Twenty-First Symposium on NAVAL HYDRODYNAMICS -- Copyright -- FOREWORD -- Contents -- Twenty-First Symposium on NAVAL HYDRODYNAMICS Opening Remarks -- Dr. Fred E.Saalfeld Deputy Chief of Naval Research/Technical Director -- Twenty-First Symposium on NAVAL HYDRODYNAMICS Technical Sessions -- Progress Toward Understanding How Waves Break -- 1. INTRODUCTION -- 2. THE NEAR-LIMITING FORM OF STEEP STOKES WAVES -- 3. CREST INSTABILITIES -- 4. SUPERHARMONIC INSTABILITIES: DEEP WATER -- 5. INSTABILITIES IN SOLITARY WAVES -- 6. FINITE-AMPLITUDE DEVELOPMENT OF CREST INSTABILITIES -- 7. WAVE-GENERATED RIPPLES -- 8. CAPILLARY JUMPS -- 9. EFFECT OF SURFACE TENSION ON CREST INSTABILITIES -- 10. VISCOUS EFFECTS -- 11. BREAKING IN MODULATED WAVE TRAINS -- 12. CONCLUSIONS -- ACKNOWLEDGEMENTS -- References -- Radiation and Diffraction Waves of a Ship at Forward Speed -- ABSTRACT -- 1 INTRODUCTION -- 2 MEASUREMENT OF RADIATION AND DIFFRACTION WAVES -- 3 COMPUTATION OF DIFFRACTION AND RADIATION WAVES -- 4 ADDED RESISTANCE -- 5 SUMMARY -- References -- DISCUSSION -- AUTHOR'S REPLY -- Nonlinear Ship Motions and Wave-Induced Loads by a Rankine Method -- ABSTRACT -- 1 INTRODUCTION -- 2 NONLINEAR SHIP MOTIONS -- 2.1 Linear Foundation -- 2.1.1 Linear formulation -- 2.1.2 Numerical implementation -- 2.2 Nonlinear Restoring and Froude-Krylov Forces -- 2.3 Weak Scatterer Hypothesis -- 2.4 Linear and Nonlinear Motions -- 3 GLOBAL LOADS -- 3.1 Global Loads in Regular Waves -- 3.2 Extreme Value Statistics -- 4 CONCLUSIONS -- 5 ACKNOWLEDGEMENTS -- References -- DISCUSSION -- AUTHORS' REPLY -- Nonlinear Water Wave Computations Using a Multipole Accelerated, Desingularized Method -- ABSTRACT -- INTRODUCTION -- PROBLEM FORMULATION -- Boundary Value Problem for the Fluid Motion -- Mixed Boundary Value Problem for the Perturbation Potential -- SOLUTION TECHNIQUES.

Domain Decomposition -- Multipole Expansions -- Multipole Acceleration -- RESULTS -- Multipole Efficiency -- Nonlinear incident waves at forward speed -- Wave forces on a submerged submarine with forward speed -- CONCLUSIONS -- ACKNOWLEDGMENTS -- REFERENCES -- DISCUSSION -- AUTHORS' REPLY -- Computations of Wave Loads Using a B-Spline Panel Method -- ABSTRACT -- 1. INTRODUCTION -- 2. THE BOUNDARY-VALUE PROBLEM -- 3. THE B-SPLINE METHODOLOGY -- 3.1 Features of the method -- 3.2 The integral equation -- 3.3 Nonlinear methodology -- 4. RESULTS -- 4.1 First-order results -- 4.2 The second-order solution -- 4.3 The third-order solution -- 5. CONCLUSIONS -- ACKNOWLEDGMENT -- References -- DISCUSSION -- AUTHORS' REPLY -- ADDITIONAL REFERENCE -- DISCUSSION -- AUTHORS' REPLY -- ADDITIONAL REFERENCE -- Simulation of Strongly Nonlinear Wave Generation and Wave-Body Interactions Using a 3-D MEL Model -- ABSTRACT -- INTRODUCTION -- FORMULATION OF THE PROBLEM -- Boundary Value Problem -- Coupling with Body Motions -- Accounting for Nonlinear Incoming Waves -- Splitting the Incident Wave Contribution -- NUMERICAL METHODS -- Boundary Element Method -- Solution of Linear Systems of Equations -- Interpolations and Smoothing at the Free Surface -- Time Marching Scheme -- NUMERICAL RESULTS -- Nonlinear Diffraction of Long Waves by a Vertical Cylinder -- Nonlinear Motion of a Floating Dock in Regular Ambient Waves -- Large Amplitude Standing Waves in a Three Dimensional Tank -- CONCLUSION -- Acknowledgments -- References -- DISCUSSION -- AUTHOR'S RESPONSE -- Analysis of Interactions Between Nonlinear Waves and Bodies by Domain Decomposition -- ABSTRACT -- INTRODUCTION -- MATHEMATICAL FORMULATION AND NUMERICAL TECHNIQUE -- DOMAIN DECOMPOSITION TECHNIQUE -- RESULTS AND DISCUSSION -- CONCLUSIONS -- ACKNOWLEDGEMENT -- REFERENCES -- Fourier-Kochin Theory of Free-Surface Flows.

