abstract: The article describes a theoretical investigation into the shift in fundamental frequency which arises when an array of pipes is placed in a circular tank. A tank of constant section is specified to enable the problem to be reduced to two dimensions. The associated velocity potential then satisfies the Helmholtz equation. A boundary element method is used to investigate the case of a tank with an arbitrary array of pipes and is verified by the analytical solutions for circular and annular tanks. Results are presented for several cases involving arrays of internal pipes and compared with predictions obtained using an approximate method.

Slow motion dynamics of turret mooring and its approximation as single point mooring

Abstract: The mathematical model for the nonlinear dynamics of slow motions in the horizontal plane of Turret Mooring Systems (TMS) is presented. It is shown that the TMS model differs from the classical Single Point Mooring (SPM) model, which is used generally to study the TMS dynamics. The friction moment exerted between the turret and the vessel, and the mooring line damping moment resulting from the turret rotation are the sources of difference between TMS and SPM. Qualitative differences in the dynamical behavior between these two mooring systems are identified using nonlinear dynamics and bifurcation theory. In two- and three-dimensional parametric design spaces, the dependence of stability boundaries and singularities of bifurcations for given TMS and SPM configurations is revealed. It is shown that the static loss of stability of a TMS can be located approximately by the SPM static bifurcation. The dynamic loss of stability of TMS and the associated morphogenesis may be affected strongly by the friction/damping moment, and to a lesser extent, by the mooring line damping. Nonlinear time simulations are used to assess the effects of these properties on TMS and compared to SPM systems. The TMS mathematical model consists of the nonlinear horizontal plane fifth-order, large drift, low speed maneuvering equations. Mooring line behavior is modeled quasistatically by submerged catenaries, including nonlinear drag and touchdown. External excitation consists of time independent current, steady wind, and second-order mean drift forces.

On the solution of the dispersion relation for water waves

Abstract: A range of analytic approximations is derived for the roots of the water wave dispersion relation, by formulating it as an eigenvalue problem and using standard variational methods in conjunction with the Rayleigh–Ritz procedure. The analytic approximations may be enhanced by a numerical iterative procedure derived by means of the same process. Thus, for example, a relatively simple explicit expression is derived for the real, positive root of the dispersion relation, which is in error by less than 0.1% across the whole frequency range; two iterations of this approximation give the root to machine accuracy.

Wave deformation by a submerged flexible circular disk

Abstract: The interaction of incident monochromatic waves with a tensioned, flexible, circular membrane submerged horizontally below free surface is investigated in the frame of three-dimensional linear hydroelastic theory. The velocity potential is split into two parts, i.e. the diffraction potential representing the scattering of incident waves by a rigid circular disk and the radiation potential describing motion induced waves by elastic responses of the flexible membrane. The fluid domain is divided into three regions, and the diffraction and radiation potentials in each region are expressed by the Fourier-Bessel series. The displacement of the circular membrane is expanded with a set of natural functions, which satisfy the membrane equation of motion and boundary conditions. The unknown coefficients in each region are determined by applying the continuity of pressure and normal velocity at the matching boundaries. The results show that various types of wave focusing are possible by controlling the size, submergence depth, and tension of the membrane.

Deterministic wave model for short-crested ocean waves: Part II. Comparison with laboratory and field measurements

Abstract: The directional hybrid wave model (DHWM) is applied to one set of laboratory wave measurements and two sets of ocean wave measurements for the deterministic prediction of wave properties in the vicinity of measurements. The DHWM first decomposes a measured wave field into its free-wave components and then predicts the wave properties based on the decomposed free-wave components. The comparisons between the predicted signals and the corresponding laboratory measurements show excellent agreement. The discrepancies between the predicted signals and the corresponding field measurements increase in comparison with those between the predicted and laboratory-measured signals. However, the agreement between the predicted and the field-measured signals remain satisfactory. These examples indicate that the DHWM is capable of predicting wave properties of a short-crested ocean wave field in a deterministic manner. Hence, it provides a robust method for ocean wave measurements and their data analysis. It is expected that the DHWM will have many applications to ocean science and engineering in the near future.

On the measurement of directional wave spectra at the southern Brazilian coast

Abstract: The detailed reconstruction of the directional spectrum of wind waves from measurements of the wave field is an essential requirement for several applications, including the numerical modeling of wave evolution. Three reconstruction techniques that provide estimates of the directional distribution function DOf;uU; given the one-dimensional frequency spectrum, are compared using data from a coastal locality at the southern Brazilian coast. The techniques are the maximum entropy method (MEM), the Fourier Expansion Method using a cos 2 type function (FEMcos) and the Fourier Expansion Method using a sech type function (FEMsech). The main patterns of the wave climate at the study site are qualitatively assessed. Three main sea states, including swell, transition between local sea and swell, and directionally bimodal wind sea, are identified. Time series from three events associated with the main sea states provide test cases for inter comparison of the three reconstruction techniques. Maximum entropy estimates of DOf;uU provide results that are more consistent than those obtained from the two FEM techniques in all cases considered. q 1999 Elsevier Science Ltd. All rights reserved.

