Weak Nonlinearity of Ablative Rayleigh--Taylor Instability

The weakly nonlinear regime of single mode ablative Rayleigh--Taylor instability is studied, with consideration of preheat effect and the width of the ablation front. The Rayleigh--Taylor linear growth rate agrees well with the direct numerical simulation. For the density perturbation, the amplitude
distribution of the fundamental mode has one peak value whereas those of the second and third harmonics have two and three peak values, respectively. Harmonics generation versus wave number is also given and it is close to the result of direct numerical simulation.