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| Preface | |
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| Introduction | |
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| Basic concepts | |
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| The equations of fluid mechanics | |
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| Free-surface flows | |
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| Two-dimensional flows | |
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| Linear waves | |
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| The water-wave equations | |
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| Linear solutions for water waves | |
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| Superposition of linear waves | |
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| Free-surface flows that intersect walls | |
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| Free streamline solutions | |
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| Forced separation | |
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| Free separation | |
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| The effects of surface tension | |
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| Forced separation | |
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| Free separation | |
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| The effects of gravity | |
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| Solutions with �<sub>1</sub> = 0 (funnels) | |
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| Solutions with �<sub>1</sub> = 0 (nozzles and bubbles) | |
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| Solutions with �<sub>1</sub> = �/2 (flow under a gate with gravity) | |
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| The combined effects of gravity and surface tension | |
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| Rising bubbles in a tube | |
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| Fingering in a Hele Shaw cell | |
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| Further examples involving rising bubbles | |
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| Exponential asymptotics | |
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| Linear free-surface flows generated by moving disturbances | |
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| The exact nonlinear equations | |
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| Linear theory | |
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| Solutions in water of finite depth | |
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| Solutions in water of infinite depth | |
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| Discussion of the solutions | |
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| Nonlinear waves - asymptotic solutions | |
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| Periodic waves | |
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| Solutions when condition (5.55) is satisfied | |
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| Solutions when condition (5.55) is not satisfied | |
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| The Korteweg-de Vries equation | |
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| Numerical computations of nonlinear water waves | |
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| Formulation | |
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| Series truncation method | |
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| Boundary integral equation method | |
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| Numerical methods for solitary waves | |
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| Boundary integral equation methods | |
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| Numerical results for periodic waves | |
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| Pure capillary waves (g = 0, T ≠ 0) | |
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| Pure gravity waves (g ≠ 0, T = 0) | |
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| Gravity-capillary waves (g ≠ 0, T ≠ 0) | |
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| Numerical results for solitary waves | |
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| Pure gravity solitary waves | |
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| Gravity-capillary solitary waves | |
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| Nonlinear free-surface flows generated by moving disturbances | |
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| Pure gravity free-surface flows in water of finite depth | |
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| Supercritical flows | |
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| Subcritical flows | |
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| Gravity-capillary free-surface flows | |
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| Results in finite depth | |
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| Results in infinite depth (removal of the nonuniformity) | |
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| Gravity-capillary free-surface flows with Wilton ripples | |
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| Free-surface flows with waves and intersections with rigid walls | |
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| Free-surface flow past a flat plate | |
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| Numerical results | |
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| Analytical results | |
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| Free-surface flow past a surface-piercing object | |
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| Numerical results | |
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| Analytical results | |
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| Flow under a sluice gate | |
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| Formulation | |
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| Numerical procedure | |
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| Discussion of the results | |
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| Pure capillary free-surface flows | |
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| Numerical results | |
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| Analytical results | |
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| Waves with constant vorticity | |
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| Solitary waves with constant vorticity | |
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| Mathematical formulation | |
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| Numerical procedure | |
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| Discussion of the results | |
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| Periodic waves with constant vorticity | |
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| Mathematical formulation | |
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| Numerical procedure | |
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| Numerical results | |
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| Discussion | |
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| Three-dimensional free-surface flows | |
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| Green's function formulation for two-dimensional problems | |
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| Pressure distribution | |
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| Two-dimensional surface-piercing object | |
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| Extension to three-dimensional free-surface flows | |
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| Gravity flows generated by moving disturbances in water of infinite depth | |
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| Three-dimensional gravity-capillary free-surface flows in water of infinite depth | |
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| Further extensions | |
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| Time-dependent free-surface flows | |
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| Introduction | |
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| Nonlinear gravity-capillary standing waves | |
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| References | |
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| Index | |