# Scaling Index $\alpha = \frac{1}{2}$ In Turbulent Area Law

@article{Migdal2019ScalingI, title={Scaling Index \$\alpha = \frac\{1\}\{2\}\$ In Turbulent Area Law}, author={Alexander Migdal}, journal={arXiv: High Energy Physics - Theory}, year={2019} }

We analyze the Minimal Area solution to the Loop Equations in turbulence \cite{M93}. As it follows from the new derivation in the recent paper \cite{M19}, the vorticity is represented as a normal vector to the minimal surface not just at the edge, like it was assumed before, but all over the surface. As it was pointed in that paper, the self-consistency relation for mean vorticity leads to $\alpha=\frac{1}{2}$, however the similar conditions for product of two and more vorticities cannot be…

## One Citation

### Clebsch confinement and instantons in turbulence

- Physics
- 2020

We introduce a concept of Clebsch confinement related to unbroken gauge invariance and study Clebsch instantons: singular vorticity sheets with nontrivial helicity. This is realization of the…

## References

SHOWING 1-5 OF 5 REFERENCES

### Universal Area Law in Turbulence

- Physics
- 2019

We re-visit the Area Law in Turbulence discovered many years ago \cite{M93} and verified recently in numerical experiments\cite{S19}. We derive this law in a simpler way, at the same time outlining…

### Circulation in High Reynolds Number Isotropic Turbulence is a Bifractal

- PhysicsPhysical Review X
- 2019

The turbulence problem at the level of scaling exponents is hard in part because of the multifractal scaling of small scales, which demands that each moment order be treated and understood…

### Instantons and intermittency.

- MathematicsPhysical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 1996

We describe the method for finding the non-Gaussian tails of the probability distribution function (PDF) for solutions of a stochastic differential equation, such as the convection equation for a…

### Loop Equation and Area Law in Turbulence

- Physics
- 1993

The incompressible fluid dynamics is reformulated as dynamics of closed loops C in coordinate space. We derive explicit functional equation for the pdf of the circulation P c (Γ) which allows the…