E-Book Overview
The phenomena treated in this book all depend on the action of gravity on small density differences in a non-rotating fluid. The author gives a connected account of the various motions which can be driven or influenced by buoyancy forces in a stratified fluid, including internal waves, turbulent shear flows and buoyant convection. This excellent introduction to a rapidly developing field, first published in 1973, can be used as the basis of graduate courses in university departments of meteorology, oceanography and various branches of engineering. This edition is reprinted with corrections, and extra references have been added to allow readers to bring themselves up to date on specific topics. Professor Turner is a physicist with a special interest in laboratory modelling of small-scale geophysical processes. An important feature is the superb illustration of the text with many fine photographs of laboratory experiments and natural phenomena.
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BUOYANCY EFFECTS I N FLUIDS J. S. T U R N E R Assistant Director of Research in Fluid Mechanics Department of Applied Mathematics and Theoretical Physics University of Cambridge CAMBRIDGE / A T T H E UNIVERSITY PRESS I973 Published by the Syndics of the Cambridge University Press Bentley House, zoo Euston Road, London NW I 2 D B American Branch: 32 East 57th Street, New York, N.Y. I O O ~ Z O Cambridge University Press 1973 Library of Congress Catalogue Card Number: 7276085 Printed in Great Britain at the University Printing House, Cambridge (Brooke Cmtchley, University Printer) T O MY FATHER CONTENTS page xiii Preface I INTRODUCTION A N D PRELIMINARIES Z The topics to be discussed I Equilibrium and departures from it 3 6 The equations of motion and various approximations Basic parameters of heterogeneous flows 2 II LINEAR INTERNAL WAVE-S I4 Waves at a boundary between homogeneous layers Progressive waves in deep water, 15; Waves between layers of finite thickness, 18;Standing waves, 19 14 Waves in a continuously stratified fluid Description in terms of modes, 22; Description in terms of rays, 24;Laboratory experiments on waves in bounded regions, 29 21 Waves in a moving stratified fluid Velocity constant with height, 3I ; Lee waves with varying properties in the vertical, 34; Reversals of velocity and critical layers, 37 3I Weak non-linearities: interactions between waves The mechanism of resonant interaction, 39; Interactions of interfacial waves, 41; Interactions with continuous stratification, 44 39 - 3 FINITE AMPLITUDE MOTIONS I N STABLY STRATIFIED FLUIDS Internal waves of finite amplitude Interfacial waves, 48; Cnoidal and solitary waves, 52; Waves and flows in a density gradient, 55; Finite amplitude lee waves, 58 48 48 CONTENTS Internal hydraulics and related problems page 64 Steady frictionless flow of a thin layer, 64; Internal hydraulic jumps, 66; Flow down a slope, 68; The 'lock exchange' problem, 70;Gravity currents and noses, 72 Slow motions in a stratified fluid The problem of selective withdrawal, 76; Blocking ahead of an obstacle, 79; Upstream wakes and boundary layers, 82;Viscous diffusive flows, 86 76 The stability of a free shear layer The various types of instability, 92;The Kelvin-Helmholtz mechanism, 94;Interfaces of finite thickness, 97;Observations of the breakdown of parallel stratified flows, 102 92 The combined effects of viscosity and stratification Viscous effects at an interface, 107;Thermally stratified plane Poiseuille flow, 108;Flows along a sloping boundary, I I I ; Transition to turbulence, I 14