High Rayleigh number variational multiscale large eddy simulations of Rayleigh-Bénard Convection

Sondak, David; Smith, Thomas M.; Pawlowski, Roger P.; Conde, Sidafa; Shadid, John N.

doi:10.48550/arxiv.2005.10153

Cited by 1 publication

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References 53 publications

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“…Furthermore, a key nondimensional diagnostic parameter is the Nusselt number N u, measuring the vertical heat transport for a given temperature difference between the plates. Over the last several decades, there has been an intense focus on the scaling behavior of N u on Ra and P r. This relationship has been explored via experiments [5,[7][8][9][10][11][12], scaling laws [13][14][15][16][17][18][19][20], rigorous upper bounds on the allowable heat transport [21][22][23][24][25], and numerical simulations [1,2,[26][27][28][29][30][31][32][33]. The two competing scaling behaviors that emerge from this body of work are N u ∝ Ra 1/3 and N u ∝ Ra 1/2 .…”

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confidence: 99%

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

Kooloth,

Sondak,

Smith

2020

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For two-dimensional (2D) Rayleigh-Bénard convection, classes of unstable, steady solutions were previously computed using numerical continuation [1,2]. The 'primary' steady solution bifurcates from the conduction state at Ra ≈ 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, [1, 2] 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 P r = 7 and P r = 100. For transitional values of Ra, the primary and optimal-heattransport 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 P r = 7, while the optimal heat transport solutions are more easily detectable for P r = 100. In both cases P r = 7 and P r = 100, the relative prevalence of primary and optimal solutions is consistent with the N u vs. Ra scalings for the numerical data and the steady solutions.

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