Transition to the Ultimate State of Turbulent Rayleigh-Bénard Convection

He, Xiaozhou; Fünfschilling, Denis; Nobach, Holger; Bodenschatz, Eberhard; Ahlers, Guenter

doi:10.1103/physrevlett.108.024502

Cited by 239 publications

(346 citation statements)

References 30 publications

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“…The relation (17) 37,38 , it has been shown, both numerically 39 and experimentally 40,41 , that the ultimate regime scaling can be realized when the solid boundaries are absent. In RT turbulence, the observation of the ultimate state is not surprising as boundaries play no role in the system and the bulk dynamics dominate the convective turbulence in the mixing zone.…”

Section: Resultsmentioning

confidence: 99%

Temporal evolution and scaling of mixing in two-dimensional Rayleigh-Taylor turbulence

Zhou

2013

Physics of Fluids

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We report a high-resolution numerical study of two-dimensional (2D) miscible Rayleigh-Taylor (RT) incompressible turbulence with the Boussinesq approximation. An ensemble of 100 independent realizations were performed at small Atwood number and unit Prandtl number with a spatial resolution of 2048 × 8193 grid points. Our main focus is on the temporal evolution and the scaling behavior of global quantities and of small-scale turbulence properties. Our results show that the buoyancy force balances the inertial force at all scales below the integral length scale and thus validate the basic force-balance assumption of the Bolgiano-Obukhov scenario in 2D RT turbulence. It is further found that the Kolmogorov dissipation scale η(t) ∼ t 1/8 , the kinetic-energy dissipation rate ε u (t) ∼ t −1/2 , and the thermal dissipation rate ε θ (t) ∼ t −1 . All of these scaling properties are in excellent agreement with the theoretical predictions of the Chertkov model [Phys. Rev. Lett. 91, 115001 (2003)]. We further discuss the emergence of intermittency and anomalous scaling for high order moments of velocity and temperature differences. The scaling exponents ξ r p of the pth-order temperature structure functions are shown to saturate to ξ r ∞ ≃ 0.78 ± 0.15 for the highest orders, p ∼ 10. The value of ξ r ∞ and the order at which saturation occurs are compatible with those of turbulent Rayleigh-Bénard (RB) convection [Phys. Rev. Lett. 88, 054503 (2002)], supporting the scenario of universality of buoyancy-driven turbulence with respect to the different boundary conditions characterizing the RT and RB systems.

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Section: Resultsmentioning

confidence: 99%

Temporal evolution and scaling of mixing in two-dimensional Rayleigh-Taylor turbulence

Zhou

2013

Physics of Fluids

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“…For example, breaking of homogeneity or isotropy in the boundary conditions can affect the flow on a wide range of scales (Biferale & Procaccia 2005). As a result the turbulent statistical properties might be strongly sensitive to symmetry breaking mechanisms and be described by different statistical attractors even in highly turbulent regimes as recently suggested to explain puzzling transition observed at high Rayleigh numbers in some experimental set-ups (He et al 2012;Ahlers et al 2009a) and in highly sheared flow (Cortet et al 2010). Clearly, understanding the effects of possible -small-boundary heterogeneities for such critical behavior could be key to improve our understanding of such a general question.…”

Section: Non-homogeneous Rayleigh-bénard Convectionmentioning

confidence: 98%

Natural convection with mixed insulating and conducting boundary conditions: low- and high-Rayleigh-number regimes

et al. 2014

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We investigate the stability and dynamics of natural convection in two dimensions, subject to inhomogeneous boundary conditions. In particular, we consider a Rayleigh-Bénard (RB) cell, where the horizontal top boundary contains a periodic sequence of alternating thermal insulating and conducting patches, and we study the effects of the heterogeneous pattern on the global heat exchange, both at low and high Rayleigh numbers. At low Rayleigh numbers, we determine numerically the transition from a regime characterized by the presence of small convective cells localized at the inhomogeneous boundary to the onset of bulk convective rolls spanning the entire domain. Such a transition is also controlled analytically in the limit when the boundary pattern length is small compared with the cell vertical size. At higher Rayleigh number, we use numerical simulations based on a lattice Boltzmann method to assess the impact of boundary inhomogeneities on the fully turbulent regime up to Ra ∼ 10 10 .

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“…In The deviation of the exponent from 1/2 (ultimate regime 9 ) is due to nontrivial correlation C uθres between u z and θ res . In Table IV 63 , which will occur when C uθres will become independent of Ra. …”

Section: B Nusselt Number Scalingmentioning

confidence: 99%

Scaling of large-scale quantities in Rayleigh-Bénard convection

Pandey

Verma

2016

Physics of Fluids

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We derive a formula for the Péclet number (Pe) by estimating the relative strengths of various terms of the momentum equation. Using direct numerical simulations in three dimensions we show that in the turbulent regime, the fluid acceleration is dominated by the pressure gradient, with relatively small contributions arising from the buoyancy and the viscous term; in the viscous regime, acceleration is very small due to a balance between the buoyancy and the viscous term. Our formula for Pe describes the past experiments and numerical data quite well. We also show that the ratio of the nonlinear term and the viscous term is ReRa −0.14 , where Re and Ra are Reynolds and Rayleigh numbers respectively; and that the viscous dissipation, where U is the root mean square velocity and d is the distance between the two horizontal plates. The aforementioned decrease in nonlinearity compared to free turbulence arises due to the wall effects.

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Transition to the Ultimate State of Turbulent Rayleigh-Bénard Convection

Cited by 239 publications

References 30 publications

Temporal evolution and scaling of mixing in two-dimensional Rayleigh-Taylor turbulence

Temporal evolution and scaling of mixing in two-dimensional Rayleigh-Taylor turbulence

Natural convection with mixed insulating and conducting boundary conditions: low- and high-Rayleigh-number regimes

Scaling of large-scale quantities in Rayleigh-Bénard convection

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