Mean wind in convective turbulence of mercury

The large-scale circulation, often called "wind," in the confined thermal turbulence of mercury is studied experimentally. The instantaneous velocity profile at 128 points is directly measured using ultrasonic velocimetry. The periodic velocity oscillation is observed in the case of the aspect-ratio Gamma = 1,2 but not in Gamma = 0.5. Its peak frequency is scaled by f(c) proportional Ra(gamma(c)), where Ra is the Rayleigh number and gamma(c) = 0.43,0.45 for Gamma = 1,2. f(c) is close to the wind circulation frequency f(p), and has the same order of transit time from the bottom to the top of the convection cell. A single roll circulation is expected in Gamma = 1; however, axisymmetric toroidal rings may exist near the upper and lower plate for Gamma = 0.5, which are stable up to Ra = 7 x 10 (10).     

Two-dimensional turbulence of dilute polymer solutions

We investigate theoretically and numerically the effect of polymer additives on two-dimensional turbulence by means of a viscoelastic model. We provide compelling evidence that, at vanishingly small concentrations, such that the polymers are passively transported, the probability distribution of polymer elongation has a power law tail: Its slope is related to the statistics of finite-time Lyapunov exponents of the flow, in quantitative agreement with theoretical predictions. We show that at finite concentrations and sufficiently large elasticity the polymers react on the flow with manifold consequences: Velocity fluctuations are drastically depleted, as observed in soap film experiments; the velocity statistics becomes strongly intermittent; the distribution of finite-time Lyapunov exponents shifts to lower values, signaling the reduction of Lagrangian chaos.     

Two-dimensional turbulence: a physicist approach

Much progress has been made on two-dimensional turbulence, these last two decades, but still, a number of fundamental questions remain unanswered. The objective of the present review is to collect and organize the available information on the subject, emphasizing on aspects accessible to experiment, and outlining contributions made on simple flow configurations. Whenever possible, open questions are made explicit. Various subjects are presented: coherent structures, statistical theories, inverse cascade of energy, condensed states, Richardson law, direct cascade of enstrophy, and the inter-play between cascades and coherent structures. The review offers a physicist's view on two-dimensional turbulence in the sense that experimental facts play an important role in the presentation, technical issues are described without much detail, sometimes in an oversimplified form, and physical arguments are given whenever possible. I hope this bias does not jeopardize the interest of the presentation for whoever wishes to visit the fascinating world of Flatland.     

Lagrangian dispersion and heat transport in convective turbulence

Lagrangian studies of the local temperature mixing and heat transport in turbulent Rayleigh-Bénard convection are presented, based on three-dimensional direct numerical simulations. Contrary to vertical pair distances, the temporal growth of lateral pair distances agrees with the Richardson law, but yields a smaller Richardson constant due to correlated pair motion in plumes. Our results thus imply that Richardson dispersion is also found in anisotropic turbulence. We find that extremely large vertical accelerations appear less frequently than lateral ones and are not connected with rising or falling thermal plumes. The height-dependent joint Lagrangian statistics of vertical acceleration and local heat transfer allow us to identify a zone which is dominated by thermal plume mixing.     

Scaling properties of the temperature field in convective turbulence

We report the scaling properties of temperature in turbulent convection in water. In the central region of the convection cell, we find that the peak frequency of the temperature dissipation spectra may be identified as the "Bolgiano frequency," with respect to which the temperature power spectra are universal functions; and that the usual inertial range is taken up entirely by the buoyancy subrange, so that a "high frequency" scaling subrange emerges only through an extended-self-similarity-type analysis. Moreover, the buoyancy subrange assumes the value of 2/5 predicted for the Bolgiano-Obukhov scaling only in the central region of the cell; in the mixing zone the exponent for the high frequency scaling exponent has a value of 2/3.     

Two-dimensional ion velocity diffusion due to ion-acoustic turbulence

The diffusion of an ion beam caused by ion-acoustic turbulence is demonstrated experimentally by measuring the two-dimensional velocity distribution function f_b(v_⊥, v_⌈). The obtained ratio between the perpendicular and the parallel diffusion coefficient D_⊥/D_⌈ ≈ 21 is in reasonable agreement with three-dimensional quasi-linear theory.     

