Scaling Theory of Singularities
Department of Physics,
Owing to the nonlinear character of the equations of motion describing
fluid motion, sudden discontinuities in the pressure, the density,
or the surface shape of a fluid often occur. Examples are shock waves,
the separation of a fluid drop, bubbles rising in a viscous fluid,
or drops in strong electric fields. Singularities are the crucial events
in the evolution of a flow, and signal the emergence of new structures.
Physically, smaller and smaller structures are produced near the
singularity, so it lacks a characteristic length scale. Singular solutions
thus must be invariant under a change of scale, and have a simple
scaling form. Moreover, singularities turn out to be universal,
so the same structure is found in a broad variety of circumstances.
This talk explores the mathematics and the physical consequences of
these two fundamental properties.