Harmonic growth in classical Rayleigh-Taylor instability (RTI) on a spherical interface is analytically investigated using the method of the parameter expansion up to the third order. Our results show that the amplitudes of the first four harmonics will recover those in planar RTI as the interface radius tends to infinity compared against the initial perturbation wavelength. The initial radius dramatically influences the harmonic development. The appearance of the second-order feedback to the initial unperturbed interface (i.e., the zeroth harmonic) makes the interface move towards the spherical center. For these four harmonics, the smaller the initial radius is, the faster they grow. 

http://dx.doi.org/10.1063/1.4936096

We would like to thank the anonymous referee for the valuable suggestions that greatly improved this paper. This work was supported by the National Natural Science Foundation of China (Grant Nos. 11472278 and 11372330), the Scientific Research Foundation of Mianyang Normal University (Grant Nos. 15ZA0296, QD2014A009 and 2014A02), and the National High-Tech ICF Committee.

Liu WH,Chen YL,Yu ZP,et al. Harmonic growth of spherical Rayleigh-Taylor instability in weakly nonlinear regime[J]. PHYSICS OF PLASMAS,2015,22(11):112112.