Fluid Waves

Description

The book derives the mathematical basis for the most encountered waves in science and engineering. It gives the basis to undertake calculations required for important occupations such as maritime engineering, climate science, urban noise control, and medical diagnostics. The book initiates with fluid dynamics basis with subsequent chapters covering surface gravity waves, sound waves, internal gravity waves and waves in rotating fluids, and details basic phenomena such as refraction. Thereafter, specialized application chapters include description of specific contemporary problems. All concepts are supported by narrative examples, illustrations, and case studies. Features:- Explains the basis of wave mechanics in fluid systems. Provides tools for the analysis of water waves, sound waves, internal gravity, and rotating fluid waves through different examples. Includes comprehensible mathematical derivations at the expense of fewer theoretical topics. Reviews cases describable by linear theory and cases requiring nonlinear and wave-interaction theories. Supports concepts with narrative examples, illustrations, and case studies. This book aims at Senior Undergraduates/Graduate students and Researchers in Fluid Mechanics, Applied Mathematics, Mechanical Engineering, Civil Engineering, and Physical Oceanography. Cover Half Title Title Page Copyright Page Dedication Contents Nomenclature Preface I. Theory and classical applications 1. Fundamentals 1.1. Summary of key points 1.2. Basic uid dynamics 1.2.1. Fluid mechanics and uid dynamics 1.2.2. Constitutive relations for uid continua 1.2.2.1. Stress 1.2.2.2. Strain 1.2.2.3. Relation between pressure and volumetric strain 1.2.2.4. Relation between shear stress and the rate of shear strain 1.2.2.5. Surface tension 1.2.3. Conservation laws 1.2.3.1. Conservation of mass 1.2.3.2. Conservation of momentum 1.2.4. Scaling of equations and dimensionless groups 1.3. Flow descriptions 1.4. Euler and Bernoulli equations 1.5. Wave tools 1.5.1. Complex exponentials 1.5.2. Wave equation notations 1.5.3. Separation of variables and d'Alembert solutions 1.5.4. Measuring a wave 1.5.5. Oscillators and resonance 1.5.6. Introduction to spectra and Fourier transforms 1.6. Problems 2. Water-surface waves 2.1. Summary of key points 2.2. An example 2.3. Linear water-wave theory 2.3.1. The waves we see 2.3.2. Potential flow 2.3.2.1. Physical assumptions that lead to potential ow 2.3.3. Laplace's equation 2.3.4. Boundary conditions for water waves 2.3.5. Airy's solution for surface gravity waves 2.3.5.1. Separation of variables solution 2.3.5.2. Applying the boundary conditions 2.3.5.3. Dispersion relation 2.3.5.4. Ripples 2.3.5.5. Phase speed 2.3.5.6. Velocity field 2.3.6. Surface elevation 2.3.7. Particle trajectories 2.3.8. Group velocity 2.3.9. Deep-water approximation 2.3.10. Consequences of deep water 2.3.10.1. Maximum wavelength of ocean swell 2.3.10.2. V-shaped wakes in deep water 2.3.10.3. Deep-water wave focusing 2.3.11. Shallow-water approximation 2.3.12. Consequences of shallow water 2.4. Problems 3. Sound waves 3.1. Summary of key points 3.2. An example 3.3. Linear sound-wave theory 3.3.1. Use and control of sound 3.3.2. The wave equation for sound waves 3.3.3. Solution of the wave equation 3.3.4. Relation to shallow-water waves 3.3.5. Refraction 3.3.6. Acoustic impedance 3.3.7. Reflection, scattering and transmission 3.3.8. Representation and measurement of sound 3.3.8.1. Spectral representation of sound 3.3.8.2. Sound-measurement instruments 3.3.9. Geometrical spreading 3.3.10. Doppler effect 3.4. Building acoustics 3.4.1. Reverberation 3.5. Problems 4. Internal gravity waves 4.1. Summary of key points 4.2. An example 4.3. Linear internal gravity-wave theory 4.3.1. The in uence