# Analysis Seminar

#### Energy flux and high-order statistics of hydrodynamic turbulence

**Speaker:**
Yuri Lvov, Rensselaer Polytechnic Institute

**Location:**
Warren Weaver Hall 1302

**Date:**
Thursday, September 14, 2023, 11 a.m.

**Synopsis:**

The Kolmogorov-1941 theory emphasizes the crucial role played by the

flux of energy across the scales in the hydrodynamic turbulence. In

wave turbulence theory the flux of energy also plays a crucial role in

the Kolmogorov-Zakharov spectrum.

Flux of energy depends on the value of the third order correlator of

the field variable.

We demonstrate how and why the triple correlator determines the entire

statistics of the hydrodynamic and wave turbulence. All higher order

correlation functions are expressed as the convolution polynomials of

the triple correlator.

This is achieved through the use of the Dyson-Wyld diagrammatic

technique. I will review the Dyson-Wyld diagrammatic technique and

will analyze the infinite series for the correlation functions and

will suggest the {\it{triangular}} resummation of the infinite

diagrammatic series for multi-point correlation functions.

As a consequence, our results explain why the inverse cascade of the

two-dimensional hydrodynamic turbulence is close to Gaussian.

Since the triple correlator dictates the flux of energy through the

scales, we support the Kolmogorov-1941 idea that the energy flux is

one of the main characteristics of hydrodynamic turbulence.

This is the joint work with Professor Victor Lvov from the Weizmann

Institute, Israel.

**Notes:**

This is a joint talk with the **Wave Turbulence Seminar**.