Chapter 25 - Internal Waves and Solitons

Abstract

This chapter discusses internal waves and solitons. The influence of internal solitons and solitary waves on various kinds of operations on and below the ocean's surface has become increasingly important in the past few decades as man has explored greater depths in search of ocean resources and for defense purposes. Particle velocities in long internal waves can generate forces on ships, on fixed and compliant surface piercing, and/or underwater structures or floating vehicles. Hence, there is the potential for exceeding design loads in structures and for disturbing the ballast of floating underwater vessels of all types. A preliminary measurement program, conducted by Exxon Production Research Company, revealed currents as high as 1.6 m/s. These data contained most of the qualitative features of the theory of the Korteweg-deVries (KdV) equation, and some quantitative comparisons were also carried out. The area in which the measurements were made was in the southern Andaman Sea. The theory of the KdV equation as a simple nonlinear model for long internal wave motions is discussed. The spectral decomposition in terms of cnoidal waves can of course be used for trains of solitons. In this case, the spectral decomposition consists of the solitons themselves plus nonlinear interactions (interaction phase shifts).