Scientists discover new mechanism of symmetry restoration in turbulence
Fang XU | 02/27/2025

Symmetry has become a central dogma in modern science, guiding its development in many aspects. Symmetry breaking, especially spontaneous symmetry breaking (SSB), by which a symmetric state spontaneously ends up in an asymmetric or lower-symmetry state without explicitly introducing symmetry-breaking terms, has played an indispensable role in the developments of many branches of modern physics, such as high energy and condensed matter physics.

In turbulent Rayleigh-Bénard convection with cylindrical geometry, one would expect the large-scale flow structure to exhibit axis symmetry as dictated by the underlying governing equations and boundary conditions, e.g., a fountain-like structure. However, the actual flow topology turns out to be a single-roll large-scale circulatory flow (LSC) with upwelling and downwelling in the opposite peripheries rather than an axisymmetric pattern. This is a case of SSB, and it cannot be attributed to imperfections in the experimental setup, as it has also been found in numerical simulations. The origin of the SSB, i.e., why the flow takes a topology of a lower symmetry in the first place, remains a mystery.

Adding a small amount of polymers to the fluid flow leads to several intriguing phenomena, including drag reduction along with momentum and heat transport modification. The interaction of polymers with turbulence is one of the most challenging subjects in turbulence research. Polymers also alter how energy is transferred through the inertial range of scales. However, how these additives change the large-scale structures and the system’s symmetry in turbulence has been much less explored.

Professor Ke-Qing Xia’s research group from the Center for Complex Flows and Soft Matter Research and the Department of Mechanics and Aerospace Engineering at the Southern University of Science and Technology (SUSTech) has recently made new discoveries in their study of turbulent thermal convection.

Their paper, titled “Restoration of Axisymmetric Flow Structure in Turbulent Thermal Convection by Polymer Additives”, has been published in Physical Review Letters, the world’s premier physics journal for original research.

Professor Xia’s group designed a novel experiment to measure the large-scale flow of a turbulent thermal convection system with polymer additives. The experiment was carried out in a cylindrical convection cell, and a small amount of long-chain polymers was added to the fluid. For the Newtonian fluid in Figure 1a, the dominant flow structure is the well-known single-roll LSC with a tilted elliptical primary vortex and two small diagonally opposite corner vortices. With a minute amount of long-chain polymers, the large-scale flow is dominated by intense upwelling along the symmetry axis and downwelling along the periphery (Figure 1b). The fountain-like flow pattern is consistent with the axisymmetry of the system and is what would be expected had it not been for the SSB that led to the LSC.

Figure 1. Time-averaged velocity field measured in two vertical orthogonal planes at polymer concentrations of (a) c = 0 showing a flow topology with spontaneous symmetry breaking, and (b) 20 ppm exhibiting an axisymmetric fountain-shaped flow topology

The researchers explored the parameter space for the observed large-scale flow topologies. Figure 2 shows a phase diagram based on measurements with various polymer concentrations and values of Ra. The anisotropy of velocity fluctuations is related to the topology of large-scale flow, i.e., the same flow topology has nearly the same value of Wrms/Urms, which is a measure of the anisotropy of fluctuations. This correspondence further suggests that axisymmetric structure results from anisotropic suppression of velocity fluctuations.

Figure 2. Phase diagram of the large-scale flow structure overlaid with the global-averaged ratio Wrms/Urms

The group also examined how polymer additives change the energy transfer between mean flow and turbulence, quantified by the turbulent kinetic energy production. For the Newtonian fluid (Figure 3a), the energy transfer primarily occurs near the boundaries, where the viscous boundary layers develop. The net value is positive when integrated over the whole measurement plane, indicating that overall, the mean flow supplies energy to the turbulent fluctuations. With added polymers, the volume-integrated net turbulent kinetic energy production vanishes, and the turbulence production distribution significantly changes (Figure 3b). Therefore, adding polymers effectively changes the mechanism of energy transfer between the mean flow and turbulence.

Figure 3. Turbulence production measured in the vertical plane at polymer concentrations of (a) c = 0, and (b) 20 ppm

This study demonstrated that polymer additives can be used to manipulate, through the small scales, the large-scale coherent flow topology and the level of symmetry in turbulent flows. While symmetry restorations occurring in nature are usually a result of increased thermal fluctuations, this study demonstrates a fascinating example of symmetry restoration as a result of reduced fluctuations.

Dr. Fang Xu from Ke-Qing Xia’s group is the first author of this paper, with Professor Xia serving as the corresponding author. Other contributors to this work include Xiao-Shen Liu and Dr. Xiao-Ming Li.

 

Paper link: https://link.aps.org/doi/10.1103/PhysRevLett.134.084001

 

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2025, 02-27
By Fang XU

From the Series

Research

Proofread ByAdrian Cremin, Yingying XIA

Photo ByDepartment of Mechanics and Aerospace Engineering

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