ABSTRACT -- INTRODUCTION -- BACKGROUND -- FOURIER-KOCHIN FORMULATION -- COUPLING OF VISCOUS AND POTENTIAL FLOWS -- FOURIER REPRESENTATION OF GENERIC DISPERSIVE WAVES -- TIME-HARMONIC SHIP WAVES -- Dispersion curves -- Component wave systems -- General features of component waves -- Fourier representations of wave components -- Illustrative calculations -- CONCLUSION -- ACKNOWLEDGMENTS -- REFERENCES -- 24-Inch Water Tunnel Flow Field Measurements During Propeller Crashback -- ABSTRACT -- INTRODUCTION -- TEST FACILITY AND PDV SETUP -- UNSTEADY FLOW BEHAVIOR -- PDV IMAGE PROCESS -- VELOCITY AND VORTICITY DISTRIBUTIONS -- CONCLUSIONS AND RECOMMENDATIONS -- ACKNOWLEDGMENT -- REFERENCES -- Accuracy of Wave Pattern Analysis Methods in Towing Tanks -- INTRODUCTION -- LONGITUDINAL CUT METHOD (LCM) -- Description -- Transverse position -- Truncation -- DISCRETE DECOMPOSITION METHOD (DDM) -- Description -- Discussion of results -- THE SINGULARITY DISTRIBUTION IDENTIFICATION METHOD (SDIM) -- Description -- Near field wave correction -- Discrete source distribution -- Application to experimental data -- Influence of signal length -- Probe transverse position -- CONCLUSIONS -- ACKNOWLEDGEMENTS -- NOMENCLATURE -- REFERENCES -- Unsteady Three-Dimensional Cross-Flow Separation Measurements on a Prolate Spheroid Undergoing Time-Dependent Maneuvers -- ABSTRACT -- NOMENCLATURE -- 1. INTRODUCTION -- 1.1 Unsteady Aerodynamics -- 1.2 6:1 Prolate Spheroid -- 1.3 Overview of Present Research Program -- 2. DYNAMIC PLUNGE-PITCH-ROLL MODEL MOUNT (DYPPIR) -- 2.1 Stability and Control Wind Tunnel -- 2.2 DyPPiR Hardware Overview -- 2.3 Maneuvers Tested -- 2.3.1 The 0.33s, 30° Ramp Pitchup -- 2.3.2 The 0.25s Submarine Maneuver -- 2.4 Model Geometry -- 3. HOT-FILM MEASUREMENTS -- 3.1 Theory of Operation -- 3.2 Experimental Apparatus And Uncertainties -- 3.3 Steady Results.

