Irregular Wave Motion Research Articles

Nonlinear Dynamics of Nearshore Irregular Waves: A Three-Dimensional Numerical Model and Its Verification

A three-dimensional numerical model based on the potential wave theory is developed for nonlinear irregular wave motion. The σ-transformation is employed to map the irregular and time-dependent domain of definition of the physical problem onto a strip of unit width so as to facilitate the implementation of the free surface and bottom boundary conditions. The finite difference method is used to solve the governing equations in the mapped coordinates. Non-reflective wave-generation is realized by combining virtual sources and a sponge layer. The numerical model is verified by the known solutions for nonlinear regular and irregular waves in water of constant depth. Standing waves in front of a vertical wall, runup of long waves on a sloping beach, and wave decomposition phenomenon over submerged bars are also studied. The model is also applied to a three-dimensional problem of nonlinear wave transformation over an elliptical shoal. The computational results are shown to agree well with the experimental data.

Prediction of Extreme Ship Motions in Irregular Waves

AbstractThe occurrence of indirectly excited large amplitude roll motions of ships is investigated under the influence of a time‐varying righting lever curve in waves. In order to account for the irregular character of ocean waves appropriately, the ship motions are described within the framework of nonlinear dynamics and stochastic process theory. The analysis of roll motions in regular waves provides a qualitative understanding of the occurrence of unpredictable large amplitude roll motions as observed in ocean waves. However, quantitative information on the rolling behavior in irregular waves may be retrieved only from a probabilistic analysis. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Improved Understanding of the Nonlinear Properties of Ionization Instabilities in Plasmas

AbstractIn this paper we review our experimental and theoretical investigations of ionization waves in a low‐pressure discharge of neon. The main results are connected with the transition between regular and irregular wave motions. The experimental observed stability boundaries can well be understood within the hydrodynamic model. The point is the explanation of the experimentally observed mode transitions by means of a quintic amplitude equation of the Ginzburg‐Landau type. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

SEAKEEPING OF A FAST DISPLACEMENT CATAMARAN

The paper presents a complex method for the calculation of pitch and heave of a fast displacement catamaran. It incorporates speed factors, interference of catamaran hulls, stabilization factors and possibility to apply different stabilization cases including a stabilizer activation possibility. In the method the possibility to evaluate catamaran motions in irregular waves is also included. On the base of the presented method the computer program is developed and applied to calculate seakeeping characteristics of a catamaran stabilized with a fore passive wing. The results of calculation are in good compatibility with the experimental model tests of this catamaran in irregular waves. The calculation method could be effectively applied in the design stage of fast displacement catamarans or of fin stabilizers determining their effectiveness.

Sand Suspension and Transport on Equilibrium Beach

A time-dependent cross-shore model for sand suspension and transport in the surf zone on a beach is compared with an irregular wave experiment that was conducted on an equilibrium terraced beach, consisting of fine sand in a wave flume. The measured free surface elevations and cross-shore velocities dominated by irregular wave motions are predicted within errors of the order of 20%. The measured sand concentrations dominated by intermittent high suspension events are predicted only within a factor of about two, because this ID numerical model does not account for sand suspension processes due to eddies and turbulence generated by irregular breaking waves. The computed net cross-shore sediment transport rate is relatively small and is not zero when the net rate must be zero for the equilibrium beach. Relatedly, the computed difference between the time-averaged sand suspension and settling rates is relatively small and is not zero. A better understanding of sand suspension processes will be required to predict the small net rates more accurately.

A theoretical and experimental investigation of indirectly excited roll motion in ships

The phenomenon of indirectly exciting the roll motion of a vessel due to nonlinear couplings of the heave, pitch and roll modes is investigated theoretically and analytically. Two nonlinear mechanisms that cause large-amplitude rolling motions in a head or following sea are investigated. The first mechanism is internal or autoparametric resonance and the second is parametric resonance. The energy put into the pitch and heave modes by the wave excitations may be transferred into the roll mode by means of nonlinear coupling among these modes; thus, the roll can be indirectly excited. As a result, a ship in a head or following sea can spontaneously develop severe rolling motion. In the analytical approach, the method of multiple scales is used to determine a system of nonlinear first-order equations governing the modulation of the amplitudes and phases of the system. The fixed-point solutions of these equations are determined and their bifurcations are investigated. Hopf bifurcations are found in the case of two-to-one internal resonance. Numerical simulations are used to investigate the bifurcations of the ensuing limit cycles and how they produce chaos. Experiments are conducted with tanker and destroyer models. They demonstrate some of the nonlinear effects, such as the jump phenomenon, the subcritical instability, and the coexistence of multiple solutions. The experimental results are in good qualitative agreement with the results predicted theoretically.

