Preface |
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xv | |
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Part I Fluid Dynamics and Waves |
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1 | (94) |
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Elements of fluid dynamics |
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3 | (18) |
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3 | (5) |
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Mass, momentum and velocity |
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3 | (2) |
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Material trajectories and derivatives |
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5 | (1) |
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Lagrangian and Eulerian variables |
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6 | (1) |
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Evolution of material elements |
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6 | (2) |
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8 | (3) |
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8 | (1) |
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9 | (1) |
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The polytropic fluid model |
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10 | (1) |
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Conservation laws and energy |
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11 | (1) |
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Circulation and vorticity |
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12 | (4) |
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12 | (2) |
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Vorticity and potential vorticity |
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14 | (2) |
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Rotating frames of reference |
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16 | (2) |
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18 | (2) |
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Available potential energy |
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19 | (1) |
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20 | (1) |
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21 | (17) |
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22 | (15) |
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Particle displacements and the virial theorem |
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23 | (1) |
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24 | (1) |
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Kinematics of plane waves |
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25 | (2) |
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Shallow-water plane waves |
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27 | (3) |
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30 | (2) |
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WKB theory for slowly varying wavetrains |
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32 | (4) |
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Related wave equations and adiabatic invariance |
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36 | (1) |
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37 | (1) |
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38 | (15) |
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Two-dimensional refraction |
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39 | (5) |
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Characteristics and Fermat's theorem |
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39 | (2) |
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Ocean acoustic tomography |
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41 | (1) |
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42 | (2) |
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44 | (8) |
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Green's function representation |
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44 | (1) |
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High-wavenumber boundary-value problem |
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45 | (1) |
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Stationary phase approximation |
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46 | (2) |
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Curved wave fronts and focusing |
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48 | (1) |
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The phase shift across caustics |
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49 | (1) |
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Solution directly on the caustic |
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50 | (1) |
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Non-smooth wavemakers and diffraction |
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51 | (1) |
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52 | (1) |
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Dispersive waves and ray tracing |
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53 | (42) |
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53 | (11) |
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54 | (1) |
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Boundary forcing and radiation condition |
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54 | (2) |
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Asympotic solution to initial-value problem |
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56 | (4) |
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Asymptotic wave energy dynamics |
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60 | (2) |
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The case of equal-and-opposite frequencies |
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62 | (2) |
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Examples of dispersive waves |
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64 | (6) |
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64 | (3) |
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Two-dimensional Rossby waves |
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67 | (3) |
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Ray tracing for dispersive wavetrains |
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70 | (7) |
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72 | (2) |
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Generic ray-tracing equations |
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74 | (2) |
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Symmetries and ray invariants |
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76 | (1) |
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A note on the asymptotic phase in ray tracing |
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77 | (1) |
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Ray tracing in moving media |
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77 | (8) |
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Doppler shifting and the intrinsic frequency |
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78 | (1) |
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Refraction by the basic flow |
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79 | (1) |
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Fermat's principle for dispersive wavetrains |
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80 | (3) |
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Wave action conservation and amplitude prediction |
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83 | (2) |
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Wave activity conservation laws |
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85 | (8) |
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Ensemble conservation law in discrete mechanics |
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86 | (1) |
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Ensemble conservation law for linear waves |
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87 | (1) |
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Pseudomomentum and pseudoenergy |
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88 | (2) |
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Wave action for slowly varying wavetrains |
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90 | (1) |
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Moving media and several dimensions |
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91 | (2) |
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93 | (2) |
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Part II Wave---Mean Interaction Theory |
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95 | (164) |
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Zonally symmetric wave---mean interaction theory |
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97 | (6) |
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98 | (5) |
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Small-amplitude wave-mean interactions |
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98 | (2) |
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100 | (1) |
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101 | (2) |
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103 | (39) |
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Boussinesq system and stable stratification |
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103 | (3) |
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Momentum, energy and circulation |
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105 | (1) |
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Linear Boussinesq dynamics |
