Intermittency of velocity fluctuations in turbulent thermal convection

Reversals in infinite-Prandtl-number Rayleigh-Bénard convection

Using direct numerical simulations, we study the statistical properties of reversals in two-dimensional Rayleigh-Bénard convection for infinite Prandtl number. We find that the large-scale circulation reverses irregularly, with the waiting time between two consecutive genuine reversals exhibiting a Poisson distribution on long timescales, while the interval between successive crossings on short timescales shows a power-law distribution. We observe that the vertical velocities near the sidewall and at the center show different statistical properties. The velocity near the sidewall shows a longer autocorrelation and 1/f^{2} power spectrum for a wide range of frequencies, compared to shorter autocorrelation and a narrower scaling range for the velocity at the center. The probability distribution of the velocity near the sidewall is bimodal, indicating a reversing velocity field. We also find that the dominant Fourier modes capture the dynamics at the sidewall and at the center very well. Moreover, we show a signature of weak intermittency in the fluctuations of velocity near the sidewall by computing temporal structure functions.

Route to non-Gaussian statistics in convective turbulence

Motivated by the work of Li and Meneveau [Phys. Rev. Lett. 95, 164502 (2005)], we propose and solve a model for the Lagrangian evolution of both longitudinal and transverse velocity and temperature increments for Boussinesq convection. From this model, the short-time evolution of an initially imposed Gaussian joint probability density function (PDF) of both velocity and temperature increments is computed analytically and the trend to non-Gaussian statistics shown in a quantitative way. Predictions for moments of the joint PDF are obtained and their behavior analyzed with respect to known experimental and numerical results. The obtained results do not depend on the model free parameters, a fact in favor of their robustness.

Velocity intermittency in a buoyancy subrange in a two-dimensional soap film convection experiment

In a two-dimensional soap film convection experiment, the velocity fields are found to be strongly intermittent in the buoyancy subrange, which was reported to be nonintermittent in a recent numerical simulation. The structure functions Sq(l)(= <delta(upsilon)l(q)>) exhibit self-similar structures and can be described by power laws l(zetaq) for integers 8 > or = q < or = 1. By extending Kolmogorov's refined similarity hypothesis to our system, an analytical form is derived for the scaling exponent zeta(q) = q/2 + (mu/18)(3q - q2). Our measurements yield mu = 0.42, which is significantly greater than 0.2 found in high Reynolds number turbulence in wind tunnels.

Extraction of plumes in turbulent thermal convection

We present a scheme to extract the velocity of buoyant structures in turbulent thermal convection from simultaneous local velocity and temperature measurements. Applying this scheme to measurements taken at positions within the convection cell where the buoyant structures are dominated by plumes, we obtain the temperature dependence of the plume velocity and understand our results using the equations of motion. We further obtain the scaling behavior of the average local heat flux in the vertical direction at the cell center with the Rayleigh number and find that the scaling exponent is different from that measured for the Nusselt number. This difference leads to the conclusion that heat cannot be mainly transported through the central region of the convection cell.

Hierarchical structure description of spatiotemporal chaos

We develop a hierarchical structure (HS) analysis for quantitative description of statistical states of spatially extended systems. Examples discussed here include an experimental reaction-diffusion system with Belousov-Zhabotinsky kinetics, the two-dimensional complex Ginzburg-Landau equation, and the modified FitzHugh-Nagumon equation, which all show complex dynamics of spirals and defects. We demonstrate that the spatial-temporal fluctuation fields in the above-mentioned systems all display the HS similarity property originally proposed for the study of fully developed turbulence [Phys. Rev. Lett. 72, 336 (1994)]]. The derived values of a HS parameter beta from experimental and numerical data in various physical regimes exhibit consistent trends and characterize the degree of turbulence in the systems near the transition, and the degree of heterogeneity of multiple disorders far from the transition. It is suggested that the HS analysis offers a useful quantitative description for the complex dynamics of two-dimensional spatiotemporal patterns.