Lagrangian investigation of the interface dynamics in single-mode Rayleigh–Taylor instability

Abstract

We apply Lagrangian particle tracking to the two-dimensional single-mode Rayleigh–Taylor (RT) instability to study the dynamical evolution of fluid interface. At the onset of the nonlinear RT stage, we select three ensembles of tracer particles located at the bubble tip, at the spike tip, and inside the spiral of the mushroom structure, which cover most of the interfacial region as the instability develops. Conditional statistics performed on the three sets of particles and over different RT evolution stages, such as the trajectory curvature, velocity, and acceleration, reveals the temporal and spatial flow patterns characterizing the single-mode RT growth. The probability density functions of tracer particle velocity and trajectory curvature exhibit scalings compatible with local flow topology, such as the swirling motion of the spiral particles. Large-scale anisotropy of RT interfacial flows, measured by the ratio of horizontal to vertical kinetic energy, also varies for different particle ensembles arising from the differing evolution patterns of the particle acceleration. In addition, we provide direct evidence to connect the RT bubble re-acceleration to its interaction with the transported fluid from the spike side, due to the shear driven Kelvin–Helmholtz instability. Furthermore, we reveal that the secondary RT instability inside the spiral, which destabilizes the spiraling motion and induces complex flow structures, is generated by the centrifugal acceleration.