General Fluid-Displacement Equations for Acoustic-Gravity Waves

International audienceGeneral equations are derived for the dynamics of a fluid under initial stress in an arbitrary potential field and perturbed from equilibrium. The motion is described in terms of the displacements of the fluid particles from their equilibrium position. A class of equations is obtained which is applicable to large displacements. Complete linearization leads to two types of equations. One type called ``un‐modified'' corresponds to the viewpoint of the theory of elasticity. The ``modified'' equations representing the other type are expressed in terms of buoyancy forces. The modified equations lead to a conceptually useful analog model for internal gravity waves in a liquid. For a constant gravity field the linear equations are also applicable to large displacements. Classical examples for a constant gravity field are discussed as illustrations