Weakly Nonlinear Multi-Mode Bell-Plesset Growth In Cylindrical Geometry*

Bell-Plesset (BP) effect caused perturbation growth plays an important role in better understanding of characteristics of the convergence effect. Governing equations for multi-mode perturbation growth on a cylindrically convergent interface are derived. The second-order weakly nonlinear (WN) solutions for two-mode perturbations at the interface which is subject to uniformly radical motion are obtained. Our WN theory is consistent with the numerical result in terms of mode-coupling effect in converging Richtmyer-Meshkov instability. Nonlinear mode-coupling effects will cause irregular deformation of the convergent interface. The mode-coupling behavior in convergent geometry depends on the mode number, Atwood number A and convergence ratio C-r. The A = -1.0 at the interface results in larger perturbation growth than A = 1.0. The growth of generated perturbation modes from two similar modes at the initial stage are smaller than that from two dissimilar modes.