Patterns and bifurcations in low-Prandtl number Rayleigh-Benard convection

We present a detailed bifurcation structure and associated flow patterns for low-Prandtl number ($P=0.0002, 0.002, 0.005, 0.02$) Rayleigh-B\'{e}nard convection near its onset. We use both direct numerical simulations and a 30-mode low-dimensional model for this study. We observe that low-Prandtl number (low-P) convection exhibits similar patterns and chaos as zero-P convection \cite{pal:2009}, namely squares, asymmetric squares, oscillating asymmetric squares, relaxation oscillations, and chaos. At the onset of convection, low-P convective flows have stationary 2D rolls and associated stationary and oscillatory asymmetric squares in contrast to zero-P convection where chaos appears at the onset itself. The range of Rayleigh number for which stationary 2D rolls exist decreases rapidly with decreasing Prandtl number. Our results are in qualitative agreement with results reported earlier

Role of Bulk flow in Turbulent Convection

In this paper we present scaling of large-scale quantities like Pecl\'{e}t and Nusselt numbers, and the dissipation rates of kinetic energy and entropy. Our arguments are based on the scaling of bulk quantities and earlier experimental and simulation results. We also present the inertial-range properties of spectra and fluxes of kinetic energy and entropy.Comment: 15 pages, to Appear in the proceedings of "Senfest, International Conference on Complex Processes in Plasmas and Nonlinear Dynamical Systems

Scaling of heat flux and energy spectrum for "very large" Prandtl number convection

Under the limit of infinite Prandtl number, we derive analytical expressions for the large-scale quantities, e.g., P\'{e}clet number Pe, Nusselt number Nu, and rms value of the temperature fluctuations $\theta_\mathrm{rms}$. We complement the analytical work with direct numerical simulations, and show that $\mathrm{Nu} \sim \mathrm{Ra}^{\gamma}$ with $\gamma \approx (0.30-0.32)$, $\mathrm{Pe} \sim \mathrm{Ra}^{\eta}$ with $\eta \approx (0.57-0.61)$, and $\theta_\mathrm{rms} \sim \mathrm{const}$. The Nusselt number is observed to be an intricate function of $\mathrm{Pe}$, $\theta_\mathrm{rms}$, and a correlation function between the vertical velocity and temperature. Using the scaling of large-scale fields, we show that the energy spectrum $E_u(k)\sim k^{-13/3}$, which is in a very good agreement with our numerical results. The entropy spectrum $E_\theta(k)$ however exhibits dual branches consisting of $k^{-2}$ and $k^0$ spectra; the $k^{-2}$ branch corresponds to the Fourier modes $\hat{\theta}(0,0,2n)$, which are approximately $-1/(2n \pi)$. The scaling relations for Prandtl number beyond $10^2$ match with those for infinite Prandtl number.Comment: 14 pages, 14 figure

Field correlations and the ultimate regime of turbulent convection

Using direct numerical simulations of Rayleigh-B\'{e}nard convection (RBC) under free-slip boundary condition, we show that the normalized correlation function between the vertical velocity field and the temperature field, as well as the normalized viscous dissipation rate, scales as $Ra^{-0.22}$ for moderately large Rayleigh number $Ra$. This scaling accounts for the Nusselt number ($Nu$) exponent to be around 0.3 observed in experiments. Numerical simulations also reveal that the above normalized correlation functions are constants for the convection simulation under periodic boundary conditions.Comment: 4 pages, 4 figure

Moving beyond translation: Glucose-TOR signaling in the transcriptional control of cell cycle

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