Singularities in the classical RayleighTaylor flow  Formation and subsequent motion
Abstract
The creation and subsequent motion of singularities of solution to classical RayleighTaylor flow (two dimensional inviscid, incompressible fluid over a vacuum) are discussed. For a specific set of initial conditions, we give analytical evidence to suggest the instantaneous formation of one or more singularities at specific points in the unphysical plane, whose locations depend sensitively on small changes in initial conditions in the physical domain. Onehalf power singularities are created in accordance with an earlier conjecture; however, depending on initial conditions, other forms of singularities are also possible. For a specific initial condition, we follow a numerical procedure in the unphysical plane to compute the motion of a onehalf singularity. This computation confirms our previous conjecture that the approach of a onehalf singularity towards the physical domain corresponds to the development of a spike at the physical interface. Under some assumptions that appear to be consistent with numerical calculations, we present analytical evidence to suggest that a singularity of the onehalf type cannot impinge the physical domain in finite time.
 Publication:

Proceedings of the Royal Society of London Series A
 Pub Date:
 June 1993
 DOI:
 10.1098/rspa.1993.0076
 Bibcode:
 1993RSPSA.441..501T
 Keywords:

 Boundaries;
 Incompressible Flow;
 Inviscid Flow;
 Kinematics;
 Singularity (Mathematics);
 Vacuum;
 Computation;
 Logarithms;
 Position (Location);
 Fluid Mechanics and Heat Transfer