Uncovering the turbulence structure of Rayleigh-Taylor instabilities through direct numerical simulations on a small spatial domain*

The buoyant turbulence generated by Rayleigh-Taylor (RT) instabilities plays a central role in the physics of wildfires, supernovae, and inertial confinement fusion. While the global evolution of RT instabilities has been extensively documented in experiment and simulation, the local turbulence structure is poorly understood; the presence of small-scale anisotropy seems to contradict Kolmogorov theory. To analyze this structure, a new simulation framework is developed to isolate the small scales of turbulence generation from the large spatial domain of an RT instability. This framework, referred to as homogeneous buoyant turbulence (HBT), is a direct numerical simulation (DNS) in a 3D periodic box. To ensure the periodic boundary conditions are applicable, a transformation is performed on the RT flow variables in the Navier-Stokes (NS) equations. This leads to new equations similar in form to the NS equations with additional terms that act to maintain the turbulence. These terms are closed by leveraging data from prior RT DNS. HBT is distinct from the homogeneous isotropic turbulence (HIT) framework, where the turbulence is maintained by a linear forcing term in the momentum equation. The results are first validated against existing RT DNS. The statistics are then compared to the corresponding HIT results to identify the key factors that separate buoyant turbulent structure from isotropic, Kolmogorov turbulence.