English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Pro

Presents the zaia usage as premium feature

ZAIA

Presents AI Discovery search usage as a premium feature

AI Discovery

Presents AI Discovery explain and summary usage as a premium feature

Content Analysis

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Presents the pdf analysis as premium feature

PDF Analysis

1500 Top-up

3000 Top-up

Zendy Basic

2500 Top-up

Zendy Unlimited

Presents the access of premium content as premium feature

Premium Content

We propose an exact analytical formula for the anomalous scaling exponents ofinertial range structure functions in incompressible fluid turbulence. Theformula is a gravitational Knizhnik-Polyakov-Zamolodchikov (KPZ)-type relation,and is valid in any number of space dimensions. It incorporates intermittencyby gravitationally dressing the Kolmogorov linear scaling via a coupling to arandom geometry. The formula has one real parameter $\gamma$ that depends onthe number of space dimensions. The scaling exponents satisfy the convexityinequality, and the supersonic bound constraint. They agree with theexperimental and numerical data in two and three space dimensions, and withnumerical data in four space dimensions. Intermittency increases with $\gamma$,and in the infinite $\gamma$ limit the scaling exponents approach the valueone, as in Burgers turbulence. At large $n$ the $n$th order exponent scales as$\sqrt{n}$. We discuss the relation between fluid flows and black hole geometrythat inspired our proposal.

The Anomalous Scaling Exponents of Turbulence in General Dimension from Random Geometry