Flow Topology Transition via Global Bifurcation in Thermally Driven Turbulence

Xie, Yi-Chao; Ding, Guang-Yu; Xia, Ke‐Qing

doi:10.1103/physrevlett.120.214501

Cited by 42 publications

(32 citation statements)

References 29 publications

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“…When a swirl is present, it can act as a source of toroidal vorticity (i.e., the vorticity associated with the poloidal movement), as can be checked by taking the curl of Eqs. (1) and (2). The vorticity is thus not conserved anymore, making the dynamics intermediate between 2D and 3D.…”

Section: Axisymmetric Turbulencementioning

confidence: 99%

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Transition from non-swirling to swirling axisymmetric turbulence

et al. 2020

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Strictly axisymmetric turbulence, i.e., turbulence governed by the Navier-Stokes equations modified such that the flow is invariant in the azimuthal direction, is a system intermediate between two-and three-dimensional turbulence. We investigate statistically steady states of this system by direct numerical simulation using a forcing protocol, which allows the injected energy in the toroidal and in the poloidal directions to be tuned independently. A sharp transition between a two-dimensional two-component (2D2C, nonswirling) flow and a two-dimensional three-component (2D3C, swirling) flow is observed. We derive a statistical model which reproduces this transition.

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Section: Axisymmetric Turbulencementioning

confidence: 99%

“…are gradually or abruptly broken, when increasing the Reynolds number. More recently, transitions between different turbulent states with different statistical symmetries were evidenced either experimentally [1,2] or numerically [3,4], still falling into the classical paradigm of spontaneous symmetry breaking.…”

Section: Introductionmentioning

confidence: 99%

Transition from non-swirling to swirling axisymmetric turbulence

et al. 2020

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“…Several findings have suggested that wall-bounded turbulent flows can take different statistically stationary turbulent states, with different length scale of the flow structures and with different transport properties, even for the very same values of the control parameters. Examples for the coexistence of such multiple turbulent states include turbulent (rotating) Rayleigh-Bénard convection [2][3][4][5][6][7][8], Taylor-Couette turbulence [9][10][11], double-diffusive convection turbulence [12], von Karman flow [13][14][15][16], rotating spherical Couette flow [17], Couette flow with span-wise rotation [18], but also geophysical flows [19,20] such as in ocean circulation [21][22][23], in the liquid metal core of Earth [24][25][26][27], or in the atmosphere [28,29].…”

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confidence: 99%

Multiple States in Turbulent Large-Aspect-Ratio Thermal Convection: What Determines the Number of Convection Rolls?

et al. 2020

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“…Tsinober 16 postulated that the enstrophy production is large in S4 topology whereas the strain rate production is concentrated in regions of S1 topology. The flow topology distributions in Rayleigh–Bénard convection, where temperature and velocity fields are intrinsically coupled, are yet to be analysed in detail 17 – 20 in comparison to the vast body of literature (e.g. Refs.…”

Section: Introductionmentioning

confidence: 99%

“…The analyses by Dabbagh et al 17 – 19 revealed the existence of the teardrop shape in the bulk region away from the walls in Rayleigh–Bénard convection but the small scale structures in the vicinity of the hot and cold walls have not been discussed there in terms of Q and R . Xi et al 20 reported a transition of flow topologies from a quadruple structure to a dipole structure based on Rayleigh number in turbulent Rayleigh–Bénard convection, which has implications on the Nusselt number (or heat transfer rate). A recent analysis revealed that large-scale circulation in Rayleigh–Bénard convection is affected by Prandtl number 21 .…”

Section: Introductionmentioning

confidence: 99%

Near wall Prandtl number effects on velocity gradient invariants and flow topologies in turbulent Rayleigh–Bénard convection

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Haßlberger

Klein

et al. 2020

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The statistical behaviours of the invariants of the velocity gradient tensor and flow topologies for Rayleigh–Bénard convection of Newtonian fluids in cubic enclosures have been analysed using Direct Numerical Simulations (DNS) for a range of different values of Rayleigh (i.e. $$Ra=10^7-10^9$$ R a = 10 7 - 10 9 ) and Prandtl (i.e. $$Pr=1$$ P r = 1 and 320) numbers. The behaviours of second and third invariants of the velocity gradient tensor suggest that the bulk region of the flow at the core of the domain is vorticity-dominated whereas the regions in the vicinity of cold and hot walls, in particular in the boundary layers, are found to be strain rate-dominated and this behaviour has been found to be independent of the choice of Ra and Pr values within the range considered here. Accordingly, it has been found that the focal topologies S1 and S4 remain predominant in the bulk region of the flow and the volume fraction of nodal topologies increases in the vicinity of the active hot and cold walls for all cases considered here. However, remarkable differences in the behaviours of the joint probability density functions (PDFs) between second and third invariants of the velocity gradient tensor (i.e. Q and R) have been found in response to the variations of Pr. The classical teardrop shape of the joint PDF between Q and R has been observed away from active walls for all values of Pr, but this behavior changes close to the heated and cooled walls for high values of Pr (e.g. $$Pr=320$$ P r = 320 ) where the joint PDF exhibits a shape mirrored at the vertical Q-axis. It has been demonstrated that the junctions at the edges of convection cells are responsible for this behaviour for $$Pr=320$$ P r = 320 , which also increases the probability of finding S3 topologies with large negative magnitudes of Q and R. By contrast, this behaviour is not observed in the $$Pr=1$$ P r = 1 case and these differences between flow topology distributions in Rayleigh–Bénard convection in response to Pr suggest that the modelling strategy for turbulent natural convection of gaseous fluids may not be equally well suited for simulations of turbulent natural convection of liquids with high values of Pr.

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Flow Topology Transition via Global Bifurcation in Thermally Driven Turbulence

Cited by 42 publications

References 29 publications

Transition from non-swirling to swirling axisymmetric turbulence

Transition from non-swirling to swirling axisymmetric turbulence

Multiple States in Turbulent Large-Aspect-Ratio Thermal Convection: What Determines the Number of Convection Rolls?

Near wall Prandtl number effects on velocity gradient invariants and flow topologies in turbulent Rayleigh–Bénard convection

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