Vortical perturbations of the unsteady motion of a fluid with a free boundary
Abstract
Smallperturbation equations are derived in Lagrange generalized coordinates for the unsteady flow of a fluid with a free boundary. A simple expression for the normal component of the perturbing vector is obtained. It is shown that in the case of potential mass forces, the system of equations can be reduced to a single equation for a certain scalar function with an evolutionary condition at the free boundary. A theorem for the existence and uniqueness of solutions is formulated and proved.
 Publication:

PMTF Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki
 Pub Date:
 October 1975
 Bibcode:
 1975PMTF........58A
 Keywords:

 Fluid Flow;
 Free Boundaries;
 Small Perturbation Flow;
 Unsteady Flow;
 Vorticity Equations;
 Flow Theory;
 Lagrange Coordinates;
 Perturbation Theory;
 Fluid Mechanics and Heat Transfer