Variational principles for acoustic-gravity waves

Maurice A. Biot (1)

1 Columbia University [New York]

Variational principles are developed for the dynamics of a fluid under initial stress in an arbitrary potential field and disturbed from equilibrium. They are formulated in terms of the fluid displacement. Two distinct principles are obtained which are mathematically equivalent but differ fundamentally from the physical viewpoint. The difference results from expressing the potential energy in terms of buoyancy forces or strain energy. A very general stability criterion is obtained. An important new feature is the inclusion of surface integrals in the potential energy. The simplified principle for the case of a liquid is interpreted by means of an analog model. Lagrangian equations and methods of normal coordinates for the evaluation of transient propagation are applicable along with general theorems on the equivalence of group velocity and energy flux. As an illustration the case of a constant gravity field is discussed.

Domaines: Mécanique [physics.med-ph]

Maurice A. Biot. Variational principles for acoustic-gravity waves. Physics of Fluids, 1963, 6 (6), pp.772-778. ⟨10.1063/1.1706812⟩. ⟨hal-01368703⟩