Table of Contents

Preface vii Sir James Lighthill: Chronology xi
1 An Early Life History and Career of Sir James Lighthill 1
2 Music and Swimming 41
3 Personal Reminiscence 45
4 Sir James Lighthill's Books 57
4.1 Introduction to Fourier Analysis and Generalised Functions, Cambridge University Press, Cambridge, 1958 57
4.2 Higher Approximations in Aerodynamic Theory, Princeton University Press, Princeton, 1960 61
4.3 Mathematical Biofluiddynamics, SIAM, Philadelphia, 1975 65
4.4 Waves in Fluids, Cambridge University Press, Cambridge, 1978 71
4.5 Newer Uses of Mathematics, Penguin Books Ltd., Harmondsworth, U.K., 1978 104
4.6 Monsoon Dynamics, (Eds. Lighthill, J. and Pearce, R. B.), Cambridge University Press, Cambridge, 1981 108
4.7 An Informal Introduction to Theoretical Fluid Mechanics, Oxford University Press, Oxford, 1986 110
4.8 Tropical Cyclone Disasters, (Eds. Lighthill, J., Zhang, Z., Holland, G., and Emanuel, K.), Peking University Press, Beijing, China, 1993 114
4.9 Fluid Mechanics, A Chapter in Twentieth Century Physics (Eds. Laurie M. Brown, Abraham Pais, and Sir Brian Pippard), Institute of Physics and American Institute of Physics, New York, Volume II, 1995 117
5 Supersonic and Subsonic Aerodynamic Flows 123
5.1 Introduction 123
5.2 Supersonic Airfoil Theory 124
6 Aeroacoustics and Nonlinear Acoustics 133
6.1 Introduction 133
6.2 Lighthill's Theory of Sound Generated Aerodynamically 134
7 Boundary Layer Theory and Vorticity Dynamics 147
7.1 Introduction 147
7.2 Lighthill's Contributions to Boundary Layer Theory 150
8 Linear and Nonlinear Waves in Fluids 165
8.1 Sound Waves and Shock Waves 165
8.2 Kinematic Waves188
8.3 Linear Dispersive Waves 193
9 Geophysical Fluid Dynamics 201
9.1 Introduction 201
9.2 Dynamics of Rotating Fluids 202
9.3 The Navier-Stokes Equations of Motion in a Rotating Frame of Reference 208
9.4 Linear Rossby Waves in a Non-Uniformly Rotating Ocean 209
9.5 General Class of Traveling Wave Solutions of the Rossby Wave Equation 213
9.6 Small Amplitude Waves in a Rotating Ocean 214
9.7 Poincare, Kelvin and Rossby Waves in a Rotating Ocean 216
9.8 Dynamic Response of the Indian Ocean to the Southwest Monsoon 225
9.9 Concluding Remarks 237
10 Nonlinear Dispersive Waves 239
10.1 Introduction 239
10.2 Lighthill's Theory of Nonlinear Dispersive Waves 240
11 Nonlinear Diffraction of Water Waves by Offshore Structures 255
11.1 Introduction 255
11.2 Morison's Equation 256
11.3 Basic Equations of Water Waves in Cylindrical Polar Coordinates and Boundary Conditions 260
11.4 Linear Diffraction Theory and Morison's Coefficient 265
11.5 Nonlinear Wave Forces on Offshore Structures and Nonlinear Modification of the Morison Equation 268
12 Biofluid Mechanics 281
12.1 Introduction 281
12.2 External Biofluiddynamics 282
12.3 Internal Biofluiddynamics 288
13 Books and Major Research Papers of Sir James Lighthill 301 Bibliography 313 Index 321