Vortices as Brownian particles in turbulent flows

Vortices as Brownian particles in turbulent flows


View ORCID ProfileKai Leong Chong1, Jun-Qiang Shi2, Guang-Yu Ding1,3, View ORCID ProfileShan-Shan Ding2, View ORCID ProfileHao-Yuan Lu2, View ORCID ProfileJin-Qiang Zhong2,* and View ORCID ProfileKe-Qing Xia3,1,*
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Science Advances 19 Aug 2020:
Vol. 6, no. 34, eaaz1110
DOI: 10.1126/sciadv.aaz1110

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Abstract

Brownian motion of particles in fluid is the most common form of collective behavior in physical and biological systems. Here, we demonstrate through both experiment and numerical simulation that the movement of vortices in a rotating turbulent convective flow resembles that of inertial Brownian particles, i.e., they initially move ballistically and then diffusively after certain critical time. Moreover, the transition from ballistic to diffusive behaviors is direct, as predicted by Langevin, without first going through the hydrodynamic memory regime. The transitional timescale and the diffusivity of the vortices can be collapsed excellently onto a master curve for all explored parameters. In the spatial domain, however, the vortices exhibit organized structures, as if they are performing tethered random motion. Our results imply that the convective vortices have inertia-induced memory such that their short-term movement can be predicted and their motion can be well described in the framework of Brownian motions.

INTRODUCTION

Brownian motion is an example of stochastic processes that occur widely in nature (1). Einstein was the first to provide a theoretical explanation for the movement of pollen particles in a thermal bath (2). Later, Langevin considered the inertia of the particles and predicted that the motion of particles would be ballistic in a short time and then changes over to a diffusive one after certain time (3). Because this transition occurs in a very short time scale, its direct observation had to wait for over 100 years (4).

However, the “pure” Brownian motion, as predicted by Langevin, is never observed in liquid systems, i.e., the mean squared displacement (MSD) of the Brownian particles changes directly from a t2 dependence to a t dependence. Rather, the transition spans a broad range of time scales, as is the case in (4). This slow and smooth transition is caused by the so-called hydrodynamic memory effect (5), which arises as the surrounding fluid displaced by moving particles reacting back through entrainment, thereby generating long-range correlations (6). This also manifests in the spectrum of the stochastic force in the Langevin equation being “colored” (7, . The hydrodynamic memory effect has been observed in a number of systems, for instance, colloidal suspensions (9), particles suspended in air (10), and trapped particles in optical tweezers (4, 7, 11).

In the studies of Brownian motion, a common assumption is that the objects should have distinct density or mass difference from their environment such that inertia plays a role initially (3). Here, we demonstrate, by both experiment and numerical simulations, that vortices in highly turbulent convective flows behave like inertial particles performing pure Brownian motion, i.e., their MSD changes sharply from a t2 dependence to a t dependence without being influenced by the hydrodynamic effect. The system here is thermally driven rotating turbulent flows in which the convective Taylor columns move two-dimensionally in a highly turbulent background flow that serves as a heat bath. Our results suggest that within a well-determined time, the inertia of vortices becomes effective such that it persists to drift along the previous direction. This may entail the capability of predicting the vortex motion within certain period of time in astro- and geophysical systems.

In many situations in astrophysics, geophysics, and meteorology, thermal convection occurs while being influenced by rotation. The existence of Coriolis force leads to the formation of vortices (12), which appear ubiquitously in nature, for instance, tropical cyclones in the atmosphere (13), oceanic vortices (14), and long-lived giant red spot in Jupiter (15). Another intriguing example is the convective Taylor columns in Earth’s outer core, which is believed to play a major role in Earth’s dynamo (16) and is therefore closely related to Earth’s magnetic field variation and the corresponding seismic activities (17). A challenge in the astro- and geophysical research communities is whether one can predict the movement of vortices within certain period of time.

A model system used in the study of vortices in convective flows is the so-called rotating Rayleigh-Bénard (RB) convection (18–21), which is a fluid layer of fixed height (H) heated from below and cooled from above while being rotated about the vertical axis at an angular velocity Ω. Here, the temperature difference destabilizes the flow such that convection occurs when the thermal driving is sufficiently strong. Three dimensionless parameters are used to characterize the flow dynamics of this sytem, which are the Rayleigh number Ra = αgΔTH3/κν, the Prandtl number Pr = ν/κ, and the Ekman number Ek = ν/2ΩH2 (another often used dimensionless parameter to quantify the effect of rotation is the Rossby number Ro=EkRa/Pr−−−−−√). Here, α, κ, and ν are the thermal expansion coefficient, thermal diffusivity, and kinematic viscosity of the fluid, respectively; tg is the gravitational acceleration, and ΔT is the temperature difference across the fluid layer.

In the absence of rotation, fragmented thermal plumes are detached from the thermal boundary layer and being transported to the opposite boundary layer. When rotation is present, especially when its effect becomes non-negligible, vortical structures emerge that can be seen as fluid parcels spiraling up or down (Fig. 1). It is known that these vortical plumes arise as a result of Ekman pumping and can enhance heat transport (22). When rotation becomes rapid yet not too strong so the flow is not completely laminarized, the Taylor-Proudman effect (23, 24) becomes dominant, which suppresses flow variation along the axis of rotation. The resultant flow field is the long-lived columnar structure extending throughout the entire cell height known as convective Taylor columns (25–27). Because of their importance in the momentum and heat transport, previous works had studied extensively the morphology and statistical properties of these vortices (20, 25, 26, 28, 29).

More at link:
https://advances.sciencemag.org/content/6/34/eaaz1110

Keep in mind:  

http://milesmathis.com/brown.html

BROWNIAN MOTION. and the charge field by Miles Mathis. Brownian motion is another unexplained phenomenon. You will say that we have long had equations for it, and that Einstein's equations are quite successful. True, but I am not talking about equations. I am talking about a physical explanation.

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Once again, without the charge field, there can be no physical answer. We can write equations for the motions, but we cannot explain their genesis. But it turns out that Brownian motion at the lowest levels is more clear evidence for the reality of the charge field. And it turns out that this is one more thing modern physics is hiding from you.

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Thanks Chromium6. Of course I re-read Brownian Motion and the Charge Field before replying, I hope it's not my imagination, Miles' papers get easier to understand each time I read them.

It makes perfect sense that random charge field photon collisions cause Brownian motion. Some mainstream details concerning Brownian Vortices is a nice addition, or twist. Interpreting with respect to the charge field, I would say that vortices are part of the charge flow, beginning with each spinning and recycling charge particle. Strong N/S Charge flows between many parallel oriented atomic nuclei may easily generate the ‘ballistic’ flows identified. Then atoms may redirect some portion of the main channel into orthogonal or sideways directions, creating the ‘diffuse’ flows between more isolated nuclei.

The sciencemag.org source pdf has plenty of details to consider and reinterpret in light of the charge field.

I also had to try that like button.

Separate subject. I've had log in difficulties three or four times, being unable to into this site with either chrome or brave, over several tries over the course of several hours. The browser screens remain blank. I was finally able to log in much later or the next day.
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