Mellin

Universal Theory of Decaying Turbulence

Announce Type: replace-cross Abstract: We derive an exact solution of the loop equation for freely decaying incompressible turbulence in arbitrary spatial dimension $d>1$. Using the Mandelstam identity in the loop dynamics, we prove that the nonlinear advection term reduces to a pure derivative and drops out of the momentum-loop equation. As a result, the momentum-loop equation becomes purely diffusive, admitting an exact geometric solution as a random walk on a circle. Despite this distinct...