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106 | (5) |
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107 | (1) |
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Plane internal gravity waves |
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107 | (3) |
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Spatial structure of time-periodic waves |
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110 | (1) |
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Two-dimensional vertical slice model |
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111 | (1) |
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Zonal pseudomomentum of internal waves |
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111 | (5) |
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Lagrangian and Eulerian pseudomomentum |
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112 | (3) |
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Forcing and dissipation of pseudomomentum |
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115 | (1) |
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Mountain lee waves and drag force |
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116 | (9) |
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Linear lee waves in two dimensions |
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117 | (4) |
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Hydrostatic solution using Hilbert transforms |
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121 | (1) |
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Drag force and momentum flux |
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122 | (3) |
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125 | (8) |
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125 | (1) |
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Mean buoyancy and pressure response |
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126 | (3) |
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129 | (1) |
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Mass, momentum and energy budgets |
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130 | (3) |
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133 | (4) |
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Radiative damping and secular mean-flow growth |
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134 | (1) |
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Non-acceleration and the pseudomomentum rule |
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135 | (2) |
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Extension to variable stratification and density |
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137 | (4) |
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Variable stratification and wave reflection |
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138 | (1) |
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Density decay and amplitude growth |
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139 | (2) |
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141 | (1) |
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142 | (29) |
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Linear Boussinesq dynamics with shear |
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143 | (5) |
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Wave activity measures with shear |
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144 | (1) |
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Energy changes for a sheared wavetrain |
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145 | (1) |
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Rayleigh's theorem for shear instability |
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146 | (1) |
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Ray tracing in a shear flow |
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147 | (1) |
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148 | (12) |
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Validity of ray tracing in critical layers |
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149 | (1) |
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Failure of steady linear theory for critical layers |
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150 | (2) |
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Causal linear theory for critical layers |
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152 | (2) |
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Singular wave absorption by dissipation |
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154 | (2) |
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Strongly nonlinear critical layers |
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156 | (2) |
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Numerical simulations and drag parametrization |
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158 | (1) |
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Saturation parametrization of critical layers |
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158 | (2) |
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Joint evolution of waves and the mean shear flow |
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160 | (10) |
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Multi-scale expansion in wave amplitude |
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161 | (3) |
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Examples of joint wave-mean dynamics |
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164 | (4) |
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The quasi-biennial oscillation |
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168 | (2) |
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170 | (1) |
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Three-dimensional rotating flow |
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171 | (15) |
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Rotating Boussinesq equations on an f-plane |
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171 | (1) |
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172 | (8) |
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Balanced vortical mode and Rossby adjustment |
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172 | (3) |
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Internal inertia-gravity waves |
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175 | (3) |
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Rotating lee waves and mountain drag |
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178 | (2) |
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Mean-flow response and the vortical mode |
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180 | (3) |
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Leading-order response and the TEM equations |
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181 | (1) |
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Forcing of mean vortical mode |
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182 | (1) |
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Rotating vertical slice model |
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183 | (2) |
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Stratification and rotation symmetry |
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183 | (1) |
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Wave-mean interactions in the slice model |
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184 | (1) |
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185 | (1) |
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Rossby waves and balanced dynamics |
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186 | (18) |
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Quasi-geostrophic dynamics |
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186 | (7) |
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187 | (2) |
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189 | (2) |
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Quasi-geostrophic β-plane |
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191 | (1) |
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Response to effective zonal mean force |
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192 | (1) |
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Small amplitude wave-mean interactions |
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193 | (3) |
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Rossby-wave pseudomomentum |
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194 | (1) |
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Localized forcing and dissipation |
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194 | (2) |
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Rossby waves and turbulence |
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196 | (7) |
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The Taylor identity for quasi-geostrophic dynamics |
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196 | (2) |
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198 | (2) |
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PV staircases and self-sharpening jets |
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200 | (3) |
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203 | (1) |
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204 | (45) |
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Lagrangian and Eulerian averaging |
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205 | (6) |
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207 | (2) |
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Stokes drift, pseudomomentum and bolus velocity |
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209 | (2) |
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211 | (18) |
