At
t = 0.5, RTI occurs initially and most of the tracers are still at the origin. At the same time, diffusion occurs between the two fluids due to the density gradient, causing the tracers near the interface to acquire a certain velocity. As shown in the
x −
y projection of figure
2(a1), the
ux of the heavy fluid particles
type-a fluctuates around
ux = 0, which is related to the initial perturbation. The
uy of
type-a particles shows a band distribution along the
x direction, and the main part still fluctuates around
uy = 0. However, because the heavy fluid particles near the interface diffuse downward, a non-narrow band structure is formed in the region of
uy < 0. As shown in figure
2(a2), the
ux of
type-a particles has a symmetric spike distribution along the
y direction, and the larger
y is, the narrower the velocity distribution interval is. After
y is larger than a certain value
ux is about 0. And the
uy also has a similar spike distribution along the
y direction, except that there is an abrupt change near
y = 0.2. This indicates that the perturbations at the interface are not massively transmitted to other locations in the fluid system at this time. At
t = 1.5, both
type-a particles and
type-b particles show a very regular and beautiful characteristic pattern in either subspace. The velocity phase diagrams (
y −
z projection in the second row) of both form a laminar ‘shuttle’ structure. The tip of the velocity diagram of the
type-a particles is facing downward, while the tip of the
type-b particles is facing upward, indicating that most of the two particles have opposite trends of motion. The
ux and
uy form a continuous undulating ‘crest-valley’ structure along the
x direction respectively, which corresponds to the final stage of linear growth of RTI. And
ux and
uy still have symmetric spike distribution pattern along the
y direction respectively, only that the lower part of the distribution is fuller at this time, making the characteristic
y coordinate with zero velocity become larger, which indicates that the mixing zone is obviously wider and the spike inserts the bubble deeper. As the mixing intensifies, the pattern in the three-dimensional subspace starts to become more turbulent. At
t = 2.5, the spike of
ux and
uy along the
y direction can be roughly observed, and the mixing zone is getting closer to the boundary. At
t = 4.5, the flow field has been initially mixed. Due to time constraints, this research is still relatively qualitative and preliminary. However, it is obvious that the description of structural morphology, overall or local statistics and their evolutionary patterns are fascinating and, of course, extremely challenging. Giving a mathematical physical equation to accurately describe these distributions and evolutions is difficult. But it is possible to advance step by step, with different perspectives and partial descriptions of properties.