3.4 Unsteady Results -- 3.4.1 Pitchup Maneuver -- 3.4.2 Submarine Maneuver -- 4. PRESSURE MEASUREMENTS -- 4.1 Experimental Apparatus and Uncertainties -- 4.2 Steady Results -- 5. FORCES AND MOMENTS -- 5.1 Introduction -- 5.2 Two-point Balance and Light-weight Model -- 5.3 Steady Results -- 5.4 Unsteady Results -- 5.5 Future Improvements -- 6. DISCUSSION -- 7. CONCLUSIONS -- ACKNOWLEDGEMENTS -- References -- Time-Domain Calculations of First- and Second-Order Forces on a Vessel Sailing in Waves -- ABSTRACT -- NOMENCLATURE -- INTRODUCTION -- 1 TIME-DOMAIN ALGORITHM -- 1.1 The interior problem -- 1.2 The exterior problem -- 1.3 The total problem -- 1.4 Movement and forces -- 2 INCREASING THE SPEED -- 2.1 Upwind discretization -- 3 RESULTS -- 4 CONCLUSIONS AND FURTHER RESEARCH -- ACKNOWLEDGEMENTS -- References -- Third-Order Volterra Modeling of Ship Responses Based on Regular Wave Results -- ABSTRACT -- 1 INTRODUCTION -- 2 EXPERIMENTS -- 3 THE THIRD ORDER VOLTERRA MODEL -- 4 THE RESULTS -- 4.1 Time Histories -- 4.2 Response Spectra -- 4.3 Sample Probability Densities -- 4.4 Peak-Peak Probability Densities -- 5 DISCUSSION AND CONCLUSION -- ACKNOWLEDGEMENTS -- References -- NOMENCLATURE -- DISCUSSION -- AUTHOR'S REPLY -- Nonlinearly Interacting Responses of the Two Rotational Modes of Motion-Roll and Pitch Motions -- ABSTRACT -- 1. INTRODUCTION -- 2. EQUATIONS OF MOTION -- 3. ANALYSIS -- 4. PRIMARY RESONANCE OF THE PITCH MODE -- 4.1 Modulation Equations -- 4.2 Fixed Points -- 4.3 Stability of Fixed Points -- 4.4 Numerical Results and Discussion -- 4.4.1 Breaking of Saturation in Force-Response Curves -- 4.4.2 Effect of Quadratic Roll Damping on Frequency-Response Curves -- 4.4.3 Hopf Bifurcation Region -- 5. PRIMARY RESONANCE OF THE ROLL MODE -- 5.1 Modulation Equations -- 5.2 Fixed Points -- 5.3 Stability of Fixed Points.

5.4 Numerical Results and Discussion -- 6. SUMMARY AND CONCLUSIONS -- REFERENCES -- Nonlinear Shallow-Water Flow on Deck Coupled with Ship Motion -- ABSTRACT -- INTRODUCTION -- SHIP MOTION IN THE TIME DOMAIN -- NONLINEAR SHALLOW WATER FLOW ON DECK -- Governing Equations -- The Flux Difference Splitting Scheme -- COMPUTATION OF FORCES -- Forces Caused by Water Flow on Deck -- Nonlinear Froude-Krylov Forces -- Forces due to the Radiated and Diffracted Waves -- Viscous Roll Damping Moment -- Resistance, Cross-Flow Drag and Thrust -- Maneuvering Forces -- Rudder Forces and Autopilot -- RESULTS AND DISCUSSION -- CONCLUSIONS -- ACKNOWLEDGMENTS -- References -- Radar Backscatter of a V-like Ship Wake from a Sea Surface Covered by Surfactants -- ABSTRACT -- 1 INTRODUCTION -- 2 WAVE ELEVATIONS INDUCED BY A MOVING SHIP. -- 3 THE GREEN FUNCTION OF A MOVING SURFACE DISTURBANCE. -- 3.1 Governing equations. -- 3.2 Boundary conditions. -- 3.3 Fourier transformation of the boundary-value problem -- 3.4 Poles of the integrand. -- 3.5 The Kochin function. -- 3.6 Simplified waterline -- 3.7 Asymptotic expression for the wave elevation. -- 4 ASYMPTOTIC EXPRESSION FOR THE RADAR BACK SCATTER CROSS-SECTION. -- 5 NUMERICAL SIMULATION. -- 6 SUMMARY. -- 7 ACKNOWLEDGMENT -- References -- Turbulent Free-Surface Flows: A Comparison Between Numerical Simulations and Experimental Measurements -- ABSTRACT -- 1 INTRODUCTION -- 2 MATHEMATICAL FORMULATIONS -- 2.1 Field Equations -- 2.2 Free-Surface Boundary Conditions -- 2.3 Sub-Grid Scale Modeling -- 2.4 Stirring -- 2.5 Initialization -- 3 NUMERICAL FORMULATION -- 4 LABORATORY EXPERIMENTS -- 5 NUMERICAL RESULTS -- 5.1 Grid-Stirred Turbulence -- 5.2 A Model-Scale Frigate -- 6 CONCLUSIONS -- ACKNOWLEDGEMENTS -- REFERENCES -- Conductivity Measurements in the Wake of Submerged Bodies in Density-Stratified Media -- ABSTRACT.

INTRODUCTION.