#### Table of Contents

#### Front Matter R1-R16

#### Opening Remarks 1-4

#### Progress Toward Understanding How Waves Break 5-28

#### Radiation and Diffraction Waves of a Ship at Forward Speed 29-44

#### Nonlinear Ship Motions and Wave-Induced Loads by a Rankine Method 45-63

#### Nonlinear Water Wave Computations Using a Multipole Accelerated, Desingularized Method 64-74

#### Computations of Wave Loads Using a B-Spline Panel Method 75-92

#### Simulation of Strongly Nonlinear Wave Generation and Wave-Body Interactions Using a 3-D Model 93-109

#### Analysis of Interactions Between Nonlinear Waves and Bodies by Domain Decomposition 110-119

#### Fourier-Kochin Theory of Free-Surface Flows 120-135

#### 24-inch Water Tunnel Flow Field Measurements During Propeller Crashback 136-146

#### Accuracy of Wave Pattern Analysis Methods in Towing Tanks 147-160

#### Unsteady Three-Dimensional Cross-Flow Separation Measurements on a Prolate Spheroid Undergoing Time-Dependent Maneuvers 161-176

#### Time-Domain Calculations of First-and Second-Order Forces on a Vessel Sailing in Waves 177-188

#### Third-Order Volterra Modeling Ship Responses Based on Regular Wave Results 189-204

#### Nonlinearly Interacting Responses of the Two Rotational Modes of Motion-Roll and Pitch Motions 205-219

#### Nonlinear Shallow-Water Flow on Deck Coupled with Ship Motion 220-234

#### Radar Backscatter of a V-like Ship Wake from a Sea Surface Covered by Surfactants 235-248

#### Turbulent Free-Surface Flows: A Comparison Between Numerical Simulations and Experimental Measurements 249-265

#### Conductivity Measurements in the Wake of Submerged Bodies in Density-Stratified Media 266-277

#### Macro Wake Measurements for a Range of Ships 278-290

#### Time-Marching CFD Simulation for Moving Boundary Problems 291-311

#### Yaw Effects on Model-Scale Ship Flows 312-327

#### A Multigrid Velocity-Pressure-Free Surface Elevation Fully Coupled Solver for Calculation of Turbulent Incompressible Flow around a Hull 328-345

#### The Shoulder Wave and Separation Generated by a Surface-Piercing Strut 346-358

#### Vorticity Fields due to Rolling Bodies in a Free Surface-Experiment and Theory 359-376

#### Numerical Calculations of Ship Stern Flows at Full-Scale Reynolds Numbers 377-391

#### Near-and Far-Field CFD for a Naval Combatant Including Thermal-Stratification and Two-Fluid Modeling 392-407

#### Water Entry of Arbitrary Two-Dimensional Sections with and Without Flow Separation 408-423

#### Coupled Hydrodynamic Impact and Elastic Response 424-437

#### A Practical Prediction of Wave-Induced Structural Responses in Ships with Large Amplitude Motion 438-452

#### Evaluation of Eddy Viscosity and Second-Moment Turbulence Closures for Steady Flows Around Ships 453-469

#### On the Modeling of the Flow Past a Free-Surface-Piercing Flat Plate 470-477

#### Self-Propelled Maneuvering Underwater Vehicles 478-489

#### Spray Formation at the Free Surface of Turbulent Bow Sheets 490-505

#### Numerical Simulation of Three-Dimensional Breaking Waves About Ships 506-519

#### Generation Mechanisms and Sources of Vorticity Within a Spilling Breaking Wave 520-533

#### The Flow Field in Steady Breaking Waves 534-549

#### Freak Waves-A Three-Dimensional Wave Simulation 550-560

#### Bluff Body Hydrodynamics 561-579

#### Large-Eddy Simulation of the Vortical Motion Resulting from Flow over Bluff Bodies 580-591

#### The Wake of a Bluff Body Moving Through Waves 592-604

#### Low-Dimensional Modeling of Flow-Induced Vibrations via Proper Orthogonal Decomposition 605-621

#### Measurements of Hydrodynamic Damping of Bluff Bodies with Application to the Prediction of Viscous Damping of TLP Hulls 622-634