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Lifting map and Lagrangian averaging |
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211 | (2) |
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The mean material derivative and trajectories |
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213 | (1) |
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214 | (3) |
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Small-amplitude relations for the mass density |
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217 | (1) |
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217 | (3) |
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Mean surface elements and conservation laws |
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220 | (3) |
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Circulation and pseudomomentum |
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223 | (2) |
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Why pseudomomentum is conserved |
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225 | (1) |
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Vorticity and potential vorticity |
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226 | (3) |
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Wave activity conservation in GLM theory |
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229 | (8) |
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General wave activity equation |
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230 | (2) |
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Pseudomomentum and pseudoenergy |
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232 | (2) |
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234 | (1) |
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Angular momentum and pseudomomentum |
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235 | (2) |
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Coriolis forces in GLM theory |
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237 | (8) |
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Rotating circulation and pseudomomentum |
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238 | (1) |
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239 | (1) |
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Angular momentum and pseudomomentum |
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240 | (1) |
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Gauged pseudomomentum and the β-plane |
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241 | (4) |
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Lagrangian-mean gas dynamics and radiation stress |
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245 | (3) |
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Radiation stress and pseudomomentum flux |
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246 | (2) |
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248 | (1) |
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Zonally symmetric GLM theory |
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249 | (10) |
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GLM theory for the Boussinesq equations |
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249 | (5) |
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Dissipative pseudomomentum rule |
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252 | (1) |
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Pseudomomentum with vertical shear |
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253 | (1) |
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Rotating Boussinesq equations on an f-plane |
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254 | (3) |
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Residual and Lagrangian-mean circulations |
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255 | (1) |
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255 | (1) |
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Rotating vertical slice model in GLM theory |
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256 | (1) |
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257 | (2) |
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Part III Waves and Vortices |
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259 | (76) |
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A framework for local interactions |
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261 | (28) |
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A geometric singular perturbation |
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262 | (1) |
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Examples of mean pressure effects |
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263 | (11) |
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Mean-flow response to acoustic wavetrain |
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264 | (3) |
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Mean force on a wavemaker |
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267 | (3) |
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Large-scale return flow beneath surface waves |
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270 | (4) |
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Vortical mean-flow response |
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274 | (7) |
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Local interactions in shallow water |
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275 | (1) |
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276 | (2) |
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278 | (2) |
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Strong interactions and potential vorticity |
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280 | (1) |
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Impulse and pseudomomentum conservation |
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281 | (7) |
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281 | (4) |
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Impulse and pseudomomentum in GLM theory |
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285 | (3) |
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288 | (1) |
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Wave-driven vortex dynamics on beaches |
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289 | (28) |
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Wave-driven longshore currents |
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289 | (2) |
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Classic theory based on simple geometry |
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291 | (7) |
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292 | (2) |
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294 | (4) |
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Theory for inhomogeneous wavetrains |
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298 | (1) |
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Vorticity generation by wave breaking and shock formation |
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299 | (4) |
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Vortex dynamics on sloping beaches |
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303 | (8) |
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Impulse for one-dimensional topography |
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304 | (1) |
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Self-advection of vortices |
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305 | (3) |
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Mutual interaction of vortices and rip currents |
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308 | (1) |
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A statistical argument for vortex locations |
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309 | (2) |
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Barred beaches and current dislocation |
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311 | (4) |
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Current dislocation by vortex dynamics |
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313 | (1) |
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Bottom fricton and turbulence |
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314 | (1) |
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315 | (2) |
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Wave refraction by vortices |
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317 | (18) |
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Anatomy of wave refraction |
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318 | (3) |
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Refraction by a bath-tub vortex |
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320 | (1) |
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321 | (3) |
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Wave capture of internal gravity waves |
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324 | (9) |
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Impulse and pseudomomentum for stratified flow |
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326 | (3) |
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Wavepacket and vortex dipole example |
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329 | (1) |
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Mean-flow response at the wavepacket |
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330 | (3) |
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Wave-vortex duality and dissipation |
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333 | (1) |
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334 | (1) |
References |
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335 | (4) |
Index |
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339 | |