Twenty-Third Symposium on Naval Hydrodynamics

Below are the first 10 and last 10 pages of uncorrected machine-read text (when available) of this chapter, followed by the top 30 algorithmically extracted key phrases from the chapter as a whole.
Intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text on the opening pages of each chapter. Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.

Do not use for reproduction, copying, pasting, or reading; exclusively for search engines.

OCR for page 143
About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as SECOND ORDER WAVES GENERATED BY SHIP MOTIONS 143 Second Order Waves Generated by Ship Motions M.Ohkusu, M.Yasunaga (RIAM, Kyushu University, Japan) ABSTRACT We present measured contour maps of unsteady wave elevation generated by oscillatory motions of a ship navigating at constant speed. A ship model used for this experiment is S175. The model is forced to pitch at two different amplitude. Our computerized wave measuring system gives accurate wave contour map of the fundamental frequency and the second harmonics component separately. Existence of the second order wave whose magnitude is 15 to 20 percent of the first order's is confirmed. Pattern of the second order wave is discussed in the light of asymptotic analysis and a theoretical method of predicting the second order wave is tested in its accuracy on the measured wave contour maps. 1. INTRODUCTION Rational understanding of seakeeping and accurate prediction of ship behaviors in rough seas are required more than ever. Nonlinear theory of three dimensional flow of ships, moving at forward speed in high waves, is indispensable for these to be feasible. That is why various nonlinear theories and computational methods have been proposed and implemented. However experimental evidence directly supporting or disproving those theoretically sophisticated methods is scarce. This is what I argued at 22nd ONR Symposium as well (Ohkusu (1998)). Examination of the accuracy of theories in predicting measured wave field generated by ship motions or the diffraction of the incident wave will be more appropriate because the accuracy of the measurement is expected to be more reliable than that of hydrodynamic pressure and the less integration effect of the wave field than hydrodynamic forces will be suitable for proving or disproving nonlinear theories more vividly. Furthermore the accurate prediction of wave elevation close to the hull surface is crucial for practical purpose such as accurate estimate of wave load on bow flare and deck wetness. Wave field away from the ship is related to damping of the ship motion and added resistance in waves. Hydrodynamics of waves generated by ship motions or the diffraction of the incident waves when the ship's advance speed is not zero is a challenging and interesting subject for its own sake (for example Cao, Shultz and Beck (1994)). Although several authors have presented their results on the computed wave field but experimental data obtained under the exactly controlled condition is very rare (Ohkusu and Wen (1996)). Actually they are not visible clearly in the tank test because other effect like the Kelvin wave pattern and the incident waves are mingled. Yet we wish to see experimentally how those unsteady waves are generated, not at a spot but a whole area around the ship, and how the nonlinearity is exhibited in the wave field. In this paper an example of the second order effect manifesting itself in the structure of measured wave field generated by a ship motion is presented. We investigate hydrodynamic characteristics of this nonlinear effect with asymptotic analysis and the computation of the second order wave elevation by the so-called 2.5D theory. 2. MEASUREMENT OF THE SECOND ORDER WAVES An objective of our study is to visualize nonlinear effect in the flow (unsteady free surface elevation) around a ship moving at forward speed in sea waves. A ship model is undergoing an oscillatory motion and towed at a constant speed in the water tank; the wave field, e.g. the contour map of instantaneous unsteady free surface elevation, around the ship model is what we wish the authoritative version for attribution.

