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"ATMOSPHERIC CONVECTION Kerry A. Emanuel Center for Meteorology and Physical Oceanography Massachusetts Institute of Technology New York Oxford OXFORD UNIVERSITY PRESS 1994 Copyright (c) 1994 by Oxford University Press, Inc. Published by Oxford University Press, Inc., 200 Madison Avenue, New York, New York 10016 Oxford is a registered trademark of Oxford University Press All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior permission of Oxford University Press. Library of Congress Cataloging-in-Publication Data Emanuel, Kerry A., 1955 Atmospheric convection Kerry A. Emanuel p. cm. Includes bibliographical references and index ISBN 0-19-506630-8 1. Convection (Meteorology) 2. Atmospheric physics I Title QC880.4.C64E5 1994 551.515-dc20 93-10414 Figure 7.4 is reprinted with permission of the Research Council of Canada from MacPherson, J. I., and G. A. Issac, 1977: J. Appl. Meteor. 16,81-90. Figure 9.3 is reproduced by courtesy of H. Bluestein (c) 1993. Contents Part I. DRY CONVECTION 1. General Principles 3 1.1 Definition of convection, 4 1.2 The buoyancy force, 8 1.3 The Boussinesq and anelastic approximations, 8 Exercises, 13 Convective flow from local sources 14 2.1 The similarity approach and definitions of thermal and plumes, 14 2.2 Turbulent plumes originating from a maintained point source, 16 2.3 Turbulent plumes originating from a maintained line source, 18 2.4 Turbulent convection from an instantaneous point source (thermals), 20 2.5 Turbulent starting plumes, 21 2.6 Laminar plumes originating from a maintained point source, 23 2.7 Turbulent convection in stably stratified fluid, 25 2.8 Experiments and observations, 30 Exercises, 40 Global convection: the Rayleigh-Bénard problem and dry convective boundary layers 7 3.1 Linear stability analysis of Rayleigh convection: the original Rayleigh problem, 9 3.2 Parallel-plate convection with insulating boundaries, 10 3.3 Inclusion of rotational effects, 65 3.4 Parallel-plate convection in shear flows, 73 3.5 Nonlinear parallel-plate convection, 82 3.6 Convective boundary layers, 89 Exercises, 7 Part II. MOIST THERMODYNAMICS AND STABILITY 4. Moist thermodynamic processes 10 4.1 Moisture variables, 10 4.2 Thermodynamics of unsaturated moist air, 13 4.3 Virtual and density temperatures, 15 4.4 Phase equilibrium of water substance, 18 4.5 Conserved moisture thermodynamic variables, 27 4.6 Processes leading to saturation in the atmosphere, 30 4.7 Reversible and pseudoadiabatic processes, 39 4.8 Microphysical considerations, 43 4.9 Thermodynamics of the ice phase, 51 Exercises, 5 Graphical techniques 5. 5.1 Thermodynamic diagrams, 62 5.2 Conserved-variable diagrams, 70 Exercises, 6 Stability 6. 6.1 Static stability of moist unsaturated air, 83 6.2 Static stability of cloudy air, 94 6.3 Stability to finite-amplitude displacements: the parcel method, 105 6.4 Stability diagrams, 117 6.5 The "slice Method," 125 6.6 Available potential energy of barotropic moist atmospheres, 133 Remarks on conditional versus potential instability, Exercises, 145 Part III. LOCAL PROPERTIES OF MOIST CONVECTION 7. Observed characteristics of nonprecipitating cumuli 159 7.1 Measurement of clouds, 160 7.2 Kinematic structure of nonprecipitating cumuli, 163 7.3 Distributions of cloud water, temperature, and mixing ratio in nonprecipitating cumuli, 168 7.4 Inferences about entrainment and mixing from conserved-variable diagrams, 175" Ключевые слова: horizontal planforms, rayleigh, complex conjugate, global dry, taylor, dimensional analysis, reynolds number, dimensionless parameter, equation, surface, fluid, mass, oo, heat capacity, velocity, rayleigh number, source, atmospheric science, behavior, mach number, kinetic energy, scale, time, uniform temperature, critical rayleigh, stationary overturning, uniform stratification, independent, cross-roll instability, molecular diffusion, disturbance, global, plate, successive outline, displaced parcel, layer, point source, total force, entrainment velocity, turbulent, dimensionless, height, ha, stratified, gaussian profile, boussinesq approximation, experiment, archimedes, equilibrium, entrainment parameter, critical, fluid mech, problem, free-slip, vertical gradient, soc, atmos, spatial structure, general, critical rayleigh number, transition, dry convection, order, radial profile, local sources, free-slip boundary, individual particle, convective overturning, instability, turner, fully turbulent, dry, twodimensional roll, occurs, dimensionless constant, form, experimental data, earths atmosphere, continuity equation, boundary condition, premdtl number, stationary, molecular viscosity, moist, incremental volume, horizontal, horizontal plane, roy, rotation, velocity component, boundary layer, free-slip condition, oscillatory, exercises, small compared, gradient, roll, moist convection, mech, defined, vertical, plume, relation, constant, note, rouse yih, chandrasekhar, convective cell, slip, radial dependence, passive tracer, anelastic approximation, atmosphere, horizontal boundary, rate, infinite number, small, parameter, convecting layer, linear, boundary, dimensional, temperature, asterisk denote, froude number, angular momentum, morton taylor, buoyant, solution, semi-infinite layer, advancing cap, number, solved analytically, heat, variable, point, taylor number, horizontal velocity, phys, air, constant geopotential, perturbation, meteor, function, flux, result, horizontally uniform, definition, specific heat, wave propagation, vertical profile, molecular flux, force, cloud, ra, governing equation, conical cross, rotating coordinate, quantity, vertical velocity, nusselt number, no-slip free-slip, rayleigh-benard problem, flow, momentum, no-slip, free, consideration, mode, prandtl number, navier-stokes equation, theorem, velocity divergence, horizontal structure, case, striking aspect, set, pressure, molecular diffusivities, stability, parameter describing, specific volume, small parameter, vertical advection, ideal gas, cumulus, heat flux, condition, external parameter, dz, cyclostrophic equilibrium, proc, vertical component, term, motion, buoyancy, heat diffusion, density, energy, shearing instability, thermal, acceleration, convection, remaining equation, growth rate, unstable, local, horizontal wavenumbers, radial, dependence, stratification, oscillatory instability, boussinesq, analysis, minimizing, profile, convective, shear