The University of Arizona

Hamiltonian Equations for Three Wave Resonant Interaction in Adiabatic Gas Dynamics

Hamiltonian Equations for Three Wave Resonant Interaction in Adiabatic Gas Dynamics

Series: Fluids and Mechanics Seminar
Location: Econ 200
Presenter: Garry Webb, Lunar and Planetary Science, University of Arizona

Equations describing three-wave resonant interactions in adiabatic gas dynamics derived by Majda and Rosales are expressed in terms of Lagrangian and Hamiltonian variational principles. The equations consist of two coupled integro-differential Burgers equations for the backward and forward sound waves that are coupled by integral terms that describe the resonant reflection of a sound wave off an entropy wave disturbance to produce a reverse sound wave. Similarity solutions and conservation laws for the equations are discussed.

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