# Universal Area Law in Turbulence

@article{Migdal2019UniversalAL, title={Universal Area Law in Turbulence}, author={Alexander Migdal}, journal={arXiv: High Energy Physics - Theory}, year={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 the limits of its applicability. Using the PDF for velocity circulation as a functional of the loop in coordinate space, we obtain explicit formulas for vorticity correlations in presence of velocity circulation. These functions are related to the shape of the scaling function of the PDF as well as…

## 9 Citations

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

- Physics
- 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…

### The area rule for circulation in three-dimensional turbulence

- PhysicsProceedings of the National Academy of Sciences
- 2021

It is shown that the hitherto unknown connection between minimal surfaces and turbulence is highlighted, and it is found that circulation statistics match in the two cases only when normalized by an internal variable such as the SD.

### Exact Area Law for Planar Loops in Turbulence in Two and Three Dimensions

- Mathematics
- 2019

We study properties of the minimal surface in the Area Law Solution \cite{M93}, \cite{M19a}, \cite{M19b}. We find out that Area Law holds exactly for 2D turbulence as well as for arbitrary planar…

### Area rule for circulation and minimal surfaces in three-dimensional turbulence

- Physics
- 2020

An important idea underlying a plausible dynamical theory of circulation in 3D turbulence is the so-called Area Rule, according to which the probability density function (PDF) of the circulation…

### Analytic and Numerical Study of Navier-Stokes Loop Equation in Turbulence

- Mathematics
- 2019

We developed analytic approach to the non-planar loop equation, which we derived in previous papers \cite{M19a},\cite{M19b},\cite{M19c}. We found quadratic integral equation for the vorticity…

### Turbulence, String Theory and Ising Model

- Physics
- 2019

We advance the vortex cell approach to turbulence \cite{TSVS} by elaborating the Clebsch field dynamics on the surface of vortex cells. We argue that resulting statistical system can be described as…

### Turbulence in Two-Dimensional Relativistic Hydrodynamic Systems with a Lattice Boltzmann Model

- Physics
- 2022

Using a Lattice Boltzmann hydrodynamic computational modeler to simulate relativistic fluid systems we explore turbulence in two-dimensional relativistic flows. We first a give a pedagogical…

### STATISTICAL EQUILIBRIUM OF CIRCULATING FLUIDS

- Physics
- 2022

: We develop a new theory of circulation statistics in strong turbulence, treated as a ﬁxed point of a Hopf equation. Strong turbulence is the limit of vanishing viscosity in the Navier-Stokes…

### 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 1-6 OF 6 REFERENCES

### 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…

### Asymptotic exponents from low-Reynolds-number flows

- Physics
- 2006

The high-order statistics of fluctuations in velocity gradients in the crossover range from the inertial to the Kolmogorov and sub-Kolmogorov scales are studied by direct numerical simulations (DNS)…

### Turbulence as Statistics of Vortex Cells

- Physics
- 1993

We develop the formulation of turbulence in terms of the functional integral over the phase space configurations of the vortex cells. The phase space consists of Clebsch coordinates at the surface of…

### 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…

### A.Donzis, Anomalous exponents in strong turbulence in:Physica D: Nonlinear Phenomena

- Volumes 384–385,
- 2018