Coherent Solutions and Transition to Turbulence in Two-Dimensional Rayleigh-Bénard Convection

Abstract

For two-dimensional Rayleigh-Bénard convection, classes of unstable, steady solutions were previously computed using numerical continuation (Waleffe, 2015; Sondak, 2015). The `primary' steady solution bifurcates from the conduction state at $Ra\approx 1708$, and has a characteristic aspect ratio (length/height) of approximately $2$. The primary solution corresponds to one pair of counterclockwise-clockwise convection rolls with a temperature updraft in between and an adjacent downdraft on the sides. By adjusting the horizontal length of the domain, (Waleffe, 2015; Sondak, 2015) also found steady, maximal heat transport solutions, with characteristic aspect ratio less than $2$ and decreasing with increasing $Ra$. Compared to the primary solutions, optimal heat transport solutions have modifications to boundary layer thickness, the horizontal length scale of the plume, and the structure of the downdrafts. The current study establishes a direct link between these (unstable) steady solutions and transition to turbulence for $Pr=7$ and $Pr=100$. For transitional values of $Ra$, the primary and optimal heat transport solutions both appear prominently in appropriately-sized sub-fields of the time-evolving temperature fields. For $Ra$ beyond transitional, our data analysis shows persistence of the primary solution for $Pr=7$, while the optimal heat transport solutions are more easily detectable for $Pr=100$. In both cases $Pr=7$ and $Pr=100$, the relative prevalence of primary and optimal solutions is consistent with the $Nu$ vs. $Ra$ scalings for the numerical data and the steady solutions.

arXiv comment34 pages, 23 figures

References in corpus (31)

• Large scale dynamics in turbulent Rayleigh-Benard convection
• Scaling in thermal convection: A unifying theory
• Dedalus: A Flexible Framework for Numerical Simulations with Spectral Methods
• Visualizing the geometry of state space in plane Couette flow
• The unifying theory of scaling in thermal convection: The updated prefactors
• Enforcing Statistical Constraints in Generative Adversarial Networks for Modeling Chaotic Dynamical Systems
• Aspect ratio dependence of heat transfer and large-scale flow in turbulent convection
• Transition to the ultimate regime in two-dimensional Rayleigh-Bénard convection
• Turbulent thermal superstructures in Rayleigh-Bénard convection
• Connecting flow structures and heat flux in turbulent Rayleigh-Bénard convection
• Boundary layer structure in turbulent Rayleigh-Benard convection
• Multiple states in turbulent large-aspect ratio thermal convection: What determines the number of convection rolls?
• "Ultimate state" of two-dimensional Rayleigh-Benard convection between free-slip fixed temperature boundaries
• Energy spectra and fluxes for Rayleigh-Benard convection
• Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems
• Transition to the ultimate regime in a radiatively driven convection experiment
• Large-scale mean patterns in turbulent convection
• Wall to Wall Optimal Transport
• Reservoir computing model of two-dimensional turbulent 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 $\Gamma =1.00$
• Heat Transport by Coherent Rayleigh-Bénard Convection
• Searching turbulence for periodic orbits with dynamic mode decomposition
• Optimal Heat Transport in Rayleigh-Bénard Convection
• The energy flux spectrum of internal waves generated by 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
• Maximal heat transfer between two parallel plates
• Reply to "Absence of Evidence for the Ultimate Regime in Two-Dimensional Rayleigh-Bénard Convection"
• Multi-scale steady solution for Rayleigh-Bénard convection
• Ultimate heat transfer in `wall-bounded' convective turbulence
• High Rayleigh number variational multiscale large eddy simulations of Rayleigh-Bénard Convection

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• Steady Rayleigh--Bénard convection between no-slip boundaries
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