A vector-potential approach to radiation from forcelike sources: Further developments

As reported previously [J. Acoust. Soc. Am. Suppl. 1 68, S107 (1980)], it is convenient to represent the pressure field in response to a moving force as the divergence of a vector potential function; the associated fluid particle velocity field is proportional to the time divergence of the vector potential function. In this paper, it is shown that using the representation υ = ∇φ − c−2∂A/∂t for the irrotational velocity field in linearized fluid dynamic equations leads to separate wave equations in φ and A: The latter arises directly from the momentum equation and has a source term the force exerted on the fluid. The equation in φ is obtained from the continuity and thermodynamic state equations; its source term represents a mass-flow fluctuation. The applications of this method to viscous and thermally conducting fluids will be discussed.