Towards Finding the Conformal Invariance of the Multi-point Vorticity Statistics in 2d Turbulence - Grebenev, Vladimir N.; Grishkov, Alexandre N. (Journal of Vibration Testing and System Dynamics, 2026)
The conformal invariance of certain statistics in the inviscid two-dimensional turbulence is derived. For this we investigate the transport equation for the two-point probability density functions of vorticity from the infinite Lundgren-Monin-Novikov hierarchy and give the conditions under which the probability measure is conformally invariant. This is an extension of our previous analyses of the one-point statistics, which also paves the way for further generalisation to arbitrary n-point statistics.