Nonlinear behaviour of convergent Richtmyer–Meshkov instability

Abstract

A novel shock tube is designed to investigate the nonlinear feature of convergent Richtmyer–Meshkov instability on a single-mode interface formed by a soap film technique. The shock tube employs a concave–oblique–convex wall profile which first transforms a planar shock into a cylindrical arc, then gradually strengthens the cylindrical shock along the oblique wall, and finally converts it back into a planar one. Therefore, the new facility can realize analysis on compressibility and nonlinearity of convergent Richtmyer–Meshkov instability by eliminating the interface deceleration and reshock. Five sinusoidal $\text{air}{-}\text{SF}_{6}$ interfaces with different amplitudes and wavelengths are considered. For all cases, the perturbation amplitude experiences a linear growth much longer than that in the planar geometry. A compressible linear model is derived by considering a constant uniform fluid compression, which shows a slight difference to the incompressible theory. However, both the linear models overestimate the perturbation growth from a very early stage due to the presence of strong nonlinearity. The nonlinear model of Wang et al. (Phys. Plasmas, vol. 22, 2015, 082702) is demonstrated to predict well the amplitude growth up to a normalized time of 1.0. The prolongation of the linear increment is mainly ascribed to the counteraction between the promotion by geometric convergence and the suppression by nonlinearity. Growths of the first three harmonics, obtained by a Fourier analysis of the interface contour, provide a first thorough validation of the nonlinear theory.

On divergent Richtmyer–Meshkov instability of a light/heavy interface

“…It is found that at early stages the growth of the third harmonic in divergent geometry is much smaller than that in a planar or convergent geometry (Luo et al. 2019), which provides a further demonstration of weak nonlinearity. Although nonlinearity increases at late stages, the positive growth of the third harmonic approximately counteracts its negative feedback to the basic mode, which suggests a negligible influence of nonlinearity on the growth of overall perturbation amplitude.…”

“…2015; Luo et al. 2019). The growth of the third harmonic together with its feedback to the primary mode, predicted by the nonlinear model of Wang et al.…”

Statistical characteristics of turbulent mixing in spherical and cylindrical converging Richtmyer–Meshkov instabilities

“…Experimental investigations of cylindrical converging RMI in shock tubes had been conducted by several researchers, such as Hosseini & Takayama (2005), Biamino et al (2015), Luo et al (2015Luo et al ( , 2018Luo et al ( , 2019a, Zhai et al (2017), Rodriguez et al (2017), Ding et al (2017Ding et al ( , 2019, Lei et al (2017), Li et al (2020), Vandenboomgaerde et al (2018, Courtiaud et al (2019), Sun et al (2020b) and Zou et al (2019). These experimental results are particularly helpful for the development of theory and numerical simulation.…”

Effects of the secondary baroclinic vorticity on the energy cascade in the Richtmyer–Meshkov instability

“…Hill, Pantano & Pullin 2006;Li et al 2019) and converging geometries (e.g. Lombardini & Pullin 2009;Luo et al 2019).…”