OCR for page 143
About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as SECOND ORDER WAVES GENERATED BY SHIP MOTIONS 144 to obtain experimentally. Accurate measurement of oscillatory wavefield around a ship model, which is doing oscillatory motions and running at constant forward speed, is not straightforward. One of the present authors has already reported at many occasions our technique to realize the measurement. General idea of this technique is briefly described below (refer Ohkusu and Wen (1996) for the details). Wave is recorded at several locations continuously during a run of a ship model; the locations are fixed to the water tank and set on a line parallel to the ship model track. These records are transferred to time series of wave elevation at every location in the reference frame moving with the ship model if the locations are on the line parallel to the ship model track. The transformation is based on the fact that the wave probes reach to an identical location in the moving reference frame at different time instants. The transformation requires some mathematical computation at every location; a computer must be involved with the measuring system. The measurement is to be repeated at different lines of the wave probe locations so that it covers some region around the ship model Our wave measuring technique enables us to obtain ζ 0, ζ1 and ζ2 so on at every location (x, y) in the expression of the wave field (1) where the coordinate system moves with the average position of the ship model. The x−y plane coincides with the calm water surface and the positive z is vertically upward; the origin is at FP of the ship model and the x axis directs rearward; ω is the frequency of the ship model's oscillatory motion. The first term on the right of (1) is the steady wave elevation the dominant part of which is the Kelvin wave pattern. It will contain possibly the higher order effect resulting from the interaction of the oscillatory part. The second term is the oscillatory part at the fundamental frequency and the third is of the second harmonics. Main part of the fundamental frequency term will be the linear effect and the second harmonics part will be the second order effect. The unsteady waves might be interacted with the steady part. It is however impossible to confirm it by experiment because the unsteady waves without the steady part is not realistic to be compared with the one with it as long as the ship has forward speed; the unsteady waves generated by the ship motions at no forward speed is physically other thing than what we are concerned. Consistency and repeatablity of the measured waves are almost perfect. It enables us to draw accurate wave contour map with the results of the repeated measurement. The steady wave component is hardly affected by the existence of the unsteady motion; the steady free surface elevation measured when the ship model is given oscillatory motion is in good agreement with the one when it is towed on calm water at the same speed with the motion suppressed. One exception we observed so far is a small steady depression of the free surface in very front of bluff bow produced by the effect of the wave diffraction. S175 model was forced to pitch at two different magnitudes expecting the larger nonlinearity with the larger magnitude of motion. Our computerized wave measuring system enables us to obtain the instantaneous wave contour map of the first harmonics ω component and the second harmonics 2ω component separately. The former is considered to correspond to the first order effect and the latter the second order effect. Examples of the measured wave contour map are shown in Figs.1 and 2. Figure 1 is two snap shots of the contour map of the first order ζ1eiωt, the upper part of the figure represents the real part of ζ 1 (cos component) and the lower part the negative of the imaginary part (sin component). Elevation is displayed gradationally black-to-white as well as in the contour map. The elevation is normalized by the amplitude of vertical motion at FP; this figure is the result for larger amplitude of the pitch, 0.00185 radian. This gives the vertical motion at the bow as large as 70% of the draft. the authoritative version for attribution.

OCR for page 143
About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as SECOND ORDER WAVES GENERATED BY SHIP MOTIONS 146 The ship speed is Fn =0.275 and the frequency ω of pitch normalized by the ship length L and the gravity constant g is 5.26. τ, the frequency normalized by the ship speed U and g, is 1.446. With Fig. 1 and other result at smaller amplitude of pitch though not shown here, we may conclude that the measured wave contour map at the fundamental frequency, when its altitude normalized by the pitch magnitude, is identical regardless of difference in magnitude of the pitch motion. It suggests that Fig. 1 shows certainly a linear effect. A wave system is noticeable in Fig. 1. The line connecting the peaks of the wave system makes about 21° with the x axis. Wave pattern of Fig. 1 almost perfectly agrees with the predicted on linear assumptions as described later. Figure 2 is the snapshots of the instantaneous free surface elevation of ζ2ei2ωt at the same condition of frequency of pitch and the ship speed, and with the same normalization as Fig. 1. While the contour map can be drawn with this case, we display the wave elevation only gradationally; it apparently exhibits the characteristics of the wave pattern more distinctly. ζ2 measured at half the amplitude, not shown here, does not reveal so clearly the feature of the wave pattern. It suggests ζ 2 will be of the second order with respect to the amplitude of the motion. Existence of the second order waves, whose magnitude is 15 to 20 percent of the first order's, was confirmed. Wave pattern demonstrated in Fig. 2 is so distinct that it is certain that it has a clear physical meaning. Two wave systems are seen in Fig. 2. One wave is almost like the wave system seen in Fig. 1; the line connecting the peaks of the wave system makes about 21° with the x axis, though the wave length (the distance between two adjacent peaks) is different from the one in Fig. 1. Other wave system has the narrower angle wake; the peak-line makes 13.5° with the x axis. We suppose that the second order waves have two components. The so-called bound component which has the same phase speed as the first order wave (with an analogy of unidirectional 2D Stokes wave), and the free wave component which satisfies the same dispersive relation as the first order wave. Each effect of those two components in the measured waves is to be separated by utilizing the fact that their wave lengths are different from each other. The free wave component will be mainly due to the nonlinearity in the ship body condition and the bound component is a result of the nonlinearity in the free surface condition (again with an analogy with Stokes wave). The former will correspond to the 13.5° wake in Fig. 2. The latter will be manifested as the 21° wake. This conjecture will be confirmed more quantitatively in the next section. 3. ASYMPTOTIC CHARACTERISTCS We study asymptotic characteristics of the oscillatory wave pattern (Eggers (1957), Becker (1958)). ζ1(x, y) at a distance relatively far to the wave length is given in the form of (2) where The direction θ that does not give real k1,2 is to be excluded from the integration of (2). When is large, method of stationary phase will give a good estimate of the wave pattern (2) except at a caustic (Iwashita (1990)): Wave elevation at a location (x, y) is contributed by a discrete number of wave components whose direction θ are given as the solutions of (3) Equation (3) is rewritten into (4) the authoritative version for attribution.

