Lévy Walks as a Universal Mechanism of Turbulence Nonlocality

• Published in: Foundations (Basel) Vol. 3; no. 3; pp. 602 - 620
• Main Authors: Kukushkin, Alexander B., Kulichenko, Andrei A.
• Format: Journal Article
• Language: English
• Published: MDPI AG 20.09.2023
• Subjects: Biberman–Holstein equation; cross-correlation reflectometry; Lévy walk; nonlocality; superdiffusion; turbulence
• ISSN: 2673-9321; 2673-9321
• DOI: 10.3390/foundations3030036

The nonlocality (superdiffusion) of turbulence is expressed in the empiric Richardson t3 scaling law for the mean square of the mutual separation of a pair of particles in a fluid or gaseous medium. The development of the theory of nonlocality of various processes in physics and other sciences based on the concept of Lévy flights resulted in Shlesinger and colleagues’ about the possibility of describing the nonlocality of turbulence using a linear integro-differential equation with a slowly falling kernel. The approach developed by us made it possible to establish the closeness of the superdiffusion parameter of plasma density fluctuations moving across a strong magnetic field in a tokamak to the Richardson law. In this paper, we show the possibility of a universal description of the characteristics of nonlocality of transfer in a stochastic medium (including turbulence of gases and fluids) using the Biberman–Holstein approach to examine the transfer of excitation of a medium by photons, generalized in order to take into account the finiteness of the velocity of excitation carriers. This approach enables us to propose a scaling that generalizes Richardson’s t3 scaling law to the combined regime of Lévy flights and Lévy walks in fluids and gases.