Towards Finding the Conformal Invariance of the Multi-point Vorticity Statistics in $2d$ Turbulence
DOI:
https://doi.org/10.5890/JVTSD.2024.03.003Abstract
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.References
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