Analysis Seminar

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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.