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

Abstract

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. V C 2015 AIP Publishing LLC.

Lattice Boltzmann study on Kelvin-Helmholtz instability: Roles of velocity and density gradients

“…On the one hand, in fundamental research, KHI is of great importance in the fields of turbulent mixing [33], supernovae dynamics [34][35][36], and the interaction of the solar wind with the earth's magnetosphere [37], etc. On the other hand, in engineering applications, the KHI plays a key role in small-scale mixing of Rayleigh-Taylor (RT) [38,39] and Richtmyer-Meshkov (RM) instabilities in inertial confinement fusion (ICF) [40][41][42]. In the final regime of RT and RM instabilities, KHI is initiated due to the shear velocity difference at the spike tips [43], and, therefore, the appearance of the KHI aggravates the development of final nonlinearity of RT instability or RM instability, and quickens the process of fluid flock mixing round the interface.…”

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

“…When the typical perturbation amplitude is close to its wavelength, the second and third harmonics are generated successively, and then the perturbation enters the nonlinear regime. In the weakly nonlinear growth regime, [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39] within the framework of the third-order weakly nonlinear theory, [24][25][26][27][28] the interface function is gðx; tÞ ¼ g 1 cosðkxÞ þ g 2 cosð2kxÞ þ g 3 cosð3kxÞ, where g n (n ¼ 1, 2, 3) is the amplitude of the nth harmonic…”

Bell-Plessett effect on harmonic evolution of spherical Rayleigh-Taylor instability in weakly nonlinear scheme for arbitrary Atwood numbers

“…[1][2][3] The RTI has been extensively investigated theoretically, [4][5][6][7][8][9][10][11][12][13][14] experimentally, 15,16 and numerically. [17][18][19][20] Before the RTI enters a strong nonlinear stage, [21][22][23][24] it will undergo a linear stage, and then a weakly nonlinear stage.…”