On combination formulae for the extremes of wave-frequency and low-frequency responses

Abstract: One special feature in moored floating platforms is the co-existence of the first-order wave-frequency (WF) response and the second-order low-frequency (LF) resonant response. Non-linear properties inherent in moored floating platforms cause the platform motions and mooring cable tensions to be non-Gaussian (not normal) distributed, both for the WF and for the LF components. As the LF and the WF components are not independent, it is important and necessary to find a simple, reliable and yet physically sound technique to estimate their combination. In this paper, on the basis of some model test results, different combination formulae are compared and a formula considering WF and LF correlation effects is suggested. A simple approach is also proposed to estimate the correlation factor.

The motion of a rigid body impelled by sea-wave impact

Abstract: A wave breaking against a sea wall causes high pressure gradients to act along the sea bed, pushing objects away from the wall. This situation is modelled using pressure impulse theory to show that, for a large object near a sea wall, the impulsive force due to the wave will move the object. This force can be found, given knowledge of the added mass and volume of an object. In particular, if the wall is thought of as a plane, gently sloping beach, then this theory may explain how shingle beaches are graded according to the size of the shingle, with larger boulders being moved farthest by the impact of a wave. In order to obtain estimates for the distances moved up, or down, the beach, a single boulder is treated as a spherical body which is free to move.

Water wave scattering by a submerged thick wall with a gap

Abstract: This article is concerned with scattering of surface water waves by a thick submerged rectangular wall with a gap in finite depth water. Multi-term Galerkin approximations involving ultraspherical Gegenbauer polynomials for solving first kind integral equations are utilised in the mathematical analysis to obtain very accurate numerical estimates for the reflection coefficient, which are depicted graphically against the wave number.

A comparison of a heuristic wave drift damping formula with experimental results

Abstract: This paper reviews several approaches to wave drift damping experienced by floating bodies. A heuristic approach first introduced by Aranha giving the wave drift damping tensor for the surge and sway modes of motion in finite depth is used. Results for the surge wave drift damping are compared with experimental results from model tests. These tests were carried out with three different floaters, one tanker and two barges in different water depths. Close agreement is founf for the tanker case. Some discrepancies are observed for the two barges. Although the theoretical foundations of the Aranha formula are not completely understood, it nevertheless provides reasonable estimates, which are quite valuable for engineering applications in the offshore industry.

A new representation for the free-surface channel Green’s function

Abstract: A new representation is derived for the free-surface Green’s function, appropriate to water wave problems in channels of constant depth and width, which is rapidly convergent throughout the fluid domain. The new representation depends on two arbitrary positive parameters a and a , and by varying these parameters the convergence characteristics of this new representation can be altered. Letting a and a tend to zero results in the known eigenfunction expansion. The results of computations are presented showing the accuracy and efficiency of the new representation.

On the relationships between the mean wavelength and wave-period of wind waves in deep water

Abstract: Relationships between the mean wavelength and mean wave-period of wind waves are derived for fetch-limited and fully developed seas. The derivations start from the Rice solution of zero-crossing problem and use the JONSWAP and Pierson–Moscowitz spectra, respectively. The spectral moments of order 4 involved in the derivations are estimated through a time-averaging technique. Experiments were conducted in a wind-wave channel. Comparisons between the relationships and the experimental results show a favorable agreement.

The propagation of water waves along a channel of variable width

Abstract: This paper studies surface waves in a channel with corrugated sidewalls in water of constant depth according to linear theory. Waves propagating along the channel encounter a finite patch of step-like corrugations in the channel walls. The main method of solution employed is one of expansion in terms of eigenfunctions in each region and matching them at the boundaries between regions. It is found that the equation proposed by Liu in 1987 gives excellent predictions of the reflected energy flux for small-amplitude corrugations in a narrow channel (but not in more general circumstances). For channels wider than half a wavelength of the incident wave, at least one higher mode will be propagating rather than evanescent. These higher modes can transport energy away from the irregularities, thus invalidating approaches to the problem which ignore them. In some circumstances, an incident wave may be totally reflected from just a single indentation in the channel wall. The technique is also used to study channels with continuously-varying wall profiles by approximating such profiles by a series of steps.

Turbidity currents generated by seafloor impact of geotextile fabric containers

Abstract: The disposal of waste material via a geosynthetic fabric container (GFC) may produce a turbidity current when the GFC impacts with the seafloor. Under this heretofore unrecognized scenario, rupture of a GFC could result in dispersal of contaminants over the seafloor by the turbidity current for far greater than expected distances. Simple estimates indicate that a turbidity current could carry entrained contaminants several kilometers from the GFC impact site.