Deconstructing the Notion of Mergers and Inverse Cascades in 3D Rayleigh-Taylor Flows

We identify two main processes for energy transfer across scales in Rayleigh-Taylor (RT) flows: baropycnal work Λ, due to pressure gradients, and deformation work π, due to flow strain. We show how these fluxes exhibit a quadratic-in-time self-similar evolution similar to RT mixing layer. Λ is a conduit for potential energy, transferring energy non-locally from the largest scales to smaller scales where π takes over. In 3D, π continues a persistent cascade to yet smaller scales, whereas in 2D, π re-channels the energy back to larger scales. This gives rise to a positive feedback loop in 2D-RT (absent in 3D) in which mixing layer growth and the associated potential energy release are enhanced relative to 3D, yielding the well-known larger α values in 2D simulations. Despite higher bulk kinetic energy levels in 2D, small scales are weaker than in 3D. We also find that net upscale cascade in 2D tends to isotropize the large-scale flow, in stark contrast to 3D-RT. These fundamental differences pinpoint the misleading physics inherent to 2D-RT simulations in ICF modeling. Our findings also indicate the absence of net upscale energy transfer in 3D-RT as is often claimed; growth of large-scale bubbles and spikes is not due to "mergers" but solely due to baropycnal work Λ.