Turbulent mixing in high-energy-density environments plays a critical role across numerous fields. For instance, in astrophysics, it influences heavy-element synthesis and energy transport, serving as a key mechanism in supernova explosions and neutron star mergers. In inertial confinement fusion (ICF) physics, turbulent mixing induced by fluid instabilities leads to fuel-shell material mixing, thereby reducing fusion efficiency and posing a core challenge for ICF implosion dynamics. This study investigates turbulent mixing driven by fluid instabilities in light-heavy media during cylindrical implosions under indirect drive. Utilizing the large-scale parallel multi-material Eulerian radiation hydrodynamics code LARED-S with multigroup radiation diffusion and electron-ion flux-limited thermal conduction modeling, simulations were conducted under megaloule-scale two-step laser loading conditions. Results reveal dual-scaling behavior in the azimuthal turbulent kinetic energy spectrum during shock convergence-rebound or deceleration phases:   and , consistent with classical two-dimensional turbulence theory. By evaluating viscous and thermal diffusion coefficients of high-temperature plasma alongside flow field distributions, ionization states, and temperature profiles of heavy media, key turbulent parameters during the compression phase were quantified: Reynolds number Re∼10^7 and Prandtl number Pt ~ 3×10^-3. These values confirm fully developed turbulent mixing. Additionally, temporal evolution characteristics of key turbulent quantities were analyzed.
 

High-energy-density turbulent mixing; Complex loading in cylindrical geometry; Turbulent kinetic energy spectrum; Dual-scaling behavior; Reynolds number; Prandtl number; Megajoule laser conditions