Work

Quantum solution of classical turbulence: Decaying energy spectrum

Year: 2024

Type: article

Abstract: This paper investigates the recently found \cite{migdal2023exact} reduction of decaying turbulence in the Navier-Stokes equation to a Number Theory problem of finding the statistical limit of the Euler ensemble. We reformulate the Euler ensemble as a Markov chain and show the equivalence of this formulation to the quantum statistical theory of free fermions on a ring, with an external field related to the random fractions of $\pi$. We find the solution of this system in the statistical limit $N\to \infty$ in terms of a complex trajectory (instanton) providing a saddle point to the path integral over the charge density of these fermions. This results in an analytic formula for the observable correlation function of vorticity in wavevector space. This is a full solution in quadratures, but it is too complex for an immediate computation; a separate investigation by Number Theory methods is required.

Source: Physics of Fluids

DOI: 10.1063/5.0228660

Author: Alexander Migdal

Institution: New York University Abu Dhabi

Language: English

Topic: Fluid Dynamics and Turbulent Flows

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid