Mode-coupling branches in single-mode classical Rayleigh-Taylor instability for arbitrary Atwood numbers

In this research, the effect of the mode-coupling branches/channels on harmonic amplitudes in single-mode classical Rayleigh-Taylor instability for arbitrary Atwood numbers in the weakly nonlinear stage is investigated by employing the tracking technology of the mode coupling up to the fifth order. When the effect of the mode-coupling channels is not taken into account (i.e., this effect is automatically merged in the derivation process), our results are the same as the first five-order results from the prediction of previous literatures within the framework of tenth-order perturbation theory (Liu et al., 2012). In the progress of the mode coupling, the tracking technology of the channel parameters equal to constant 1 is used and all the mode-coupling channels are distinctly extracted. It is found that the nth-harmonic amplitude with mth order mainly depends on fm,n factor. However, this factor comes from different mode-coupling branches which are either constant or variable with Atwood numbers A. For the channels with A, they can either strengthen or inhibit the growth of the relevant harmonic. For some channels, they are closed all the time for some fixed A.