Table of contents for: Waves and Mean Flows by Oliver Bühler Cambridge University Press 2009 Monographs on Mechanics. Contents.

Transcription

1 Table of contents for: Waves and Mean Flows by Oliver Bühler Cambridge University Press 2009 Monographs on Mechanics. Preface page 2 Part I Fluid Dynamics and Waves 7 1 Elements of fluid dynamics Flow kinematics Mass, momentum, and velocity Material trajectories and derivatives Lagrangian and Eulerian variables Evolution of material elements Perfect fluid dynamics Euler s equation Constitutive relations The polytropic fluid model Conservation laws and energy Circulation and vorticity Circulation theorem Vorticity and potential vorticity Rotating frames of reference Shallow-water system Available potential energy References 27 2 Linear waves Linear dynamics Particle displacements and the virial theorem Vortical and wave modes Kinematics of plane waves Shallow-water plane waves 34 iii

2 iv Refraction WKB theory for slowly varying wavetrains Related wave equations and adiabatic invariance References 45 3 Geometric wave theory Two-dimensional refraction Characteristics and Fermat s theorem Ocean acoustic tomography Ray tubes Caustics Green s function representation High-wavenumber boundary-value problem Stationary phase approximation Curved wave fronts and focusing The phase shift across caustics Solution directly on the caustic Non-smooth wavemakers and diffraction References 60 4 Dispersive waves and ray tracing Facets of group velocity Beat waves Boundary forcing and radiation condition Asympotic solution to initial-value problem Asymptotic wave energy dynamics The case of equal-and-opposite frequencies Examples of dispersive waves Rotating shallow water Two-dimensional Rossby waves Ray tracing for dispersive wavetrains Model example Generic ray-tracing equations Symmetries and ray invariants A note on the asymptotic phase in ray tracing Ray tracing in moving media Doppler shifting and the intrinsic frequency Refraction by the basic flow Fermat s principle for dispersive wavetrains Wave action conservation and amplitude prediction Wave activity conservation laws 93

3 v Ensemble conservation law in discrete mechanics Ensemble conservation law for linear waves Pseudomomentum and pseudoenergy Wave action for slowly varying wavetrains Moving media and several dimensions References 101 Part II Wave Mean Interaction Theory Zonally symmetric wave mean interaction theory Basic assumptions Small-amplitude wave mean interactions Simple geometry Zonal averaging Internal gravity waves Boussinesq system and stable stratification Momentum, energy, and circulation Linear Boussinesq dynamics Vortical mode Plane internal gravity waves Spatial structure of time-periodic waves Two-dimensional vertical slice model Zonal pseudomomentum of internal waves Lagrangian and Eulerian pseudomomentum Forcing and dissipation of pseudomomentum Mountain lee waves and drag force Linear lee waves in two dimensions Hydrostatic solution using Hilbert transforms Drag force and momentum flux Mean-flow response Eulerian-mean equations Mean buoyancy and pressure response Zonal mean-flow response Mass, momentum, and energy budgets Wave dissipation Radiative damping and secular mean-flow growth Non-acceleration and the pseudomomentum rule Extension to variable stratification and density Variable stratification and wave reflection Density decay and amplitude growth 147

4 vi 6.8 References Shear flows Linear Boussinesq dynamics with shear Wave activity measures with shear Energy changes for a sheared wavetrain Rayleigh s theorem for shear instability Ray tracing in a shear flow Critical layers Validity of ray tracing in critical layers Failure of steady linear theory for critical layers Causal linear theory for critical layers Singular wave absorption by dissipation Strongly nonlinear critical layers Numerical simulations and drag parametrization Saturation parametrization of critical layers Joint evolution of waves and the mean shear flow Multi-scale expansion in wave amplitude Examples of joint wave mean dynamics The quasi-biennial oscillation References Three-dimensional rotating flow Rotating Boussinesq equations on an f-plane Linear structure Balanced vortical mode and Rossby adjustment Internal inertia gravity waves Rotating lee waves and mountain drag Mean-flow response and the vortical mode Leading-order response and the TEM equations Forcing of mean vortical mode Rotating vertical slice model Stratification and rotation symmetry Wave mean interactions in the slice model References Rossby waves and balanced dynamics Quasi-geostrophic dynamics Governing equations Conservation properties Quasi-geostrophic β-plane Response to effective zonal mean force 200

5 vii 9.2 Small amplitude wave mean interactions Rossby-wave pseudomomentum Localized forcing and dissipation Rossby waves and turbulence The Taylor identity for quasi-geostrophic dynamics Turbulent mixing of PV PV staircases and self-sharpening jets References Lagrangian-mean theory Lagrangian and Eulerian averaging Stokes corrections Stokes drift, pseudomomentum, and bolus velocity Elements of GLM theory Lifting map and Lagrangian averaging The mean material derivative and trajectories Mean mass conservation Small-amplitude relations for the mass density The divergence effect Mean surface elements and conservation laws Circulation and pseudomomentum Why pseudomomentum is conserved Vorticity and potential vorticity Wave activity conservation in GLM theory General wave activity equation Pseudomomentum and pseudoenergy Non-barotropic flows Angular momentum and pseudomomentum Coriolis forces in GLM theory Rotating circulation and pseudomomentum Wave activity relations Angular momentum and pseudomomentum Gauged pseudomomentum and the β-plane Lagrangian-mean gas dynamics and radiation stress Radiation stress and pseudomomentum flux References Zonally symmetric GLM theory GLM theory for the Boussinesq equations Dissipative pseudomomentum rule Pseudomomentum with vertical shear 263

6 viii 11.2 Rotating Boussinesq equations on an f-plane Residual and Lagrangian-mean circulations EP flux in GLM theory Rotating vertical slice model in GLM theory References 267 Part III Waves and Vortices A framework for local interactions A geometric singular perturbation Examples of mean pressure effects Mean-flow response to acoustic wavetrain Mean force on a wavemaker Large-scale return flow beneath surface waves Vortical mean-flow response Local interactions in shallow water Bretherton flow A wavepacket life cycle Strong interactions and potential vorticity Impulse and pseudomomentum conservation Classical impulse theory Impulse and pseudomomentum in GLM theory References Wave-driven vortex dynamics on beaches Wave-driven longshore currents Classic theory based on simple geometry Wave structure Mean-flow response Theory for inhomogeneous wavetrains Vorticity generation by wave breaking and shock formation Vortex dynamics on sloping beaches Impulse for one-dimensional topography Self-advection of vortices Mutual interaction of vortices and rip currents A statistical argument for vortex locations Barred beaches and current dislocation Current dislocation by vortex dynamics Bottom fricton and turbulence References 325

7 ix 14 Wave refraction by vortices Anatomy of wave refraction Refraction by a bath-tub vortex Remote recoil Wave capture of internal gravity waves Impulse and pseudomomentum for stratified flow Wavepacket and vortex dipole example Mean-flow response at the wavepacket Wave vortex duality and dissipation References 344 Bibliography 345 Index 349