Quantifying energy cascade mechanisms in turbulence using Stokes flow regularization

Vortex stretching (VS) has long been considered as a mechanistic explanation of the transfer of energy from large to small scales in 3D turbulence, dating back to pioneering works by Taylor (1938) and Onsager (1949). More recently, others have proposed strain-rate self-amplification (SSA) as an alternative energy cascade mechanism. Both VS and SSA provably vanish for 2D flows, where an inverse cascade from small to large scales is observed, which was described by Kraichnan (1976) in terms of vortex thinning (VT). This talk will show that Stokes flow regularization (SFR) leads to an exact equation for the energy cascade rate in terms of VS, SSA, and VT. The result provides a unified theory for quantifying energy cascade mechanisms in Navier-Stokes turbulence that includes both the 3D forward cascade and 2D inverse cascade. The SFR technique is readily extensible to quantify physical mechanisms for, e.g., the helicity cascade, stratified turbulence, and MHD turbulence.