#### Hydrodynamics in Advanced Sailing Design 635-660

#### Divergent Bow Waves 661-679

#### A Method for the Optimization of Ship Hulls from a Resistance Point of View 680-696

#### Hydrodynamic Optimization of Fast-Displacement Catamarans 697-714

#### On Ships at Supercritical Speeds 715-726

#### The Influence of a Bottom Mud Layer on the Steady-State Hydrodynamics of Marine Vehicles 727-742

#### A Hybrid Approach to Capture Free-Surface and Viscous Effects for a Ship in a Channel 743-755

#### Shock Waves in Cloud Cavitation 756-771

#### Asymptotic Solution of the Flow Problem and Estimate of Delay of Cavitation Inception for a Hydrofoil with a Jet Flap 772-782

#### Examination of the Flow Near the Leading Edge and Closure of Stable Attached Cavitation 783-793

#### Numerical Investigation on the Turbulent and Vortical Flows Beneath the Free Surface Around Struts 794-811

#### Steep and Breaking Faraday Waves 812-826

#### The Forces Exerted by Internal Waves on a Restrained Body Submerged in a Stratified Fluid 827-838

#### Influence of the Cavitation Nuclei on the Cavitation Bucket when Predicting the Full-Scale Behavior of a Marine Propeller 839-850

#### Inception, Development, and Noise of a Tip Vortex Cavitation 851-864

#### Velocity and Turbulence in the Near-Field Region of Tip Vortices from Elliptical Wings: Its Impact on Cavitation 865-881

#### Calculations of Pressure Fluctuations on the Ship Hull Induced by Intermittently Cavitating Propellers 882-897

#### Hydroacoustic Considerations in Marine Propulsor Design 898-912

#### Prediction of Unsteady Performance of Marine Propellers with Cavitation Using Surface-Panel Method 913-929

#### A Comparitive Study of Conventional and Tip-Fin Propeller Performance 930-945

#### A New Way of Stimulating Whale Tail Propulsion 946-958

#### Effects of Tip-Clearance Flows 959-972

#### Experiments in the Swirling Wake of a Self-Propelled Axisymmetric Body 973-985

#### Hydrodynamic Forces on a Surface-Piercing Plate in Steady Maneuvering Motion 986-996

#### Advances in Panel Methods 997-1006

#### Effect of Ship Motion on DD-963 Ship Airwake Simulated by Multizone Navier-Stokes Solution 1007-1017

#### Large-Eddy Simulation of Decaying Free-Surface Turbulence with Dynamic Mixed Subgrid-Scale Models 1018-1032

#### Fully Nonlinear Hydrodynamic Calculations for Ship Design on Parallel Computing Platforms 1033-1047

#### Validation of Incompressible Flow Computation of Forces and Moments on Axisymmetric Bodies Undergoing Constant Radius Turning 1048-1060

#### The Validation of CFD Predictions of Nominal Wake for the SUBOFF Fully Appended Geometry 1061-1076

#### Appendix-List of Participants 1077-1084

The far field wave elevations η_{ff}(x,y), generated by a body travelling at constant speed U with no confinement (walls or bottom) are given by, __1__ and __3__:

(1)

with

where is a degenerated form of the Kochin function. We also have:

θ is the angle between Ox and the direction of propagation of a given wave component and K_{o} is the longitudinal wave number. The wave elevation η_{ff}(x,y) can also be written as a function of u, F(u) and G(u):

(2)

(3)

The functions F(u) and G(u) are the coefficients of the far field wave amplitude spectrum which, when integrated, yield the wave resistance:

(4)

These coefficients are obtained by a Fourier transform of the wave height measurements along a longitudinal cut which is required to extend to infinity downstream. In practice, the signal is truncated before the reflected waves are present in the signal (figure 1) and the coefficients F(u) and G(u) would tend to 0 for small values of u. The missing part of the signal is treated by introducing a weighted Fourier transform with an analytical asymptotic expression for *η*_{ff}(x,yc) valid when u → 0:

(5)

However, the coefficients c_{1}, c_{2}, and c_{3} can only be determined based on a regression on the signal before truncation. Hence, the amplitude coefficients of the transverse waves (θ<35°16') are to a great extent determined by the truncation correction. Since, for moderate Froude numbers, the larger part of the wave resistance is generated by transverse waves, the point where the signal is cut, and the accuracy of the correction, play a large part in the accuracy of the computed wave resistance. For higher speed models the contribution of transverse waves to the resistance diminishes as shown in figure 2.

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#### Front Matter R1-R16

#### Opening Remarks 1-4

#### Progress Toward Understanding How Waves Break 5-28

#### Radiation and Diffraction Waves of a Ship at Forward Speed 29-44

#### Nonlinear Ship Motions and Wave-Induced Loads by a Rankine Method 45-63

#### Nonlinear Water Wave Computations Using a Multipole Accelerated, Desingularized Method 64-74

#### Computations of Wave Loads Using a B-Spline Panel Method 75-92

#### Simulation of Strongly Nonlinear Wave Generation and Wave-Body Interactions Using a 3-D Model 93-109

#### Analysis of Interactions Between Nonlinear Waves and Bodies by Domain Decomposition 110-119

#### Fourier-Kochin Theory of Free-Surface Flows 120-135

#### 24-inch Water Tunnel Flow Field Measurements During Propeller Crashback 136-146

#### Accuracy of Wave Pattern Analysis Methods in Towing Tanks 147-160

#### Unsteady Three-Dimensional Cross-Flow Separation Measurements on a Prolate Spheroid Undergoing Time-Dependent Maneuvers 161-176

#### Time-Domain Calculations of First-and Second-Order Forces on a Vessel Sailing in Waves 177-188

#### Third-Order Volterra Modeling Ship Responses Based on Regular Wave Results 189-204

#### Nonlinearly Interacting Responses of the Two Rotational Modes of Motion-Roll and Pitch Motions 205-219

#### Nonlinear Shallow-Water Flow on Deck Coupled with Ship Motion 220-234

#### Radar Backscatter of a V-like Ship Wake from a Sea Surface Covered by Surfactants 235-248

#### Turbulent Free-Surface Flows: A Comparison Between Numerical Simulations and Experimental Measurements 249-265

#### Conductivity Measurements in the Wake of Submerged Bodies in Density-Stratified Media 266-277

#### Macro Wake Measurements for a Range of Ships 278-290

#### Time-Marching CFD Simulation for Moving Boundary Problems 291-311

#### Yaw Effects on Model-Scale Ship Flows 312-327

#### A Multigrid Velocity-Pressure-Free Surface Elevation Fully Coupled Solver for Calculation of Turbulent Incompressible Flow around a Hull 328-345

