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| Preface | |
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| Acknowledgments | |
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| Introduction and Review of Mathematical Tools | |
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| Objectives | |
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| Fluids and the nature of fluid dynamics | |
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| Review of useful mathematical tools | |
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| Elements of vector calculus | |
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| The Taylor series expansion | |
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| Centered difference approximations to derivatives | |
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| Temporal changes of a continuous variable | |
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| Estimating with scale analysis | |
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| Basic kinematics of fluids | |
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| Pure vorticity | |
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| Pure divergence | |
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| Pure stretching deformation | |
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| Pure shearing deformation | |
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| Mensuration | |
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| Selected references | |
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| Problems | |
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| Solutions | |
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| Fundamental and Apparent Forces | |
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| Objectives | |
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| The fundamental forces | |
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| The pressure gradient force | |
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| The gravitational force | |
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| The frictional force | |
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| Apparent forces | |
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| The centrifugal force | |
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| The Coriolis force | |
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| Selected references | |
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| Problems | |
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| Solutions | |
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| Mass, Momentum, and Energy: The Fundamental Quantities of the Physical World | |
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| Objectives | |
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| Mass in the Atmosphere | |
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| The hypsometric equation | |
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| Conservation of momentum: The equations of motion | |
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| The equations of motion in spherical coordinates | |
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| Conservation of mass | |
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| Conservation of energy: The energy equation | |
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| Selected references | |
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| Problems | |
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| Solutions | |
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| Applications of the Equations of Motion | |
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| Objectives | |
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| Pressure as a vertical coordinate | |
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| Potential temperature as a vertical coordinate | |
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| The thermal wind balance | |
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| Natural coordinates and balanced flows | |
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| Geostrophic flow | |
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| Inertial flow | |
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| Cyclostrophic flow | |
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| Gradient flow | |
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| The relationship between trajectories and streamlines | |
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| Selected references | |
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| Problems | |
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| Solutions | |
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| Circulation, Vorticity, and Divergence | |
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| Objectives | |
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| The Circulation theorem and its physical interpretation | |
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| Vorticity and potential vorticity | |
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| The relationship between vorticity and divergence | |
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| The quasi-geostrophic system of equations | |
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| Selected references | |
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| Problems | |
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| Solutions | |
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| The Diagnosis of Mid-Latitude Synoptic-Scale Vertical Motions | |
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| Objectives | |
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| The nature of the ageostrophic wind: Isolating the acceleration vector | |
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| Sutcliffe's expression for net ageostrophic divergence in a column | |
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| Another perspective on the ageostrophic wind | |
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| The Sutcliffe development theorem | |
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| The quasi-geostrophic omega equation | |
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| The Q-vector | |
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| The geostrophic paradox and its resolution | |
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| A natural coordinate version of the Q-vector | |
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| The along- and across-isentrope components of Q | |
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| Selected references | |
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| Problems | |
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| Solutions | |
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| The Vertical Circulation at Fronts | |
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| Objectives | |
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| The structural and dynamical characteristics of mid-latitude fronts | |
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| Frontogenesis and vertical motions | |
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| The semi-geostrophic equations | |
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| Upper-level frontogenesis | |
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| Precipitation processes at fronts | |
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| Selected references | |
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| Problems | |
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| Solutions | |
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| Dynamical Aspects of the Life Cycle of the Mid-Latitude Cyclone | |
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| Objectives | |
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| Introduction: The polar front theory of cyclones | |
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| Basic structural and energetic characteristics of the cyclone | |
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| The cyclogenesis stage: The QG tendency equation perspective | |
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| The cyclogenesis stage: The QG omega equation perspective | |
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| The cyclogenetic influence of diabatic processes: Explosive cyclogenesis | |
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| The post-mature stage: Characteristic thermal structure | |
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| The post-mature stage: The QG dynamics of the occluded quadrant | |
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| The Decay Stage | |
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| Selected references | |
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| Problems | |
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| Solutions | |
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| Potential Vorticity and Applications to Mid-Latitude Weather Systems | |
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| Objectives | |
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| Potential vorticity and isentropic divergence | |
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| Characteristics of a positive PV anomaly | |
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| Cyclogenesis from the PV perspective | |
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| The influence of diabatic heating on PV | |
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| Additional applications of the PV perspective | |
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| Piecewise PV inversion and some applications | |
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| A PV perspective on occlusion | |
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| A PV perspective on leeside cyclogenesis | |
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| The effects of PV superposition and attenuation | |
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| Selected references | |
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| Problems | |
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| Solutions | |
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| Virtual Temperature | |
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| Bibliography | |
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| Index | |