Theoretical study of the decaying convective turbulence in a shear-buoyancy PBL

The derivation of a theoretical model for the decaying convective turbulence in a shear-buoyancy planetary boundary layer is considered. The model is based on the dynamical equation for the energy density spectrum in which the buoyancy, mechanical and inertial transfer terms are retained. The parameterization for the buoyancy and mechanical terms is provided by the flux Richardson number. Regarding the inertial term an approach employing Heisenberg’s spectral transfer theory is used to describe the turbulence friction, caused by small eddies, responsible for the energy dissipation of the large eddies. Therefore, a novelty in this study is to utilize the Adomian decomposition method to solve directly without linearization the energy density spectrum equation, with this the nonlinear nature of the problem is preserved. Therefore, the errors found are only due to the parameterization used. Comparison of the theoretical model is performed against large-eddy simulation data for a decaying convective turbulence in a shear-buoyancy planetary boundary layer. The results show that the existence of a mechanical turbulent driving mechanism reduces in an accentuated way the energy density spectrum and turbulent kinetic energy decay generated by the decaying convective production in a shear-buoyancy planetary boundary layer.     

Sunset decay of the convective turbulence with Large-Eddy Simulation under realistic conditions

Large-Eddy Simulation is performed for a single day from the Cooperative Atmosphere-Surface Exchange Study (CASES-99) field program. This study investigates an observed case of evening transition boundary layer over land. Parameters of the ambient atmosphere in the LES-decay studies conducted so far were typically prescribed in an idealized form. To provide suitable data under the wide range of the PBL weather conditions, the LES should be able to adequately reproduce the PBL turbulence dynamics including–if possible–baroclinicity, radiation, large scale advection and not only be related to a decreasing surface heating. In addition LES-decay studies usually assume that the sensible heat flux decreases instantaneously or with a very short time scale. The main purpose of this investigation is to study the decay of boundary-layer average turbulent kinetic energy at sunset with Large-Eddy Simulation that is forced with realistic environment conditions. This allows investigating the Turbulent Kinetic Energy decay over the realistic time scale that is observed in the atmosphere. During the intermediate and last stage of decay of the boundary-layer average Turbulent Kinetic Energy the exponents of the decay power law t⁻ⁿ$t^{-n}$ go from 2 to 6, as evidenced by experimental results and recent analytical modeling in the surface layer.     

Angle-of-arrival variance’s dependence on the aperture size for indoor convective turbulence

We analyze the angle-of-arrival variance of an expanded and collimated laser beam once it has traveled through an indoor convective turbulence. A continuous position detector is set at the focus of a lens collecting the laser beam. The effect of the different turbulent scales, between the inner and the outer scales, is studied by changing the diameter of a circular pupil before the collector lens. The experimental optical setup follows the design introduced by Masciadri and Vernin [Appl. Opt., 36(6) (1997) 1320]. Tilt data measurements are studied using the fractional Brownian motion model for the turbulent wave-front phase introduced in a previous paper [Pérez et al., J. Opt. Soc. Am. A 21(10) (2004) 1962]. The Hurst exponents associated to different strengths of turbulence are obtained from the here proposed D^2H−2 dependence.     

Two-dimensional convection in a finite box dynamics of a convective pattern with variable number of rolls

We propose a model in which a convection dynamics results from the interaction of three hydrodynamic modes. At small enough Prandtl number, we show the existence of a transition from an N-roll pattern to an (N?1) one. This transition may be time dependent, giving rise to relaxation oscillations.     

Similarity methods to derive turbulence quantities and mixed-layer depth from SODAR measurements in the convective boundary layer: A review

A brief review is made of similarity methods which have been developed to calculate turbulence parameters and mixed-layer depth from SODAR measurements. Emphasis is placed on surface fluxes and mixed-layer depth. A variety of parametric relations valid in the convective boundary layer are surveyed and relevant similarity methods are outlined. The methods are primarily intended for flat and relatively homogeneous terrain. It is shown that, in most cases, horizontal homogeneity provides a less stringent constraint.Finally, some limitations of the existing methods are presented and discussed. It is proposed that the most serious errors are mainly associated with the poor accuracy of some parameters measured by the SODAR and also with the limitations of the theoretical basis employed.