Fluid Waves

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