## Atmosphere-Ocean Dynamics, Volume 30In this important new work, Dr. Gill provides a unified, comprehensive approach to the study of oceanic and atmospheric circulations. He explains how atmospheric and oceanic circulations are ultimately driven by solar energy and covers the study of observed distributions of physical quantities, including temperature. Concise treatments of basic hydrostatics and thermodynamics are also provided. This instructive work uses simple mathematical models to illustrate fundamental dynamical principles, enabling scholars from diverse disciplines to understand complex theory. Furthermore, the equations of state and dynamical equations are covered in detail, making this a self-contained text for those with advanced mathematical training. The extensive bibliography and index and the historical information included make this volume useful reading for researchers, as well as a valuable text for both undergraduate and graduate students in meteorology, oceanography, and geophysical fluid dynamics. |

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### Contents

How the OceanAtmosphere System Is Driven | 1 |

12 The Amount of Energy Received by the Earth | 2 |

13 Radiative Equilibrium Models | 7 |

14 The Greenhouse Effect | 8 |

15 Effects of Convection | 10 |

16 Effects of Horizontal Gradients | 13 |

17 Variability in Radiative Driving of the Earth | 15 |

Transfer of Properties between Atmosphere and Ocean | 19 |

812 The LiouvilleGreen or WKBJ Approximation | 297 |

813 Wave Interactions | 302 |

814 The Internal Wave Spectrum in the Ocean | 305 |

815 Wave Transport and Effects on the Mean Flow | 309 |

The Isallobaric Wind | 311 |

Forced Motion | 317 |

Ekman Transport | 319 |

93 WindGenerated Inertia Oscillations in the Ocean Mixed Layer | 322 |

22 Contrasts in Properties of Ocean and Atmosphere | 20 |

23 Momentum Transfer between Air and Sea and the Atmospheres Angular Momentum Balance | 22 |

24 Dependence of Exchange Rates on AirSea Velocity Temperature and Humidity Differences | 26 |

25 The Hydrological Cycle | 31 |

26 The Heat Balance of the Ocean | 33 |

27 Surface Density Changes and the Thermohaline Circulation of the Ocean | 36 |

Properties of a Fluid at Rest | 39 |

32 Thermodynamic Variables | 41 |

33 Values of Thermodynamic Quantities for the Ocean and Atmosphere | 43 |

34 Phase Changes | 44 |

35 Balance of Forces in a Fluid at Rest | 45 |

36 Static Stability | 50 |

37 Quantities Associated with Stability | 51 |

38 Stability of a Saturated Atmosphere | 55 |

39 Graphical Representation of Vertical Soundings | 58 |

Equations Satisfied by a Moving Fluid | 63 |

42 Mass Conservation Equation | 64 |

43 Balances for a Scalar Quantity like Salinity | 66 |

44 The Internal Energy or Heat Equation | 70 |

45 The Equation of Motion | 72 |

46 Mechanical Energy Equation | 76 |

47 Total Energy Equation | 79 |

48 Bernoullis Equation | 82 |

49 Systematic Effects of Diffusion | 83 |

410 Summary List of the Governing Equations | 84 |

411 Boundary Conditions | 85 |

412 A Coordinate System for Planetary Scale Motions | 91 |

Adjustment under Gravity in a Nonrotating System | 95 |

52 Perturbations from the Rest State for a Homogeneous Inviscid Fluid | 99 |

53 Surface Gravity Waves | 101 |

54 Dispersion | 104 |

55 ShortWave and LongWave Approximations | 106 |

56 ShallowWater Equations Derived Using the Hydrostatic Approximation | 107 |

57 Energetics of ShallowWater Motion | 111 |

58 Seiches and Tides in Channels and Gulfs | 112 |

Adjustment under Gravity of a DensityStratified Fluid | 117 |

62 The Case of Two Superposed Fluids of Different Density | 119 |

63 The Baroclinic Mode and the Rigid Lid Approximation | 127 |

64 Adjustments within a Continuously Stratified Incompressible Fluid | 128 |

65 Internal Gravity Waves | 131 |

66 Dispersion Effects | 134 |

67 Energetics of Internal Waves | 139 |

68 Internal Waves Generated at a Horizontal Boundary | 142 |

69 Effects on BoundaryGenerated Waves of Variations of Buoyancy Frequency with Height | 146 |

610 Free Waves in the Presence of Boundaries | 153 |

Normal Modes | 159 |

612 An Example of Adjustment to Equilibrium in a Stratified Fluid | 162 |

613 Resolution into Normal Modes for the Ocean | 167 |

614 Adjustment to Equilibrium in a Stratified Compressible Fluid | 169 |

615 Examples of Adjustment in a Compressible Atmosphere | 175 |

616 Weak Dispersion of a Pulse | 177 |

617 Isobaric Coordinates | 180 |

618 The Vertically Integrated Perturbation Energy Equation in Isobaric Coordinates | 186 |

Effects of Rotation | 189 |

72 The Rossby Adjustment Problem | 191 |

73 The Transients | 196 |

74 Applicability to the Rotating Earth | 204 |

75 The Rossby Radius of Deformation | 205 |

76 The Geostrophic Balance | 208 |

The Thermal Wind | 215 |

78 Available Potential Energy | 219 |

79 Circulation and Vorticity | 226 |

710 Conservation of Potential Vorticity for a Shallow Homogeneous Layer | 231 |