OCR for page 143
About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as SECOND ORDER WAVES GENERATED BY SHIP MOTIONS 147 (5) |y/x|=tan φ must be less than a value φ1,2 if (4) or (5) has real solutions θ. φ1,2 is the angle of the outer bound of the wave system outside of which the wave does not exist in the asymptotic sense. Crests and trough of the k2 wave system computed by (5) at Fn=0.275, τ=1.446 is shown in Fig. 3. The outer bound at 21° is seen clearly. The k1 wave is limited within much narrower region (about 10° to the x axis). Fig. 3 Asymptotic Wave Pattern The wave length on the line φ1,2 (the distance of two adjacent peaks of wave along the line) will be given (6) where θc is the angle of elementary waves contributing to the wave elevation along φ=φ1,2, which is the solution of (4) or (5) at |y/x |= tanφ1,2 When we look at Fig. 1 in the light of the knowledge of asymptotic waves, the k2 wave is visible but the k1 wave is not. Actually the pattern shown in Fig. 3 is just what we see in Fig. 2. φ2 of Fig. 3 is 21.1° and λ2/L 0.642. They are the same as the angle shown in Fig. 1 and the distance between two marks. It confirms that the wave system we see in Fig. 1 is the k2 wave system. We study a wave system of the narrow angle of 13.5° we see in Fig. 2 in the light of the linear theory. The wave system in Fig. 2 is of the second order, yet the linear theory can capture one feature of it. As explained in the previous section, the wave field of the second order will be interpreted to be composed of the free wave component that satisfies the body nonlinear but the free surface linear conditions and the bound component that satisfies the free surface nonlinear but the body linear conditions. At radiation problem we may consider the former as a linear wave with the second order body boundary condition at the frequency of 2ω. Naturally the body condition is decided by the first order flow but imposed on the equilibrium position of the body as long as the body surface vertically intersects the free surface. Asymptotic characteristics of this wave may be analyzed in the linear way described above. Parameters determining this wave are Fn= 0.275 and τ=2.892. These parameters give φ2=13.5° and the wave length on the angle is 0.268, which perfectly agree with the observed on a wave system of the smaller angle wake and prominent behind the ship in Fig. 2. This will not be coincidence because there is no other possibility giving the angle and the wave length exactly. We may conclude this wave is caused by the body nonlinearity but with the linear free surface condition. Other wave system at the angle φ2=21° seen in Fig. 2 will probably be the bound component originated from the free surface nonlinearity. 4. COMPARISON WITH THEORETICAL PREDICTION Validation of theoretical methods is attempted in terms of accuracy in predicting the contour map of the first order and the second order waves obtained in our experiment. Here we employ the 2.5D theory for this purpose. This theory is understood to be practical in providing relatively stable results and requiring less computational burden as far as a ship is slender and at moderate to high speed; fully nonlinear time domain computation is done often with this ap the authoritative version for attribution.

