Transition to the ultimate regime in two-dimensional Rayleigh-Bénard convection

Abstract

The possible transition to the so-called ultimate regime, wherein both the bulk and the boundary layers are turbulent, has been an outstanding issue in thermal convection, since the seminal work by Kraichnan [Phys. Fluids 5, 1374 (1962)]. Yet, when this transition takes place and how the local flow induces it is not fully understood. Here, by performing two-dimensional simulations of Rayleigh-Bénard turbulence covering six decades in Rayleigh number Ra up to $10^{14}$ for Prandtl number Pr $=1$, for the first time in numerical simulations we find the transition to the ultimate regime, namely at ${\text{Ra}}^{\ast }=10^{13}$. We reveal how the emission of thermal plumes enhances the global heat transport, leading to a steeper increase of the Nusselt number than the classical Malkus scaling $\text{Nu}\sim {\text{Ra}}^{1/3}$ [Proc. R. Soc. London A 225, 196 (1954)]. Beyond the transition, the mean velocity profiles are logarithmic throughout, indicating turbulent boundary layers. In contrast, the temperature profiles are only locally logarithmic, namely within the regions where plumes are emitted, and where the local Nusselt number has an effective scaling $\text{Nu}\sim {\text{Ra}}^{0.38}$, corresponding to the effective scaling in the ultimate regime.

arXiv comment6 pages, 4figures

References in corpus (20)

• Large scale dynamics in turbulent Rayleigh-Benard convection
• Scaling in thermal convection: A unifying theory
• Thermal convection for large Prandtl numbers
• Boundary layer structure in turbulent thermal convection and its consequences for the required numerical resolution
• Radial boundary layer structure and Nusselt number in Rayleigh-Benard convection
• The unifying theory of scaling in thermal convection: The updated prefactors
• A Comparison of Turbulent Thermal Convection Between Conditions of Constant Temperature and Constant Flux
• Comparison between two and three dimensional Rayleigh-Bénard convection
• Prandtl and Rayleigh number dependence of heat transport in high Rayleigh number thermal convection
• Roughness-facilitated local 1/2 scaling does not imply the onset of the ultimate regime of thermal convection
• Logarithmic temperature profiles in turbulent Rayleigh-Bénard convection
• Measured Instantaneous Viscous Boundary Layer in Turbulent Rayleigh-Bénard Convection
• Prandtl-Blasius temperature and velocity boundary layer profiles in turbulent Rayleigh-Bénard convection
• Heat transport by turbulent Rayleigh-Bénard convection for $\Pra\ \simeq 0.8$ and $4\times 10^{11} \alt \Ra\ \alt 2\times10^{14}$: Ultimate-state transition for aspect ratio $\Gamma =1.00$
• Wall roughness induces asymptotic ultimate turbulence
• Counter-gradient heat transport in two-dimensional turbulent Rayleigh-Bénard convection
• Logarithmic temperature profiles of turbulent Rayleigh-Bénard convection in the classical and ultimate state for a Prandtl number of 0.8
• Logarithmic mean temperature profiles and their connection to plume emissions in turbulent Rayleigh-Bénard convection
• Logarithmic temperature profiles in the ultimate regime of thermal convection
• Velocity and Energy Profiles In Two- vs. Three-Dimensional Channels: Effects of Inverse vs. Direct Energy Cascade

Cited by in corpus (45)

• Multiple states in turbulent large-aspect ratio thermal convection: What determines the number of convection rolls?
• Flow organization and heat transfer in turbulent wall sheared thermal convection
• Supergravitational turbulent thermal convection
• An efficient phase-field method for turbulent multiphase flows
• Heat transfer and flow regimes in quasi-static magnetoconvection with a vertical magnetic field
• The effect of Prandtl number on turbulent sheared thermal convection
• Settling of inertial particles in turbulent Rayleigh-Benard convection
• Large eddy simulations of turbulent thermal convection using renormalized viscosity and thermal diffusivity
• Evidences for the existence of the ultimate regime in supergravitational turbulent thermal convection
• Thermal boundary layer structure in low-Prandtl-number turbulent convection
• Absence of Evidence for the Ultimate Regime in Two-Dimensional Rayleigh-Bénard Convection
• Absence of Evidence for the 'Ultimate' State of Turbulent Rayleigh-Bénard Convection
• Steady Rayleigh--Bénard convection between no-slip boundaries
• Large-scale influence of numerical noises as artificial stochastic disturbances on a sustained turbulence
• Predictions of Reynolds and Nusselt numbers in turbulent convection using machine-learning models
• Revisiting Reynolds and Nusselt numbers in turbulent thermal convection
• Direct numerical simulations of Taylor--Couette turbulence: the effect of sand grain roughness
• Reply to "Absence of Evidence for the Ultimate Regime in Two-Dimensional Rayleigh-Bénard Convection"
• Surface Manifestation of Stochastically Excited Internal Gravity Waves
• Particle transport and deposition in wall-sheared thermal turbulence
• Coherent Solutions and Transition to Turbulence in Two-Dimensional Rayleigh-Bénard Convection
• Non-Boussinesq convection at low Prandtl numbers relevant to the Sun
• Long-distance migration with minimal energy consumption in a thermal turbulent environment
• Transition to ultimate Rayleigh-Bénard turbulence revealed through extended self similarity scaling analysis of the temperature structure functions
• Realizing the ultimate scaling of the convection turbulence by spatially decoupling the thermal and viscous boundary layers
• Towards DNS of the Ultimate Regime of Rayleigh--Bénard Convection
• Data-driven spectral turbulence modeling for Rayleigh-Bénard convection
• Marginally-Stable Thermal Equilibria of Rayleigh-Bénard Convection
• On high Taylor number Taylor vortices
• Performance of parallel-in-time integration for Rayleigh Bénard Convection
• Convective dynamics with mixed temperature boundary conditions: why thermal relaxation matters and how to accelerate it
• Scaling laws for Rayleigh-Bénard convection between Navier-slip boundaries
• Transient and steady convection in two dimensions
• Plane-layer Rayleigh-Bénard convection up to $Ra=10^{11}$: Near-wall fluctuations and role of initial conditions
• A pressure-free long-time stable reduced-order model for two-dimensional Rayleigh-Bénard convection
• Exploring the origin of Turbulent Taylor rolls
• From zonal flow to convection rolls in Rayleigh-Bénard convection with free-slip plates
• Two-layer Thermally Driven Turbulence: Mechanisms for Interface Breakup
• Determining a priori a RANS model's applicable range via global epistemic uncertainty quantification
• The large-scale footprint in small-scale Rayleigh-Bénard turbulence
• Geophysical flows over topography, a playground for laboratory experiments
• Multi-scale steady solution for Rayleigh-Bénard convection
• Influence of plume activity on thermal convection in a rectangular cell
• Internally heated and fully compressible convection: flow morphology and scaling laws
• Learning to traverse convective flows at moderate to high Rayleigh numbers