#### The Shoulder Wave and Separation Generated by a Surface-Piercing Strut 346-358

#### Vorticity Fields due to Rolling Bodies in a Free Surface-Experiment and Theory 359-376

#### Numerical Calculations of Ship Stern Flows at Full-Scale Reynolds Numbers 377-391

#### Near-and Far-Field CFD for a Naval Combatant Including Thermal-Stratification and Two-Fluid Modeling 392-407

#### Water Entry of Arbitrary Two-Dimensional Sections with and Without Flow Separation 408-423

#### Coupled Hydrodynamic Impact and Elastic Response 424-437

#### A Practical Prediction of Wave-Induced Structural Responses in Ships with Large Amplitude Motion 438-452

#### Evaluation of Eddy Viscosity and Second-Moment Turbulence Closures for Steady Flows Around Ships 453-469

#### On the Modeling of the Flow Past a Free-Surface-Piercing Flat Plate 470-477

#### Self-Propelled Maneuvering Underwater Vehicles 478-489

#### Spray Formation at the Free Surface of Turbulent Bow Sheets 490-505

#### Numerical Simulation of Three-Dimensional Breaking Waves About Ships 506-519

#### Generation Mechanisms and Sources of Vorticity Within a Spilling Breaking Wave 520-533

#### The Flow Field in Steady Breaking Waves 534-549

#### Freak Waves-A Three-Dimensional Wave Simulation 550-560

#### Bluff Body Hydrodynamics 561-579

#### Large-Eddy Simulation of the Vortical Motion Resulting from Flow over Bluff Bodies 580-591

#### The Wake of a Bluff Body Moving Through Waves 592-604

#### Low-Dimensional Modeling of Flow-Induced Vibrations via Proper Orthogonal Decomposition 605-621

#### Measurements of Hydrodynamic Damping of Bluff Bodies with Application to the Prediction of Viscous Damping of TLP Hulls 622-634

#### Hydrodynamics in Advanced Sailing Design 635-660

#### Divergent Bow Waves 661-679

#### A Method for the Optimization of Ship Hulls from a Resistance Point of View 680-696

#### Hydrodynamic Optimization of Fast-Displacement Catamarans 697-714

#### On Ships at Supercritical Speeds 715-726

#### The Influence of a Bottom Mud Layer on the Steady-State Hydrodynamics of Marine Vehicles 727-742

#### A Hybrid Approach to Capture Free-Surface and Viscous Effects for a Ship in a Channel 743-755

#### Shock Waves in Cloud Cavitation 756-771

#### Asymptotic Solution of the Flow Problem and Estimate of Delay of Cavitation Inception for a Hydrofoil with a Jet Flap 772-782

#### Examination of the Flow Near the Leading Edge and Closure of Stable Attached Cavitation 783-793

#### Numerical Investigation on the Turbulent and Vortical Flows Beneath the Free Surface Around Struts 794-811

#### Steep and Breaking Faraday Waves 812-826

#### The Forces Exerted by Internal Waves on a Restrained Body Submerged in a Stratified Fluid 827-838

#### Influence of the Cavitation Nuclei on the Cavitation Bucket when Predicting the Full-Scale Behavior of a Marine Propeller 839-850

#### Inception, Development, and Noise of a Tip Vortex Cavitation 851-864

#### Velocity and Turbulence in the Near-Field Region of Tip Vortices from Elliptical Wings: Its Impact on Cavitation 865-881

#### Calculations of Pressure Fluctuations on the Ship Hull Induced by Intermittently Cavitating Propellers 882-897

#### Hydroacoustic Considerations in Marine Propulsor Design 898-912

#### Prediction of Unsteady Performance of Marine Propellers with Cavitation Using Surface-Panel Method 913-929

#### A Comparitive Study of Conventional and Tip-Fin Propeller Performance 930-945

#### A New Way of Stimulating Whale Tail Propulsion 946-958

#### Effects of Tip-Clearance Flows 959-972

#### Experiments in the Swirling Wake of a Self-Propelled Axisymmetric Body 973-985

#### Hydrodynamic Forces on a Surface-Piercing Plate in Steady Maneuvering Motion 986-996

#### Advances in Panel Methods 997-1006

#### Effect of Ship Motion on DD-963 Ship Airwake Simulated by Multizone Navier-Stokes Solution 1007-1017

#### Large-Eddy Simulation of Decaying Free-Surface Turbulence with Dynamic Mixed Subgrid-Scale Models 1018-1032

#### Fully Nonlinear Hydrodynamic Calculations for Ship Design on Parallel Computing Platforms 1033-1047

#### Validation of Incompressible Flow Computation of Forces and Moments on Axisymmetric Bodies Undergoing Constant Radius Turning 1048-1060

#### The Validation of CFD Predictions of Nominal Wake for the SUBOFF Fully Appended Geometry 1061-1076

#### Appendix-List of Participants 1077-1084

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Accuracy of Wave Pattern Analysis Methods in Towing Tanks ." *
Twenty-First Symposium on Naval Hydrodynamics *. Washington, DC: The National Academies Press,
1997 .

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