OCR for page 143
About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as SECOND ORDER WAVES GENERATED BY SHIP MOTIONS 150 section; marching step ∆x in the x direction was chosen to be L/80. Two dimensional boundary value problem at each sectional plane, when ψ1 is given on z=0 and ψ1n given on the sectional contour, was solved with segment size 4×103L on z=0 on one side and every sectional contour divided into 30 segments. Behavior of ψ1 on z= 0 away from the body surface (|y|>0.5L) is approximated by vertical dipole behavior (Wen (1997)). We employed rather classical initial condition ψ1= η1=0 at x=0. After ψ1 and η1 are obtained, we solve for ψ2 and η2 in almost similar manner. Equations (19) and (21) are integrated to forward ψ2 and η2. We need to evaluate the forcing terms due to ψ1 and η1 on the right hand side of these equations. We must rely on numerical differentiation for evaluating ψ1zx as ψ1z is given on z=0. We evaluated ψ1zz by solving a new boundary value problem for ψ1z when ψ1z are prescribed on both the ship section and the free surface. The condition imposed at large |y| is determined as follows. The forcing terms behavior at large |y| is already known because ψ1's was assumed of vertical dipole at the first order computation. For ψ2 we assume the slowest attenuation conceivable at large |y| i.e. we assume the same behavior as ψ1. The singularity of ψ1 at the intersection of the body surface and z=0 will be Z 2 log Z where Z is the complex coordinate with the origin at the intersection (Cointe, Molin and Nays (1988)). It leads to the singularity log Z of ψ1zz. We avoided the difficulty in solving the boundary value problem in each crosssectional plane by collocating not at the intersection but at locations very close to it. Figures 4 to 13 are the comparison of the measured and the computed wave elevation ζ1eiωt in cross sectional planes at several different x/L. The measured is taken from the contour map shown in Fig. 1. Figures at the left side of each page show the wave elevation at the instant of ωt=0 (cosine component) and the right figures the wave elevation at the instant of ωt=π/2 (sine component). In those figures Theoretical (3D) depicts the computed by three dimensional and desingularized Rankine panel method (Sclavounos (1996)) using the double-model flow as the basic steady flow. First of all we see that the wave elevation normalized by the amplitude of the ship motion at x=0 is almost identical despite the difference in the amplitude (white and black circles). It implies that the measured must be accounted for by linear theories. While both the theoretical 2.5D and 3D capture the general features of the wave elevation, either of the theoretical does not succeed in predicting accurately the height of wave elevation; the measured is higher in the crest and deeper in the trough than the theoretical predictions. It is not supposed to be caused by the 2.5D's incorrect initial condition at x=0 because even the 3D not suffering from this defect fails to predict them. Figure 14 is the contour map predicted by the 3D computation. Once again we see that the whole feature of the theoretical agrees perfectly with that of the measured shown in Fig. 1. In Fig. 15 to 23 we compare the theoretical prediction of the second order wave ζ2ei2ωt given by the 2.5D theory with the measured corresponding to the result shown in Fig. 2. The format for the comparison is the same as for the first order except that the sine component represent the wave elevaation at 2ωt=π/2. It appears that the general feature of the wave elevation is predicted by the 2.5D theory. It means that the second order wave elevation observed close to the ship might be the bound component caused by the free surface nonlinearity as suggested in the previous section. The relatively large wave elevation of the second order is not predicted by our theoretica method. It may not be surprising because the prediction of the first order wave is not so correct in the magnitude of the wave. The theoretical result on the second order wave elevation far behind the ship is not available (the 2.5D theory is not capable of computing the wave field behind the ship's stern). We can not confirm our statement on the narrow angle wake we see in Fig. 2. the authoritative version for attribution.

