Does Yakhot’s Growth Law for Turbulent Burning Velocity Hold?

Abstract

Using formal renormalization theory, Yakhot derived in ([32], 1988) an \(O\left( \frac{A}{\sqrt{\log A}}\right) \) growth law of the turbulent flame speed with respect to large flow intensity A based on the inviscid G-equation. Although this growth law is widely cited in the combustion literature, there has been no rigorous mathematical discussion to date about its validity. As a first step towards unveiling this mystery, we prove that there is no intermediate growth law between \(O\left( \frac{A}{\log A}\right) \) and O(A) for two dimensional incompressible Lipschitz continuous periodic flows with bounded swirl sizes. In particular, we do not assume the non-degeneracy of critical points. In addition, other examples of flows with lower regularity, Lagrangian chaos, and related phenomena are also discussed.