of gravity within a fluid 4.3.2. Two-layer rigid-lid interfacial waves 4.3.3. Waves in continuously stratified fluids 4.4. Problems 5. Waves in rotating fluids 5.1. Summary of key points 5.2. An example 5.3. Linear inertia-wave theory 5.3.1. Coriolis force 5.3.2. Inertial oscillations in an unbounded domain 5.3.3. Relation to gravity waves 5.3.4. Inertial oscillations with boundary conditions 5.4. Problems 6. Introduction to some nonlinear wave theories 6.1. Summary of key points 6.2. An example 6.3. Nonlinearity in uid waves 6.4. Stokes drift 6.4.1. Eulerian and Lagrangian displacements 6.4.2. Perturbation approach for the drift velocity of 1D 6.4.3. Perturbation approach for the drift velocity in 2D 6.5. Solitary waves 6.5.1. Balancing nonlinear momentum and dispersion 6.6. Problems 7. Nonlinear wave interactions 7.1. Summary of key points 7.2. An example 7.3. Mean flows driven by waves 7.4. Nonlinearly coupled waves 7.5. Problems II. Further applications 8. Ocean wave energy conversion 8.1. Summary of key points 8.2. Introduction to wave-energy conversion 8.2.1. The wave-energy resource 8.3. Issues with wave-energy conversion 8.3.1. A plethora of inventions 8.3.2. The need for resonance 8.4. Wave-energy converter technologies 8.4.1. Rigid pendulum 8.4.2. Liquid pendulum (oscillating water column) 8.4.3. Heaving Buoy 8.5. Analysis of a generic WEC 8.5.1. Response of a generic WEC 8.5.2. Useful power extracted from ocean waves 9. Bubble acoustics 9.1. Summary of key points 9.2. Volumetric oscillations of bubbles 9.2.1. The collapse of a spherical cavity 9.2.2. Natural frequencies of bubbles 9.3. Rayleigh-Plesset equation 9.3.1. Surface tension, vapour and driving pressures 9.3.2. Viscous dissipation 9.4. Linear bubble acoustics 9.4.1. Linearised Rayleigh-Plesset equation 9.4.2. Thermal damping 9.4.3. Radiation damping 9.4.4. Linear damped bubble oscillator equation 9.5. Applications of linear bubble acoustics 9.5.1. Industrial measurements 9.5.2. Sounds of ocean waves 9.5.3. Volcanic bubbles 9.6. Nonlinear bubble acoustics and applications 9.6.1. Sonochemistry 9.6.2. Medical ultrasound diagnostics 9.6.3. Medical ultrasound therapeutics 10. Surface-wave breaking in weather and climate 10.1. Summary of key points 10.2. Wave breaking and air-sea exchange 10.2.1. Criteria for wave breaking 10.2.2. Types of wave breaking 10.3. Global climate consequences of ocean-wave breaking 10.3.1. Energy transfer from whitecapping to microscale processes 10.3.2. Outline of air-sea exchange 10.3.3. Influence of sea-spray aeroso ls on climate 10.3.4. Influence of bubbles from breaking waves on climate 10.3.5. Outline of the oceanic part of the carbon cycle 11. Rotating-fluid waves in space and planetary systems 11.1. Summary of key points 11.2. Rotating-fluid waves in stellar and planetary physics 11.2.1. The origin of rotation 11.2.2. Inertia waves in stars 11.2.3. Magnetism and life on planets and moons 11.2.4. Geodynamo mechanisms 11.3. Engineering of rotating spacecraft 11.3.1. Rotation for attitude control 11.3.2. Rotation for artificial gravity 12. Nonlinear environmental waves 12.1. Summary of key points 12.2. Rogue waves 12.3. The tsunami: an ocean-surface soliton 12.4. Internal solitons 12.4.1. Mesoscale atmospheric solitons 12.4.2. Gravity currents 12.4.3. Thunderstorm solitons and aviation 12.4.4. Oceanic internal solitons 13. Streaming in medicine, industry and geophysics 13.1. Summary of key points 13.2. Acoustic streaming in medicine 13.3. Acoustic microstreaming 13.3.1. Microstreaming principles 13.3.2. Microbubble microstreaming in medicine 13.4. Streaming in rotating fluids and planetary physics 13.4.1. Observations of streaming flow in rotating fluids 13.4.2. Possible mechanisms for streaming flows in rotating fluids Bibliography Index