OCR for page 143
About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as SECOND ORDER WAVES GENERATED BY SHIP MOTIONS 151 5. CONCLUDING REMARKS We presented instantaneous contour maps of the first order and the second order waves generated by a ship motion. They are not visible on usual experiment at water tank. Those contour maps were made available by our computerized technique for wave measurement. Validation of a theoretical method was attempted in terms of accuracy of predicting those contour maps of the first order and the second order waves. Theoretical prediction of the first order wave is not entirely accurate despite the slender hull form of the ship model. While pattern of the wave contour is accurately predicted, discrepancy exhibits itself in the predicted wave height being much smaller than the measured wave height near the hull surface. The discrepancy suggests that our theoretical model is to be improved since we believe the measured first order wave is of “the first order”. Two components are clearly distinguished in the second order measured wave pattern, one satisfying the linear dispersive relation and the second order body condition, and other satisfying the nonlinear free surface condition and the homogeneous body condition. The latter apparently is dominant in the wave elevation at the location close to the hull surface. A theoretical approach to compute the second order wave contour was proposed. The prediction of general feature of the wave contour does not seem so inaccurate. However the magnitude of the measured wave is larger than the predicted. This will be inevitable when we consider inaccuracy in the prediction of the first order; the second order wave was computed utilizing the first order prediction in our theoretical approach. Practical implication of our result to sea-keeping study is to be studied in future. ACKNOWLEDGEMENT The authors acknowledge the help of Prof. H.Iwashita, Hiroshima University, in providing his computational result by Rankine panel method. REFERENCES Becker E (1958) Das Wellenbild einer unter der Oberfläche eines Stromes Schwerer Flüssigkeit Pulsierenden Quelle, Z.Angewandte, Mathematik und Mechanik, Bd38 Cao YS, Schultz W and Beck R (1994) Inner-angle Wavepackets in an Unsteady Wake, Proc. 19th Symposium on Naval Hydrodynamics, Seoul Cointe R, Molin B and Nays P (1988) Nonlinear and second order transient waves in a rectangular tank, proc. BOSS'88, Trondheim Eggers K (1957) Über das Wellenbild einer Pulsierenden Störung in Translation, Schiff und Hafen, Heft 2 Faltinsen O M and Zhao R (1991) Numerical predictions of ship motions at high forward speed, Phil. Trans. Royal Soc. Lond. A 334 Iwasita H (1990) Green function method for ship motions at forward speed, PhD Thesis, Kyushu University Ohkusu M (1998) Validation of Theoretical Methods for Ship Motions by Means of Experiment, Proc. 22nd Symposium on Naval Hydrodynamics, Washington DC Ohkusu M and Wen G (1996) Radiation and Diffraction Waves of a Ship at Forward Speed, Proc. 21st Symposium on Naval Hydrodynamics, Trondheim Sclavounos P (1996) Computation of wave ship interaction, Advances in Marine Hydrodynamics edited by M Ohkusu, Computational Mechanics Publication UK Wen G C (1997) Theoretical prediction of sea-keeping of high speed ships, PhD Thesis, Kyushu University the authoritative version for attribution.

Table of Contents

Front Matter R1-R19

Modern Seakeeping Computations for Ships 1-45

Forces, Moment and Wave Pattern for Naval Combatant in Regular Head Waves 46-65

New Green-Function Method to Predict Wave-Induced Ship Motions and Loads 66-81

Validation of Time-Domain Prediction of Motion, Sea Load, and Hull Pressure of a Frigate in Regular Waves 82-97

Ship motions and loads in large waves 98-111

Prediction of Vertical-Plane Wave Loading and Ship Responses in High Seas 112-125

Basic Studies of Water on Deck 126-142

Second Order Waves Generated by Ship Motions 143-156

Prediction of Nonlinear Motions of High-speed Vessels in Oblique Waves 157-170

Optimizing Turbulence Generation for Controlling Pressure Recovery in Submarine Launchways 171-180

HULL DESIGN by CAD/CFD SIMULATION 181-190

Steady-State Hydrodynamics of High-Speed Vessels with a Transom Stern 191-205

Practical CFD Applications to Design of a Wave Cancellation Multihull Ship 206-222

Simulation of Ship Maneuvers Using Recursive Neural Networks 223-242

Flow- and Wave-Field Optimization of Surface Combatants Using CFD-Based Optimization Methods 243-261

MARINE PROPULSOR NOISE INVESTIGATIONS IN THE HYDROACOUSTIC WATER TUNNEL "G.T.H." 262-283

Propulsor Design Using Clebsch Formulation 284-300

Unsteady Flow Quantities on Two-Dimensional Foils: Experimental and Numerical Results 301-313

