The study of internal gravity waves provides many challenges: they move along interfaces as well as in fully three-dimensional space, at relatively fast temporal and small spatial scales, making them difficult to observe and resolve in weather and climate models. Solving the equations describing their evolution poses various mathematical challenges associated with singular boundary value problems and large amplitude dynamics. This book provides the first comprehensive treatment of the theory for small and large amplitude internal gravity waves. Over 120 schematics, numerical simulations and laboratory images illustrate the theory and mathematical techniques, and 130 exercises enable the reader to apply their understanding of the theory. This is an invaluable single resource for academic researchers and graduate students studying the motion of waves within the atmosphere and ocean, and also mathematicians, physicists and engineers interested in the properties of propagating, growing and breaking waves.
Bruce R. Sutherland holds a B.Math from the University of Waterloo, Ontario and a Ph.D. in Physics from the University of Toronto where, under the supervision of W. R. Peltier, he ran numerical simulations of internal waves generated by shear instability. As a Research Associate working with P. F. Linden at the University of Cambridge, he helped develop the laboratory method known as the synthetic schlieren technique, which was applied to examine internal waves generated by turbulence. Now a Professor in the Departments of Physics and of Earth and Atmospheric Sciences, and an Adjunct Professor in Mathematical and Statistical Sciences, at the University of Alberta, he continues to develop theories and to run laboratory experiments and numerical simulations that examine the generation, propagation and breaking of internal gravity waves.
Preface; 1. Stratified fluids and waves; 2. Interfacial waves; 3. Internal waves in uniformly stratified fluid; 4. Nonlinear considerations; 5. Generation mechanisms; 6. Wave propagation and spectra; Appendix. Suggestions for further reading; Index.