Weakly Nonlinear Theory for the Ablative Rayleigh-Taylor Instability

Abstract

A weakly nonlinear model is proposed for the Rayleigh-Taylor instability in the presence of ablation and thermal transport. The second harmonic generation efficiency of a single-mode disturbance is computed, as well as the nonlinear correction to the exponential growth of the fundamental modulation. Mode coupling in the spectrum of a multimode disturbance is thoroughly analyzed. The ablative stabilization can be clearly discussed because the derived formulas for the evanescent ablation rate are in agreement with previously known results for incompressible, inviscid, irrotational, and immiscible fluids [S. W. Haan, Phys. Fluids B 3, 2349 (1991)]; M. Berning and A. M. Rubenchik, Phys. Fluids 10, 1564 (1998)]].

Interface width effect on the classical Rayleigh–Taylor instability in the weakly nonlinear regime

“…The interface width effects reduce the linear growth rate, which is generally consistent with the earlier investigations. [6][7][8][9]11,[18][19][20][22][23][24][25][26][27][28] As shown in Fig. 2, the stabilization effects are striking, specially for the short .…”

“…21 The linear growth rates of the RTI with continuous density profile were investigated by Mikaelian 22,23 and Munro,24 and the corresponding analytical formulas were obtained. It is believed that the density gradient has the effect of reducing the linear growth rate of the RTI, [6][7][8][9]11,[18][19][20][22][23][24][25][26][27][28] particularly at short perturbation wavelengths. The interface width effects on the RTI in the WN regime, however, have not been fully understood.…”

Evidence for a Bubble-Competition Regime in Indirectly Driven Ablative Rayleigh-Taylor Instability Experiments on the NIF

“…4 and produces reasonable agreement for both cases. Although the Haan model does not include all the relevant physics for ablative RTI, such as mode coupling [23][24][25], it is remarkable how that a simple models gives reasonable agreement with the data.…”

“…For the first time we can measure the ablation front instability growth in a highly non-linear regime of the full unstable spectrum. Testing Haan theory and other theories [23][24][25][26] predicting increased bubble growth due to ablation in nonlinear regime are critical for ICF. This paper thus provides first test of the Haan theory for indirect drive in 2D planar geometry.…”

Nonlinear saturation amplitudes in classical Rayleigh-Taylor instability at arbitrary Atwood numbers

“…Before a strong nonlinear growth regime, [26][27][28][29] one has a weakly nonlinear growth regime. [30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46] Within the framework of the third-order weakly nonlinear theory, 30-34 the interface position takes the form, gðx; tÞ ¼ g …”