Renormalization group approach to interfacial motion in incompressible Richtmyer-Meshkov instability

Abstract

Nonlinear interfacial motion in incompressible Richtmyer-Meshkov instability is theoretically investigated using the renormalization group approach. The amplitude equation describing the asymptotic interfacial motion is derived using this approach. A comparison with calculations carried out by the weakly nonlinear analysis is performed for various Atwood numbers and the validity of the renormalization group approach is discussed. We show that this approach suppresses the divergence in the perturbative solutions obtained by the weakly nonlinear analysis and provides better approximations for the growth rate of bubbles and spikes and interfacial profiles at the asymptotic nonlinear stage without requiring the use of Padé approximants.