Numerical simulations of shock-driven, supersonic turbulence in colliding three-temperature laboratory plasmas

Shock-driven turbulence is central to astrophysical plasmas in which explosions and compressive driving inject energy through shocks rather than steady stirring. We present three-dimensional, three-temperature (ion, electron, and radiation; 3T) radiation-hydrodynamic simulations of a laboratory platform in which two offset CH mesh targets are irradiated by a $30\,\rm ns$ X-ray pulse. Mesh ablation launches counter-streaming supersonic flows whose vorticity is seeded baroclinically at mesh-cell corners, advected into collimated channels over $\sim15\,\rm ns$, and injected into the outgoing streams before collision. The flows first collide at $t\simeq75\,\rm ns$, forming a shocked turbulent mixing layer that persists for at least $300\,\rm ns$, reaches $\ell_0\simeq4.5\,\rm mm$, and evolves toward an effectively isothermal equation of state with $\gamma_{\rm eff}\simeq1.1$. After stagnation, $u_0(t)\propto t^{-1.1}$ while $t_0/t_{c_s}\simeq0.2$ remains nearly fixed. Compression and stretching dominate the vorticity budget, and the velocity field relaxes toward a kinetic-energy partition of approximately $70\%$ solenoidal and $30\%$ compressive. The Reynolds stress is strongly anisotropic at the outer scale and remains measurably anisotropic over much of the resolved inertial interval, indicating directional memory of the collision axis and mesh geometry across many scales. The solenoidal strain spectrum implies $\ell_{\nu,\rm s}\simeq92\,\mu\rm m$, $\ell_0/\ell_{\nu,\rm s}\simeq49$, and an effective Reynolds number $\mathrm{Re}\sim2\times10^2$. The density-gradient spectrum is directly tied to the compressive mode spectrum, which evolves independently from the incompressible cascade. Abridged.