A Study on the Sloshing Phenomena of Membrane type LNG Carrier in the Time Domain

Sloshing in the liquefied natural gas (LNG) carrier occur due to the large dimension of the tank and the characteristics of the liquefied cargo. The description of nonlinear fluid flow and random tank motion in irregular waves are required to predict the sloshing phenomena. A numerical code adopting SOLA-VOF scheme has been developed to analyse sloshing flow. For the ship motion analysis 3D panel method is applied and the results are compared with those of ABS class. Furthermore, to evaluate sloshing load in the directional waves, this study used ISSC directional wave spectrum with cosine square directional spreading function. Ship motion time histories are used as the input data of sloshing calculation. We performed sloshing analysis for No.2 tank of 138K LNG carrier with fully loaded condition. Higher sloshing responses are predicted on head see where the sloshing peak pressures are inversely proportional to the zero crossing wave periods than the other seas in high filling and severe see conditions. The calculated maximum peak pressures considering the cushioning effects of corrugated membrane in head see can be used as the external forces for the structural analysis.

Fundamental Study on Laminar Boundary Layer Characteristics under Irregular Waves

Laminar boundary layer behavior under irregular wave motion has been investigated in this paper through numerical methods. The irregular wave velocity has first been generated and later used for flow computation in the boundary layer through low Reynolds number κ-ε model. The generation of irregular wave velocity shows a satisfactory result when compared with input spectral properties. Obtained k-ε model results have then been utilized for detailed analysis of time variation of bottom shear stress with freestream velocity. Model results show that the bottom shear stress is more dominated by high frequency component waves than that for velocity. It is also very sensitive to freestream velocity variations and does not always respond in the same way to similar velocity conditions. A comparison of irregular wave bottom shear stress with that of monochromatic waves shows that the significant bottom shear stress closely corresponds to that of sinusoidal wave computed with the highest two-third of wave heights (H2/3).

係留船の長周期動揺に関する数値シミュレーション

Slow drift ship motions in irregular waves can be an important and practical problem. The large horizontal oscillations cause large forces in mooring lines, which may break in extreme cases, and difficulties in cargo handling even in less extreme sea state. This paper deals with a mathematical model of first- and second-order ship motions in irregular waves. Firstly, the first-order problem is calculated by the boundary integral equation method using Green's function. First-order quantities calculated there are then used as input to the second-order model based on the perturbation method. Both models derived from potential theory, are fully three-dimensional, and include the effect of a flat sea bed and arbitrary shape of the floating body. Some details about the model are given in the first section. There is also an examination of the facet sizes required for accurate estimation of second-order forces. The section after presents numerical results of second-order wave forces compared with a physical model of a barge. In the final section, the verification of the model is continued by comparisons between ship motions, including long period oscillations, predicted using the mathematical model and movements measured in physical model tests.

Time Simulation of Water Shipping for a Ship Advancing in Large Longitudinal Waves

The technique of time-domain numerical simulation for the occurrence of water shipping on board in head waves is presented. The nonlinear effects of the large-amplitude motion are treated. These nonlinear factors include the effect of large wave amplitude, large ship motion, the change of hull configuration below the free surface and the nonlinear resultant wave. Therefore, the variation of the potentials and the hydrodynamic coefficients for a ship at each time step must be carefully treated. While handling the determination of the instantaneous wave surface around the ship hull, the complete incident, diffracted, and radiated wave system is used rather than the incident wave only. The complexity of the ship speed effect on the related terms is also treated at each time step, especially for the radiation problems. An experimental setup is also designed to measure the motion response and the relative motion, and comparisons are made. The results show excellent agreement and the validity of the theory is confirmed. The successful development of the present technique can be extended to analyze the dynamic stability, capsize phenomena, and ship motion in irregular waves

Development of Expression for Estimating Bow Freeboard and Assessment of the 1966 Load Line Convention

This paper discusses the development and application of a new regression equation for the bow freeboard which consists of the various parameters indicating the ship's principal particulars and the hull form features. The response characteristics of relative bow motion are obtained for 67 existing ships in regular waves, based on strip theory. Using these response characteristics of the 67 ships, a regression equation is introduced to express the magnitude of the relative bow motion in irregular waves. Using the regression equation, the relation between bow freeboard and deck wetness probability can be easily derived under any given sea conditions. This method is used for assessment of the current formula of the 1966 Load Line Convention and the Chinese formula recently proposed at SLF/IMO.

Seakeeping

It is well known that ship performance is degraded in rough weather. In moderately severe conditions every task on board the ship will take longer than it does in calm weather. The passengers and crew may be seasick and they will have to take more care when moving around the ship to avoid injury. The physical performance of mechanical and electrical systems may also be reduced if the ship motions are severe. Cargo may be damaged and this may also be considered as a reduction in performance. In extreme conditions, the ship may capsize or founder and this is, of course, the ultimate loss of performance. The aim of research in seakeeping is, or should be, to develop techniques of predicting the degradation of performance a ship will experience in rough weather. If this can be achieved it will enable the ship designer to eliminate unsatisfactory and unsafe ships at an early stage in the design process. The paper begins by summarizing the standard techniques for predicting the motions a ship will experience in rough weather. These are based on well-known strip theories coupled with superposition techniques for inferring the statistics of the motions in irregular waves from the regular wave transfer functions. These techniques are quite well validated for conventional monohull ship motions in the vertical plane but predictions of motions in the lateral plane are rather less reliable and further work is needed in this area. Accurate predictions of the irregular motions in realistic sea states are only one step in achieving the ultimate goal of predicting the rough-weather performance of new designs of ships. We also need to estimate the maximum permissible levels of the motions (usually known as seakeeping criteria). There are, in principle, no universally applicable criteria. They depend on the activities within the ship while it is engaged in a given mission and also on the type of equipment used. We therefore need to quantify the way in which the performance of the various sub systems or tasks which make up the ship mission degrade in rough weather. Ideally the first step should be to examine each task (or at least a representative selection of the important tasks) and to study the way in which the performance degrades. This will allow the motions (or other rough-weather phenomena) which are important for that particular task to be identified. It is then necessary to determine the maximum permissible levels of these motions by simulation, questionnaires, trials or even guesswork. Finally there is a need to develop universally acceptable measures of performance. Ideally these might include elements of the time required to complete a task (in relation to the time required in calm weather) as well as the quality of the result.

Surface waves due to resonant horizontal oscillation

Experiments on surface waves were made using a cylindrical container oscillated horizontally with the period T close to that associated with the two known degenerate modes. Outside a certain region in the (T,x0)-plane, where x0 is the amplitude of the forcing displacement, surface waves exhibit either of the two kinds of regular motions whose amplitudes are constant. Within this region, however, the wave amplitude slowly changes, expressing the irregular or periodic motion of surface waves. In order to analyse these motions in detail, the slow evolution of four variables associated with the amplitudes and phases of the two modes is computed from the free-surface displacement at two measuring points. It is shown that the most common attractor corresponding to the irregular wave motion is the strange attractor with a positive maximum Liapunov exponent and a correlation dimension of 2.1–2.4. Furthermore, another kind of chaotic attractor and a few periodic orbits are found in a small parametric region. The route to chaos associated with period-doubling bifurcation is also observed. The above experimental results are compared with the solutions to weakly nonlinear evolution equations derived by Miles. We find that the equations can explain well many of the experimental results on regular and irregular wave motions. In particular, the most common chaotic attractors both in the experiments and in the theory have similar shapes in a phase space, and also yield similar values for maximum Liapunov exponents and correlation dimensions.

TWO DIMENSIONAL FOURIER SPECTRUM OF TURBULENT IONIZATION WAVES

The turbulence of unstable ionisation waves often takes place in the positive column of low current and low pressure discharge in noble gases. Experimentally, the neon discharge is abounding in various mechanisms leading to a loss of wave coherence and to the onset of strong irregular wave motion t1,

まき網漁船(116トン型)の動揺について-II : 横動揺の計算値と実測値の比較

It is well known that if we obtain the wave spectrum in a suitable form and the theoretical response characteristics of the ship to the regular waves, it is possible to compute the spectrum of ship motions. In this report, the author calculated the ship rolling motion in irregular waves and compared it with the measured motion. The wave spectrum applied in this calculation were obtained using the Pierson-Moskowitz wave spectrum for the not fully arisen wave, and assumed that the wave spectrum have maximum energy at the natural frequency of the ships rolling. Basic equation for the rolling motion is shown in formula (1). The calculated spectra obtained in this way are compared in Fig. (3) with spectra computed from the actual rolling motion which was measured during the trials at a speed of 8kts on three headings to the dominant wave direction. The statistical values of ship rolling calculated using the calculated roll spectra, are compared with measured values in Figs. (5)〜(6). The agreement between calculated and measured results is reasonable good, although the theory tends to under-estimate the motion in bow waves and to over-estimate it in quartering waves.

