Turbulence via intermolecular potential: Viscosity and transition range of the Reynolds number

TL;DR

This paper introduces a new turbulence model based on intermolecular potential effects, demonstrating a natural transition from laminar to turbulent flow in simulations that aligns with experimental observations.

Contribution

The work presents a novel turbulence theory where turbulence arises from mean field effects of intermolecular potential, and shows its validity through numerical simulations of flow transition.

Findings

Transition from laminar to turbulent flow occurs without external perturbations as Reynolds number increases.

The energy spectrum decay approaches Kolmogorov's -5/3 law in turbulent regime.

Simulation results are consistent with experimental data.

Abstract

Turbulence in fluids is an ubiquitous phenomenon, characterized by spontaneous transition of a smooth, laminar flow to rapidly changing, chaotic dynamics. In 1883, Reynolds experimentally demonstrated that, in an initially laminar flow of water, turbulent motions emerge without any measurable external disturbance. To this day, turbulence remains a major unresolved phenomenon in fluid mechanics; in particular, there is a lack of a mathematical model where turbulent dynamics emerge naturally from a laminar flow. Recently, we proposed a new theory of turbulence in gases, according to which turbulent motions are created in an inertial gas flow by the mean field effect of the intermolecular potential. In the current work, we investigate the effect of viscosity in our turbulence model, by numerically simulating the air flow at normal conditions in a straight pipe for different values of the Reynolds number. We find that the transition between the laminar and turbulent flows in our model occurs without any deliberate perturbations as the Reynolds number increases from 2000 to 4000. As the simulated flow becomes turbulent, the decay rate of the time averaged Fourier spectrum of the kinetic energy in our model approaches Kolmogorov's inverse five-thirds law. Both results are consistent with experiments and observations.