Hydrofoil Turbulent Boundary Layer Separation at High Reynolds Numbers 314-329

Pressure Fluctuation on Finite Flat Plate above Wing in Sinusoidal Gust 330-341

Control of the Turbulent Wake of an Appended Streamlined Body 342-354

Investigation of Global and Local Flow Details by a Fully Three-dimensional Seakeeping Method 355-367

Prediction of Wave Pressure and Loads on Actual Ships by the Enhanced Unifed Theory 368-384

Frequency Domain Numerical and Experimental Investigation of Forward Speed Radiation by Ships 385-401

INTERNATIONAL COLLABORATION ON BENCHMARK CFD VALIDATION DATA FOR SURFACE COMBATANT DTMB MODEL 5415 402-422

Validation of High Reynolds Number, Unsteady Multi-Phase CFD Modeling for Naval Applications 423-440

Free Surface Viscous Flow Computation Around A Transom Stern Ship By Chimera Overlapping Scheme 441-456

ANTI-ROLL TANK SIMULATIONS WITH A VOLUME OF FLUID (VOF) BASED NAVIER-STOKES SOLVER 457-473

Validation of Tab Assisted Control Surface Computation 474-484

Experimental And Numerical Investigation Of The Flow Around The Appendices Of A Whitbread 60 Sailing Yacht 485-492

Propeller Wake Analysis by Means of PIV 493-510

Experimental and Numerical Investigation of the Unsteady Flow around a Propeller 511-526

Simulation of Incompressible Viscous Flow Around a Ducted Propeller Using a RANS Equation Solver 527-539

On Submerged Stagnation Points and Bow Vortices Generation 540-552

Numerical Prediction of Scale Effects in Ship Stern Flows with Eddy-Viscosity Turbulence Models 553-568

The Experimental and Numerical Study of Flow Structure and Water Noise Caused by Roughness of the Body 569-578

Large-Eddy Simulations of Turbulent Wake Flows 579-598

Instability of Partial Cavitation: A Numerical/Experimental Approach 599-615

An Unsteady Three-Dimensional Euler Solver Coupled with a Cavitating Propeller Analysis Method 616-638

On the Flow Structure, Tip Leakage Cavitation Inception and Associated Noise 639-653

An Experimental Investigation of Cavitation Inception and Development of Partial Sheet Cavities on Two - Dimensional 654-669

Modeling 3D unsteady sheet cavities using a coupled UnRANS-BEM code 670-686

Ship Wake Detectability in the Ocean Turbulent Environment 687-703

An Experimental and Computational Study of the Effects of Propulsion on the Free-Surface Flow Astern of Model 5415 704-712

Breaking Waves in the Ocean and around Ships 713-745

Numerical and Experimental Study of the Wave Breaking Generated by a Submerged Hydrofoil 746-761

The Numerical Simulation of Ship Waves Using Cartesian Grid Methods 762-779

Radiation Loads on a Cylinder Oscillating in Pycnocline 780-791

Wave Resistance Computations - A Comparison of Different Approaches 792-804

Computation of Nonlinear Turbulent Free Surface Flows Using the Parallel Uncle Code 805-819

Submarine manoeuvrability assessment using Computational Fluid Dynamic tools 820-832

Simulation of UUV Recovery Hydrodynamics 833-847

Reynolds-Averaged Modeling of High-Froude-Number Free-Surface Jets 848-862

On Roll Hydrodynamics of Cylinders Fitted with Bilge Keels 863-881

Combining Accuracy and Effciency with Robustness in Ship Stern Flow Computation 882-896

An Unstructured Multielement Solution Algorithm for Complex Geometry Hydrodynamic Simulations 897-909

Ship Stern Flow Calculations on Overlapping Composite Grids 910-926

Study on the Prediction of Flow Characteristics Around a Ship Hull 927-940

Analysis of Turbulence Free-Surface Flow around Hulls in Shallow Water Channel by a Level-set Method 941-956

A Design Tool for High Speed Ferries Washes 957-967

Flow Around Ships Sailing in Shallow Water - Experimental and Numerical Results 968-982

Ship Stability Study in the Coastal Region: New Coastal Wave Model Coupled with a Dynamic Stability Model 983-992

Waves and Forces Caused by Oscillation of a Floating Body Determined through a Unified Nonlinear Shallow-Water Theory 993-1005