Model Experiments on Capsize and Its Prevention For a Small Fishing Boat in Waves

There have been frequently occured miserable accidents of capsize for small fishing boats in the northern sea area near Japan, which were attended in the most cases with loss of human lives. Such accidents occured on the salmon fishing boats in high percentage in comparison with others.The purpose of this paper is to investigate the important factors affecting to capsize for such a small fishing boat as well as the effectiveness of the mean for preventing the accidents, through the model experiments in heavy seas.In the experiments, the 1/7 scale model was navigated in regular and irregular waves of high steepness generated in the model basin so that the capsize of the model could be expected to occur at some special conditions of the model and sea.The model ship was equipped with the weight shifting device for simulating cargo shift which could occur by heavy rolling motion of ship and would promote the capsize, while, on the other hand the inflatable rubber bulges were also attached on the both sides of the model hull which will lend an additional buoyancy and the righting moment to the ship in the emergency cases.A great number of running was carried out in the experiments under the various ship conditions as well as sea conditions, and as the results some capsizing phenomena were observed in case of poor stability condition. It was deduced through analysis of the experiments that the trapped water on deck with cargo shift act most effectively to capsize the vessel in beam and quartering seas, while the inflated bulges were so efficient to prevent the capsize that no capsize was observed when the inflation of the bulges was timed in spite of the trapped water and weight shift.The theoretical analysis of ship motions, such as rolling, accelerations and relative motions in irregular waves can explain well the experiment results of capsizing phenomena which attracted attention to the danger of navigation in quartering seas having high steepness.

Correlation measurements on regular and irregular ionization waves in neon

The evolution from regular to fully irregular motion of the s′ variety of an ionization wave in neon is studied by space correlation measurements. The correlation functions clearly indicate the onset of strongly nonlinear interaction (by a change in the decay constant of correlation function) in the region of coherent wave motion, the transition to irregular wave motion (short distance correlation only) and the stochastic character of fully developed irregular wave motion (correlation only over a few wavelengths and a few periods).

SUBHARMONIC COMPONENTS IN HAWSER AND FENDER FORCES

Forces in mooring lines and fenders of a moored vessel exposed to waves have a mixed harmonic and a subharmonic character. The subharmonic oscillations, with periods well beyond the range of wave periods, may cause forces that are as large as, or even larger than the forces associated with the harmonic oscillations. The origins of the subharmonic oscillations are discussed and it is shown that in model testing, the correct reproduction of both the mooring arrangement and the irregular wave motion is essential. The subharmonic motions, and consequently the total forces, can be partially reduced by specially adapted mooring arrangements as tests on various mooring systems have shown.

Nonlinear interference of ionization waves

The onset of irregular wave motion caused by nonlinear interference of two spontaneously existing ionization wave varieties is described and compared with the situation when only a single wave becomes irregular due to forced modulation by its harmonics. A similar phenomenological explanation for the loss of periodicity based on the influence of combined frequencies and wavenumbers of the fundamental originally periodic waves can be given in this case.

A Theoretical Calculation of the Motion of a Moored Floating vessel among the Regular Waves

The motion is investigated of a box-type floating vessel which is moored among regular waves in a sea of finite depth by chains and on which a constant drifting force acts. The present authors assume the floating vessel to be very blunt, and the length-breadth ratio of 1. The aim of the present report is to investigate the following problem: (1) Is the strip method acceptable for such a blunt body as the above mentioned from engineering standpoint? (2) How much is the nonlinear effect of the chain reaction on the motion of the floating vessel? The linearized equations of motion are solved analytically. On the other hand, the nonlinear equations of motion are integrated numerically by Runge-Kutta-Gill method. The results of the theoretical calculations show the following: (1) If the various damping forces of the rolling motion could be estimated in any way, the motion of the blunt body among the waves may be estimated by the strip method. (2) If the initial tensions of the chains are small, the nonlinear effect of the chain reaction on the stationary harmonic motion of the floating vessel is very small. A rough standard condition for small tension is that the chains touch horizontally the sea bottom at the anchoring points. (3) When the unstationary or constant drifting force acts on the moored floating vessel and it drifts from the initial equilibrium position greatly, the nonlinear effect of the chain reaction is very large. Hence, the motion in irregular waves, under a constant drifting force or under a large initial tension should be estimated considering the nonlinearity of the chain reaction.