Asymptotic predictions on the velocity gradient statistics in low-Reynolds-number random flows : onset of skewness, intermittency and alignments

Title data

Carbone, Maurizio ; Wilczek, Michael:
Asymptotic predictions on the velocity gradient statistics in low-Reynolds-number random flows : onset of skewness, intermittency and alignments.
In: Journal of Fluid Mechanics. Vol. 986 (2024) . - A25.
ISSN 0022-1120
DOI: https://doi.org/10.1017/jfm.2024.165

Official URL:

Abstract in another language

Stirring a fluid through a Gaussian forcing at a vanishingly small Reynolds number produces a Gaussian random field, while flows at higher Reynolds numbers exhibit non-Gaussianity, cascades, anomalous scaling and preferential alignments. Recent works (Yakhot & Donzis, Phys. Rev. Lett., vol. 119, 2017, 044501; Khurshid et al., Phys. Rev. E, vol. 107, 2023, 045102) investigated the onset of these turbulent hallmarks in low-Reynolds-number flows by focusing on the scaling of the velocity gradients and velocity increments. They showed that the onset of power-law scalings in the velocity gradient statistics occurs at low Reynolds numbers, with the scaling exponents being surprisingly similar to those in the inertial range of fully developed turbulence. In this work we address the onset of turbulent signatures in low-Reynolds-number flows from the viewpoint of the velocity gradient dynamics, giving insights into its rich statistical geometry. We combine a perturbation theory of the full Navier–Stokes equations with velocity gradient modelling. This procedure results in a stochastic model for the velocity gradient in which the model coefficients follow directly from the Navier–Stokes equations and statistical homogeneity constraints. The Fokker–Planck equation associated with our stochastic model admits an analytic solution that shows the onset of turbulent hallmarks at low Reynolds numbers: skewness, intermittency and preferential alignments arise in the velocity gradient statistics through a smooth transition as the Reynolds number increases. The model predictions are in excellent agreement with direct numerical simulations of low-Reynolds-number flows.

Further data

Item Type:	Article in a journal
Refereed:	Yes
Keywords:	isotropic turbulence; turbulence modelling; turbulence theory
Institutions of the University:	Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Physics > Chair Theoretical Physics I > Chair Theoretical Physics I - Univ.-Prof. Dr. Michael Wilczek Faculties Faculties > Faculty of Mathematics, Physics und Computer Science Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Physics Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Physics > Chair Theoretical Physics I
Result of work at the UBT:	Yes
DDC Subjects:	500 Science > 530 Physics
Date Deposited:	15 Feb 2025 22:00
Last Modified:	07 May 2025 06:58
URI:	https://eref.uni-bayreuth.de/id/eprint/92388