Influence of phase difference and amplitude ratio on Kelvin–Helmholtz instability with dual-mode interface perturbations
Hao Xu, Chuandong Lin, Huilin Lai
Abstract
A two-component discrete Boltzmann method (DBM) is employed to study the compressible Kelvin–Helmholtz (KH) instability with dual-mode interface perturbations, consisting of a fundamental wave and a second harmonic. The phase difference is analyzed in two distinct ranges, and the amplitude ratio is studied by varying the amplitude of either the first or second harmonic. The global average density gradient and the global mixing degree are analyzed from a hydrodynamic non-equilibrium perspective. The thermodynamic non-equilibrium (TNE) intensity is probed as a thermodynamic non-equilibrium variable. The system is also explored from a geometric perspective, with a focus on the rotation of two vortices, the mixing layer width, and the non-equilibrium area. Physically, under the influence of shear velocity, the fluid interface becomes distorted and progressively elongated, resulting in the formation of two small vortex structures and an enhancement of the physical gradient. The two vortices then begin to interact and merge into a single large vortex with complex fluid structures. Consequently, the physical gradient decreases, and the local TNE intensity weakens. Subsequently, the material interface elongates further, increasing the non-equilibrium region and enhancing the local TNE intensity. Finally, the physical gradient decreases due to dissipation and/or diffusion, weakening the local TNE intensity.