HED hydrodynamic modeling in 2D versus 3D: comparing anisotropy*

A new method to quantify anisotropy as a function of length-scales is applied  to simulations of 2D and 3D Rayleigh-Taylor (RT) turbulence, which is inhomogeneous and anisotropic. We show that 3D RT has clear shape anisotropy at large scales with approximately 4:3 vertical to horizontal aspect ratio, but tends toward isotropy at small scales as expected. In sharp contrast, we find that RT in 2D simulations, which are still the main modeling framework for many applications,  is isotropic at large scales and its shape anisotropy increases at smaller scales where structures tend to be horizontally elongated. While this may be surprising, it is consistent with recent results in [1]; large-scale isotropy in 2D RT is due to the generation of a large-scale overturning circulation via an upscale cascade, while small scale anisotropy is due to the stable stratification resultant from such overturning and the inefficient mixing in 2D.

[1] Zhao, D., Betti, R., Aluie, H., J. Fluid Mech. 930, A29 (2022).