Waves in the Ocean and Atmosphere Introduction to Wave Dynamics

For over twenty years, the Joint Program in Physical Oceanography of MIT and the Woods Hole Oceanographic Institution has based its education program on a series of core courses in Geophysical Fluid Dynamics and Physical Oceanography. One of the central courses in the Core is one on wave theory, tailored to meet the needs of both physical oceanography and meteorology students. I have had the pleasure of teaching of years, and I have particularly enjoyed the response of the the course for a number students to their exposure to the fascination of wave phenomena and theory. This book is a reworking of course notes that I have prepared for the students, and I was encouraged by their enthusiastic response to the notes to reach a larger audience with this material. The emphasis, both in the course and in this text, is twofold: the de­ velopment of the basic ideas of wave theory and the description of specific types of waves of special interest to oceanographers and meteorologists. Throughout the course, each wave type is introduced both for its own intrinsic interest and importance and as a ve­ hicle for illustrating some general concept in the theory of waves. Topics covered range from small-scale surface gravity waves to large-scale planetary vorticity waves.

1 Introduction.- 2 Kinematic Generalization.- 3 Equations of Motion; Surface Gravity Waves.- 4 Fields of Motion in Gravity Waves and Energy.- 5 The Initial Value Problem.- 6 Discussion of Initial Value Problem [Continued).- 7 Internal Gravity Waves.- 8 Internal Waves, Group Velocity and Reflection.- 9 WKB Theory for Internal Gravity Waves.- 10 Vertical Propagation of Waves: Steady Flow and the Radiation Condition.- 11 Rotation and Potential Vorticity.- 12 Large-Scale Hydrostatic Motions.- 13 Shallow Water Waves in a Rotating Fluid; Poincare and Kelvin Waves.- 14 Rossby Waves.- 15 Rossby Waves (Continued), Quasi-Geostrophy.- 16 Energy and Energy Flux in Rossby Waves.- 17 Laplace Tidal Equations and the Vertical Structure Equation.- 18 Equatorial Beta-Plane and Equatorial Waves.- 19 Stratified Quasi-Geostrophic Motion and Instability Waves.- 20 Energy Equation and Necessary Conditions for Instability.- 21 Wave-Mean Flow Interaction.- Problems.- References.