Nonlinear theory of classical cylindrical Richtmyer-Meshkov instability for arbitrary Atwood numbers

A nonlinear theory is developed to describe the cylindrical Richtmyer-Meshkov instability (RMI) of an impulsively accelerated interface between incompressible fluids, which is based on both a technique of Pade approximation and an approach of perturbation expansion directly on the perturbed interface rather than the unperturbed interface. When cylindrical effect vanishes (i.e., in the large initial radius of the interface), our explicit results reproduce those [Q. Zhang and S.-I. Sohn, Phys. Fluids 9, 1106 (1996)] related to the planar RMI. The present prediction in agreement with previous simulations [C. Matsuoka and K. Nishihara, Phys. Rev. E 73, 055304(R) (2006)] leads us to better understand the cylindrical RMI at arbitrary Atwood numbers for the whole nonlinear regime. The asymptotic growth rate of the cylindrical interface finger (bubble or spike) tends to its initial value or zero, depending upon mode number of the initial cylindrical interface and Atwood number. The explicit conditions, directly affecting asymptotic behavior of the cylindrical interface finger, are investigated in this paper. This theory allows a straightforward extension to other nonlinear problems related closely to an instable interface. (C) 2014 AIP Publishing LLC