Advances in Applied Mechanics Volume 16 Editorial Board T. BROOKE BENJAMIN Y. c. FUNG PAULGERMAIN L. HOWARTH WILLIAM PRAGER T. Y . Wu HANSZIEGLER Contributors to Volume 16 G. K. BATCHELOR ROBIN D. HILL H. KOLSKY H. K. MOFFATT D. H. PEREGRINE GEORGE I. N. ROZVANY CHIA-SHUN YIH ADVANCES IN APPLIED MECHANICS Edited by Chia-Shun Yih DEPARTMENT OF APPLIED MECHANICS AND ENGINEERING SCIENCE THE UNIVERSITY OF MICHIGAN ANN ARBOR, MICHIGAN V O L U M E 16 1976 A C A D E M I C PRESS New York San Francisco London A Subsidiary of Harcourt Brace Jovanovich, Publishers COPYRIGHT 0 1976, BY ACADEMIC PRESS, INC. ALL RIGHTS RESERVED. NO PART OF THIS PUBLICATION MAY BE REPRODUCED OR TRANSMITTED IN ANY FORM OR BY ANY MEANS, ELECTRONIC OR MECHANICAL, INCLUDING PHOTOCOPY, RECORDING, OR ANY INFORMATION STORAGE AND RETRIEVAL SYSTEM, WITHOUT PERMISSION IN WRITING FROM THE PUBLISHER. ACADEMIC PRESS, INC. 111 Fifth Avenue, New York, New York 10003 United Kingdom Edition published by ACADEMIC PRESS, INC. (LONDON) LTD. 24/28 Oval Road, London N W l LIBRARY OF CONGRESS CATALOG CARD NUMBER:48-8503 ISBN 0- 12-002016-5 PRINTED IN THE UNITED STATES OF AMERICA Contents vii viii LISTOF CONTRIBUTORS PREFACE 1 G. I. Taylor as I Knew Him G.K.Batchelor Interaction of Water Waves and Currents D. H.Peregrine 10 17 70 76 103 106 111 I. Introduction 11. Large-Scale Currents 111. Small-Scale Currents IV. Currents Varying with Depth V. Turbulence VI. Ship Waves References Generation of Magnetic Fields by Fluid Motion H.K. Moflatt I. Introduction 11. 111. IV. V. Magnetokinematic Preliminaries Convection, Distortion, and Diffusion of 5Lines Some Basic Results The Mean Electromotive Force Generated by a Random Velocity Field VI. Braginskii's Theory of Nearly +xisymmetric Fields VII. Analytical and Numerical Solutions of the Dynamo Equations VIII. Dynamic Effects and Self-Equilibration References V 120 125 130 135 139 154 163 168 176 vi Contents The Theory of Optimal Load Transmission by Flexure George I . N . Romany and Robin D . Hill I. 11. 111. IV. V. VI. VII. VIII. Introduction Static-Kinematic Optimelity Criteria-Plastic Design General Optimality Criteria-Elastic Design Optimal Flexure Fields-Basic Geometrical Properties Optimal Flexure Fields-Clamped Boundaries Optimal Flexure Fields-Mixed Boundary Conditions Optimal Flexure Fields-Further Developments Optimal Flexure Fields of Constrained Geometry List of Symbols References i84 187 20 I 206 226 2 46 292 299 303 304 The Role of Experiment in the Development of Solid Mechanics-Some Examples H . Kolsky I. Introduction 11. Viscoelastic Behavior 111. Experimental Determination of Viscoelastic Response IV. Tensile Shock Waves in Rubber V. Plastic Wave Propagation VI. Experimental Studies in Dynamic Fracture VII. Conclusion References 309 3 16 322 345 349 354 364 365 Instability of Surface and Internal Waves Chiu-Shun Y ih I. General Introduction 11. Instability of Surface Waves 111. Instability of Internal Waves References AUTHOR INDEX SUBJECT INDEX 369 37 1 393 419 42 1 42 7 List of Contributors Numbers in parentheses indicate the pngs on which the authors' contributions begin. G. K. BATCHELOR, Department of Applied Mathematics and Theoretical Physics, University of Cambtidge, Cambridge, England (1) ROBIN D. HILL, Faculty of Engineering, Monash University, Clayton, Victoria, Australia (183) H. KOLSKY,Division of Applied Mathematics, Brown University, Providence, Rhode Island (309) H. K. MOFFAIT, Department of Applied Mathematics and Theoretical Physics, U