Turbulence via intermolecular potential: Uncovering the origin

Abstract

In recent works, we proposed a hypothesis, according to which turbulence in gases is created by the mean field effect of an intermolecular potential. We discovered that, in a numerically simulated inertial flow, turbulent solutions indeed spontaneously emerge from a laminar initial condition, as observed in nature and experiments. To study the origin of turbulent dynamics, in the current work we examine the equations of a two-dimensional inertial flow, linearized around a large scale constant vorticity state. Remarkably, even in this simplified setting, we find that turbulent dynamics emerge as linearly unstable fluctuations of the velocity divergence. In particular, for the linearized dynamics at a high Reynolds number, we find that, at short time scales, the coupling of the mean field potential with the large scale background vorticity creates linearly unstable, rapidly oscillating fluctuations of the divergence of velocity at inertial scales. In the asymptotic time limit, we find a persistent eigenvector, also aligned largely with the divergence of velocity, which allows these fluctuations to propagate in the form of traveling waves in the Fourier domain. Remarkably, these traveling waves decay at a constant, scale-independent exponential rate, which is rather unusual, because all explicitly dissipative terms in the equations are viscous. Furthermore, it appears that the famous Kolmogorov scaling of the kinetic energy is produced by this persistent velocity divergence, due to a cubic relation between the physical time variable, and a pseudo-time variable, in which the dynamics become asymptotically autonomous. These effects vanish when the mean field potential is removed.