Dispersion relations for gravity waves in a deep fluid: second sound in a stormy sea
MetadataShow full item record
We consider the nonlinear processes of interaction between a random field of short deep gravity waves and a deep long gravity wave, as well as the effects of nonlinear interactions among the driven short waves. The interactions are characterized by two types of invariants. First, the short waves posses an adiabatic invariant as regards the interaction with the long waves. Second, a collision between short waves conserved frequency and wave vector. As a consequence of these invariants, extra degrees of freedom appear. This results in a two-fluid description at the surface of the liquid for the mean flow of the long wave plus a distribution of waves. The two-fluid theory implies a spectrum of oscillations of the surface where, besides the usual gravity waves, there exists a surface mode with longitudinal oscillation. The regimes of validity of this hydrodynamic description are discussed, and the solutions for the dispersion relation are also presented. The power spectrum of a stormy sea is derived within the framework on nonlinear wave interactions. Finally, we comment on the relevance of the results to phase-velocity measurement is a wind-wave laboratory experiment, as well as possible experiments to observe the theoretically predicted new mode.
Approved for public release; distribution is unlimited
Showing items related by title, author, creator and subject.
A numerical study of the nonlinear interaction of Hurricane Camille with the Gulf of Mexico Loop Current Ly, Le Ngoc; Kantha, Lakshmi H. (1993);A three-dimensional, primitive equation, ocean general circulation model is used to study the response of the Gulf of Mexico to Hurricane Camille (1969). The free-surface dynamics and the mixed-layer features are included ...
System identification and control of an Arleigh Burke Class Destroyer using an extended Kalman Filter Taylor, Michael Eric (Monterey, California. Naval Postgraduate School, 2000);Maneuvering characteristics of surface combatants in the United States Navy are often ignored during the design process. Key maneuvering parameters such as tactical diameter and turning rate are determined during sea trials ...
Papoulias, F. A.; Healey, A. J. (1992);The surface ship path control problem is formulated as a nonlinear state space control problem subject to disturbances modeling errors, and parameter uncertainty. A "destroyer study" ship using a nonlinear maneuvering ~odel ...