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- W4383534626 abstract "We develop a quantitative microscopic theory of decaying Turbulence by studying the dimensional reduction of the Navier-Stokes loop equation for the velocity circulation. We have found an infinite dimensional manifold of solutions of the Navier-Stokes loop equationcite{M93, M23PR} for the Wilson loop in decaying Turbulence in arbitrary dimension $d >2$. This family of solutions corresponds to a fractal curve in complex space $mathbb C^d$, described by an algebraic equation between consecutive positions plus a nonlinear periodicity condition. We derive the constrained SDE for the evolution of the fractal curve at a fixed moment of physical time as a function of an auxiliary stochastic time. We expect this stochastic process to cover our fixed manifold of the solutions of the decaying Turbulence. The energy density of the fluid decays as $mathcal E_0/t$, where $mathcal E_0$ is an initial dissipation rate. Presumably, we have found a new phase of extreme Turbulence yet to be observed in real or numerical experiments." @default.
- W4383534626 created "2023-07-08" @default.
- W4383534626 creator A5031765450 @default.
- W4383534626 date "2023-07-06" @default.
- W4383534626 modified "2023-10-18" @default.
- W4383534626 title "Decaying Turbulence as a Fractal Curve" @default.
- W4383534626 doi "https://doi.org/10.20944/preprints202305.0955.v5" @default.
- W4383534626 hasPublicationYear "2023" @default.
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