Effects of initial radius of the interface and Atwood number on nonlinear saturation amplitudes in cylindrical Rayleigh-Taylor instability

Abstract

Interface width effect on the classical Rayleigh-Taylor instability in the weakly nonlinear regime Phys. Plasmas 17, 052305 (2010) Nonlinear saturation amplitudes (NSAs) of the first two harmonics in classical Rayleigh-Taylor instability (RTI) in cylindrical geometry for arbitrary Atwood numbers have been analytically investigated considering nonlinear corrections up to the fourth-order. The NSA of the fundamental mode is defined as the linear (purely exponential) growth amplitude of the fundamental mode at the saturation time when the growth of the fundamental mode (first harmonic) is reduced by 10% in comparison to its corresponding linear growth, and the NSA of the second harmonic can be obtained in the same way. The analytic results indicate that the effects of the initial radius of the interface (r 0 ) and the Atwood number (A) play an important role in the NSAs of the first two harmonics in cylindrical RTI. On the one hand, the NSA of the fundamental mode first increases slightly and then decreases quickly with increasing A. For given A, the smaller the r 0 =k (with k perturbation wavelength) is, the larger the NSA of the fundamental mode is. When r 0 =k is large enough (r 0 ) k), the NSA of the fundamental mode is reduced to the prediction of previous literatures within the framework of third-order perturbation theory [J. W. Jacobs and I. Catton, J. Fluid Mech. 187, 329 (1988); S. W. Haan, Phys. Fluids B 3, 2349(1991]. On the other hand, the NSA of the second harmonic first decreases quickly with increasing A, reaching a minimum, and then increases slowly. Furthermore, the r 0 can reduce the NSA of the second harmonic for arbitrary A at r 0 Շ 2k while increase it for A Շ 0:6 at r 0 տ 2k. Thus, it should be included in applications where the NSA has a role, such as inertial confinement fusion ignition target design. V C 2014 AIP Publishing LLC.

Harmonic growth of spherical Rayleigh-Taylor instability in weakly nonlinear regime

“…RTI also plays a significant role in astrophysics 9,10 and inertial confinement fusion (ICF). [11][12][13][14][15][16][17][18][19][20][21][22][23] RTI happens on an interface separating two different fluids when a light fluid supports a heavy fluid in a gravity field or accelerates it.…”