High Schmidt-number turbulent advection and giant concentration fluctuations

Large-scale influence of numerical noises as artificial stochastic disturbances on a sustained turbulence

“…It was reported recently by McMullen et al (2022) that tiny stochastic disturbances resulting from thermal fluctuations might influence the small-scale properties of the freely decaying turbulence under their consideration, which is in agreement with the conclusions given by Gallis et al (2021), Bandak et al (2022), Bell et al (2022), Eyink & Jafari (2022), and so on. In this paper, we investigate the large-scale influence of numerical noises as a kind of tiny artificial stochastic disturbances on a sustained turbulence.…”

“…Furthermore, the transition to quadratic growth occurs at a length scale much larger than the gas molecular mean free path, namely in a regime that the NS equations are widely believed to describe. Thus they provided the first direct evidence that 'the Navier-Stokes equations do not describe turbulent gas flows in the dissipation range because they neglect thermal fluctuations' (McMullen et al 2022), which is in agreement with the results given by Bandak et al (2022), Bell et al (2022), Eyink & Jafari (2022), and others. Separately, Gallis et al (2021) used the direct simulation Monte Carlo (DSMC) method (molecular gas dynamics) and DNS of the NS equations to simulate a freely decaying turbulent flow, numerical noises are negligible compared with the 'true' physical solution, and thus the corresponding numerical result is convergent (reproducible) in an interval of time long enough for statistics, as described below.…”

“…(2022), Bell et al. (2022), Eyink & Jafari (2022), and so on. In this paper, we investigate the large-scale influence of numerical noises as a kind of tiny artificial stochastic disturbances on a sustained turbulence.…”

The Kraichnan Model and Non-Equilibrium Statistical Physics of Diffusive Mixing

“…Rather than the expected scaling S(k, t) ∝ k −4 , the numerical implementation of the DFV theory in [16] produced a result apparently more consistent with S(k, t) ∝ k −3 . On the other hand, it has now been shown by an exact mathematical analysis [17] that the DFV theory does yield S(k) ∝ k −4 , in close agreement with linearized theory, at least for a statistical steady state with random injection of concentration fluctuations. It was speculated in [17] that the simulation by DFV in [16] was not run for a sufficient time to observe the correct S(k, t) ∝ k −4 scaling or perhaps had an insufficient wavenumber range to clearly identify the power law exponent.…”

“…The paper of Donev, Fai and vanden-Eijnden [16] (hereafter DFV) has shown that the equations for the scalar concentration field in a binary fluid mixture, which describe its advection by thermal fluctuations of the velocity in an otherwise quiescent fluid, reduce in the high-Schmidt limit to a version of the Kraichnan model and yield an economical scheme for efficient numerical computation. The subsequent work [17] applied the DFV theory analytically to investigate the effects of thermal noise on high-Schmidt turbulent mixing and showed, in the process, that the many powerful mathematical methods devised to treat turbulent advection in the Kraichnan model can be applied also to mixing by thermal fluctuations. In the present paper we shall explain further this application and present a few initial results of our ongoing investigation.…”