  The Rayleigh-Taylor Instability (RTI) under multi-mode perturbation in
compressible flow is probed via the Discrete Boltzmann Modeling (DBM) with
tracers. The distribution of tracers provides clear boundaries between light
and heavy fluids in the position space. Besides, the position-velocity phase
space offers a new perspective for understanding the flow behavior of RTI with
intuitive geometrical correspondence. The effects of viscosity, acceleration,
compressibility, and Atwood number on the mixing of material and momentum and
the mean non-equilibrium strength at the interfaces are investigated separately
based on both the mixedness defined by the tracers and the non-equilibrium
strength defined by the DBM. The mixedness increases with viscosity during
early stage but decreases with viscosity at the later stage. Acceleration,
compressibility, and Atwood number show enhancement effects on mixing based on
different mechanisms. After the system relaxes from the initial state, the mean
non-equilibrium strength at the interfaces presents an initially increasing and
then declining trend, which is jointly determined by the interface length and
the macroscopic physical quantity gradient. We conclude that the four factors
investigated all significantly affect early evolution behavior of RTI system,
such as the competition between interface length and macroscopic physical
quantity gradient. The results contribute to the understanding of the
multi-mode RTI evolutionary mechanism and the accompanied kinetic effects.