711 Circulation in a Stratified Fluid and Ertels Potential Vorticity | 237 |

712 Perturbation Forms of the Vorticity Equations in a Uniformly Rotating Fluid | 241 |

713 Initialization of Fields for Numerical Prediction Schemes | 243 |

Gravity Waves in a Rotating Fluid | 247 |

Poincaré Waves | 249 |

83 Dispersion Properties and Energetics of Poincaré Waves | 254 |

84 Vertically Propagating Internal Waves in a Rotating Fluid | 256 |

85 Polarization Relations | 262 |

86 Energetics | 266 |

87 Waves Generated at a Horizontal Boundary | 268 |

88 Mountain Waves | 274 |

89 Effects of Variation of Properties with Height | 283 |

810 FiniteAmplitude Topographic Effects | 292 |

811 Dissipative Effects in the Upper Atmosphere | 294 |

94 Ekman Pumping | 326 |

Velocity Structure of the Boundary Layer | 328 |

96 The Laminar Ekman Layer | 331 |

97 The Nocturnal Jet | 332 |

98 TideProducing Forces | 334 |

The Forced ShallowWater Equation | 337 |

Use of Normal Modes | 342 |

911 Response of the Ocean to a Moving Storm or Hurricane | 346 |

912 SpinDown by Bottom Friction | 353 |

913 Buoyancy Forcing | 356 |

A Barotropic Example | 360 |

915 A Forced Baroclinic Vortex | 362 |

916 Equilibration through Dissipative Effects | 367 |

Effects of Side Boundaries | 371 |

102 Effects of Rotation on Seiches and Tides in Narrow Channels and Gulfs | 373 |

103 Poincare Waves in a Uniform Channel of Arbitrary Width | 376 |

104 Kelvin Waves | 378 |

105 The Full Set of Modes for an Infinite Channel of Uniform Width | 380 |

Seiches and Tides in a Gulf That Is Not Narrow | 382 |

107 Adjustment to Equilibrium in a Channel | 385 |

108 Tides | 391 |

The Local Solution | 394 |

Forced Kelvin Waves | 398 |

1011 Coastal Upwelling | 403 |

1012 Continental Shelf Waves | 408 |

1013 Coastally Trapped Waves | 415 |

1014 Eastern Boundary Currents | 421 |

The Tropics | 429 |

ShallowWater Equations on the Sphere | 431 |

113 Potential Vorticity for a Shallow Homogeneous Layer | 433 |

114 The Equatorial Beta Plane | 434 |

115 The Equatorial Kelvin Wave | 436 |

116 Other Equatorially Trapped Waves | 438 |

Gravity Waves | 440 |

118 Planetary Waves and Quasigeostrophic Motion | 444 |

119 Baroclinic Motion near the Equator | 449 |

1110 Vertically Propagating Equatorial Waves | 450 |

1111 Adjustment under Gravity near the Equator | 454 |

1112 Transient Forced Motion | 458 |

The Steady Limit | 465 |

1114 Steady Forced Motion | 466 |

1115 The Tropical Circulation of the Atmosphere | 472 |

1116 Tropical Ocean Currents | 482 |

Midlatitudes | 493 |

122 The Midlatitude Beta Plane | 494 |

123 Planetary Waves | 500 |

124 SpinUp of the Ocean by an Applied Wind Stress | 507 |

125 Steady Ocean Circulation | 512 |

126 Western Boundary Currents | 516 |

127 Vertical Propagation of Planetary Waves in a Medium at Rest | 523 |

128 Nonlinear Quasigeostrophic Flow in Three Dimensions | 527 |

129 Small Disturbances on a Zonal Flow Varying with Latitude and Height | 532 |

1210 Deductions about Vertical Motion from the Quasigeostrophic Equations | 543 |

Instabilities Fronts and the General Circulation | 549 |

132 Free Waves in the Presence of a Horizontal Temperature Gradient | 550 |

The Eady Problem | 556 |

The Charney Problem | 560 |

135 Necessary Conditions for Instability | 563 |

136 Barotropic Instability | 565 |

137 Eddies in the Ocean | 568 |

138 Fronts | 571 |

139 The Life Cycle of a Baroclinic Disturbance | 578 |

1310 General Circulation of the Atmosphere | 582 |

Units and Their SI Equivalents | 595 |

Useful Values | 597 |

Properties of Seawater | 599 |

A32 Other Quantities Related to Density | 600 |

A33 Expansion Coefficients | 601 |

A35 Potential Temperature | 602 |

Properties of Moist Air | 605 |

A42 Saturation Vapor Pressure | 606 |

A44 Latent Heats | 607 |

A List of Atlases and Data Sources | 609 |

613 | |

645 | |

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### Common terms and phrases

adjustment amplitude applied approximation associated atmosphere balance becomes boundary calculated called changes Chapter circulation compared component condition considered constant continuity contours corresponding currents defined density depends depth derived direction discussed dispersion displacement distance disturbance effects Ekman energy equal equation equilibrium example expression fact flow fluid flux follows forcing frequency friction function geostrophic given gives gradient gravity heat height horizontal important increases initial internal latitude layer lines mass maximum mean mode momentum motion moving namely normal observed obtained ocean particle particular perturbation phase plane potential pressure problem produced propagation properties quantity radius region relation relative response result Rossby rotation salinity satisfied scale Section shown in Fig shows side similar solution speed stress studied surface temperature unit upward variations varies velocity vertical volume wavenumber waves wind zero