## An Introduction to Atmospheric Gravity Waves, Volume 1Gravity waves exist in all types of geophysical fluids, such as lakes, oceans, and atmospheres. They play an important role in redistributing energy at disturbances, such as mountains or seamounts and they are routinely studied in meteorology and oceanography, particularly simulation models, atmospheric weather models, turbulence, air pollution, and climate research. An Introduction to Atmospheric Gravity Waves provides readers with a working background of the fundamental physics and mathematics of gravity waves, and introduces a wide variety of applications and numerous recent advances. Nappo provides a concise volume on gravity waves with a lucid discussion of current observational techniques and instrumentation. An accompanying CD-ROM contains real data, computer codes for data analysis, and linear gravity wave models to further enhance the reader's understanding of the book's material. Foreword is written by Prof. George Chimonas, a renowned expert on the interactions of gravity waves with turbulence. CD containing real data, computer codes for data analysis and linear gravity wave models included with the text |

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### Contents

FOREWORD | xv |

PREFACE | xvii |

I | 1 |

SOME WAVE MECHANICS | 6 |

FRAMES OF REFERENCE | 9 |

WAVE PHASE AND WAVE SPEED | 10 |

GROUP VELOCITY | 14 |

WAVE DISPERSION | 17 |

THE STABIL1TY OF SHEAR FLOWS | 136 |

WAVEMODULATED RICHARDSON NUMBER | 141 |

WAVETURBULENCE COUPLING | 144 |

JEFFERYS ROLLWAVE INSTABILITY MECHANISM | 149 |

WAVE SATURATION AND WAVE BREAKING | 156 |

SATURATION PARAMETERIZATION SCHEMES | 162 |

ANALOG PARAMETERIZATION SCHEMES | 169 |

SATURATION LIMITS AND OTHER PROBLEMS | 177 |

THE BOUSSINESQ APPROXIMATION | 22 |

THE TAYLORGOLDSTEIN EQUATION | 26 |

A SIMPLE SOLUTION | 31 |

CONSTANT BACKGROUND WIND SPEED | 37 |

THE WKB METHOD | 39 |

ENERGETICS | 40 |

II | 47 |

UNIFORM FLOW OVER A SURFACE CORRUGATION | 51 |

PHASE SPEED AND GROUP VELOCITY OVER A SURFACE CORRUGATION | 56 |

ENERGY FLUX OVER A SURFACE CORRUGATION | 58 |

THE TWODIMENSIONAL RIDGE | 59 |

THE THREEDIMENSIONAL MOUNTAIN | 66 |

GRAV1TY WAVE DRAG | 71 |

MATHEMATICAL DERIVATION | 72 |

THE VARIATION OF WAVE STRESS WITH HEIGHT | 74 |

WAVE STRESS OVER A SURFACE CORRUGATION | 76 |

WAVE STRESS OVER AN ISOLATED RIDGE | 77 |

SECONDARY EFFECTS OF TERRAININDUCED WAVE DRAG | 80 |

WAVE REFLECTION AT AN ELEVATED LAYER | 86 |

WAVE TRAPPING ENERGY FLUX AND WAVE RESONANCE | 91 |

REFLECTION AT THE GROUND SURFACE | 94 |

WAVE DUCTS | 98 |

THE WIND DUCT | 101 |

WIND SPIRALS AND DUCTS | 107 |

III | 111 |

WAVE ACTION | 112 |

IV | 125 |

SHEAR INSTABILITY AND UNSTABLE MODES | 129 |

KELVINHELMHOLTZ INSTABILITY | 130 |

SINGLESTATION OBSERVATIONS | 182 |

FREEBALLOON SOUNDINGS | 183 |

3 REMOTE SENSORS | 185 |

MULTIPLE STATION OBSERVATIONS | 192 |

PRESSURE PERTURBATION MEASUREMENTS | 194 |

BALLOONS AIRCRAFT AIRGLOW AND SATELLITES | 203 |

AIRCRAFT | 204 |

AIRGLOW | 205 |

SATELLITES | 206 |

DATA ANALYS1S | 210 |

PRESSUREWIND CORRELATION | 211 |

LAG ANALYSIS | 214 |

BEAMSTEERING | 217 |

WAVELET ANALYSIS | 221 |

NUMERICAL MODELS | 227 |

TERRAINGENERATED GRAVITY WAVE | 229 |

DUCTED GRAVITY WAVES | 233 |

V | 237 |

THE SCALE HEIGHT OF THE ISOTHERMAL ATMOSPHERE | 238 |

BOUSSINESQ RELATIONS | 239 |

A6 THE GEOSTROPHIC WIND | 240 |

VI | 245 |

B2 FORTRAN CODES | 246 |

RIDGE_CFOR AND RIDGEJXFOR | 247 |

WIND JUCT_SCANFOR AND WIND_DUCT_MODESFOR | 248 |

SYNTHETIC WAVE DATA | 249 |

251 | |

263 | |

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### Common terms and phrases

air parcel array assume Atmos background wind speed balloon beamsteering boundary condition Boussinesq approximation calculated Chapter Chimonas codes component constant convective convective instability critical level decreases density direction disturbance Doppler dynamic evanescent example F1GURE Figure fluid Fourier transform function Gossard gravity waves ground surface group velocity height Hines horizontal illustrated in Fig instability interface lee waves lidar linear theory maximum momentum mountain waves Nappo observed parameterization schemes phase speed phase velocity plane planetary boundary layer potential temperature pressure perturbation profiles radar region Richardson number ridge scale shown in Fig sodar solution stability stations stratification streamline surface corrugation Taylor-Goldstein equation term terrain troposphere two-dimensional upper values vertical velocity vertical wavenumber wave amplitude wave breaking wave drag wave energy wave field wave fronts wave perturbation wave propagation wave reflection wave saturation wave stress wave vector wavelength wavelet analysis wavenumber waves and turbulence ZTOP