Robustness of highly complex radial carpet beams in turbulent atmospheres.

In this study, we report observations of propagating radial carpet beams (RCBs) through a turbulent atmosphere at ground level with a 120 m path length. RCBs are a class of nondiffracting, accelerating, self-healing, and self-amplifying beams, and generated in the diffraction of a plane wave from amplitude/phase radial gratings having different spoke numbers. Observations were made at different times of the day. The intensity profile of an RCB becomes complicated when the number of grating spokes used to generate the beam is large, and includes high intensity spots, called main intensity spots (MISs), which are symmetrically placed at the central area around the beam axis and whose number is equal to (twice) the number of spokes of the amplitude (phase) grating used to generate the beam. With the aid of a telescope and a CCD camera, successive frames of the intensity pattern of the RCBs having different levels of structural complexity are recorded at the end of the path. For the data recorded at different times of the day, we calculate the variance of displacements of MISs along the radial direction. We observe that displacements of the MISs increase with increasing mean temperature of the air; on the other hand, as the complexity of the beam intensity pattern increases, the displacements of the MISs decrease. In order to compare the resilience of different RCBs and a well-known structured beam against atmospheric turbulence, we investigate deformation of the intensity profiles of a Laguerre-Gaussian (LG) beam having a topological charge 20 and different RCBs at the end of the path. It is shown that under the same turbulence condition, highly complex RCBs are more resilient to the destructive effects of the atmospheric turbulence. In particular, for the RCBs generated with gratings having 30 spokes and more, the number of MISs of the received intensity patterns is changed by less than 1% even when the turbulence strength is high. But for the LG beam, its intensity ring is clearly broken in different places, which makes it impossible to follow its maximum intensity in the radial direction.

Investigation of the anisotropy and scaling of the phase structure function of a spatially coherent light beam propagating through convective air turbulence.

We report on applications of moiré deflectometry in measurements of the anisotropy and scaling of the phase structure function (PSF), obtained after passing a laser beam through an indoor enclosure containing convective air turbulence. We combine the use of two telescopes, with a two-channel wavefront sensor based on moiré deflectometry, to attain high sensitivity and resolution to fluctuations in the wavefront phase, caused by turbulent fluctuations in the enclosure. The measurements of the wavefront PSF along two directions perpendicular to the direction of the light beam propagation at different heater temperatures show that the convective air turbulence is anisotropic turbulence, where the value of the anisotropy increases with increasing temperature gradient. Various models are fitted to the measured PSFs, and we find that the turbulent is also non-Kolmogorov, in which, for the separation distances of two points on the wavefront less than 10 cm, the von Kármán PSF is the best fit to the experimental data. For higher values of separations, the experimental data do not fit with existing models. By fitting the von Kármán PSF on the data, we estimate values of the refractive index structure constant, Cn2, as well as the outer scale of the turbulence. The value of the outer scale decreases with increasing temperature of the heater up to approximately 50°C, where it saturates, while the value of Cn2 monotonically increases. Over the complete range of heater temperatures, from 40°C to 160°C, the Rayleigh number, Ra, for the enclosed air flow varied from 5.80×108

Turbulent convection and large scale circulation in a cube with rough horizontal surfaces.

Large-eddy simulations of thermal convection are presented and discussed for a cube with rough horizontal surfaces. Two types of roughness are considered: uniformly placed pyramids, and grooves aligned parallel to one set of sidewalls. The Rayleigh number is 10^{8}, the Prandtl number 0.7, and the aspect ratio 1, as in a previous study [N. Foroozani, J. J. Niemela, V. Armenio, and K. R. Sreenivasan, Phys. Rev. E 95, 033107 (2017)10.1103/PhysRevE.95.033107], except that the meshes here are finer. When the thermal boundary layers are sufficiently large relative to the characteristic roughness height, i.e., for hydrodynamically smooth conditions, the mean properties of the large scale circulation (LSC) are qualitatively similar to the case of smooth surfaces. In particular, the LSC is always aligned along one of the diagonals of the cube. When the boundaries are hydrodynamically rough, the same result holds true only for the case of pyramidal structures; for grooved surfaces, the LSC is forced to be parallel to the sidewalls on average, alternating rapidly between the two diagonals of the cube with a mean period of the order 10 turnover times. Our analysis suggests that the difference from the pyramidal case is due to the breaking of the horizontal x-z symmetry under conditions of hydrodynamical roughness, and the corresponding directional concentration of plume emission along the grooves, from which the LSC is generated, providing a strong restoring force. Furthermore, in this study we observed a small reduction in heat transport for both roughness configurations which is in good agreement with past studies.

Reorientations of the large-scale flow in turbulent convection in a cube.

Large-eddy simulations of turbulent Rayleigh-Bénard convection were conducted for a fluid of Prandtl number Pr=0.7 confined in a cube, for Rayleigh numbers of 10^{6} and 10^{8}. The model solves the unsteady Navier-Stokes equations under the Boussinesq approximation, using a dynamic Smagorinsky model with a Lagrangian averaging technique for the subgrid terms. Under fully developed conditions the flow topology is characterized by a large-scale circulation (LSC) developing in a plane containing one of the diagonals of the cell, while two counter-rotating vortices consequently develop in the other diagonal plane, resulting in a strong inflow at the horizontal midplane. This flow structure is not static, with the LSC undergoing nonperiodic reorientations, or switching, between the two diagonal planes; hence, we supplement the observations of the three-dimensional time-averaged flow structures with single point measurements (time series) to shed light on the dynamics of the reorientations. For all observations, this switching results from a lateral rotation of the LSC in which some finite time spent in a transient state where the large-scale circulation is parallel to one set of side walls; there are, importantly, no observations consistent with so-called cessations of the LSC, in which it decays and then reforms in another plane without such a rotation. The average switching rate for the LSC is in excellent agreement with the results of Bai et al. [K. Bai, D. Ji, and E. Brown, Phys. Rev. E 93, 023117 (2016)PLEEE81539-375510.1103/PhysRevE.93.023117].

Influence of container shape on scaling of turbulent fluctuations in convection.

We perform large-eddy simulations of turbulent convection in a cubic cell for Rayleigh numbers, Ra, between 10(6) and 10(10) and the molecular Prandtl number, Pr=0.7. The simulations were carried out using a second-order-accurate finite-difference method in which subgrid-scale fluxes of momentum and heat were both parametrized using a Lagrangian and dynamic Smagorinsky model. The scaling of the root-mean-square fluctuations of density (temperature) and velocity measured in the cell center are in excellent agreement with the scaling measured in the laboratory experiments of Daya and Ecke [Phys. Rev. Lett. 87, 184501 (2001)] and differ substantially from that observed in cylindrical cells. We also observe the time-averaged spatial distributions of the local heat flux and density fluctuations, and find that they are strongly inhomogeneous in the horizontal midplane, with the largest density gradients occurring at the corners at the midheight, where hot and cold plumes mix in the form of strong counter-rotating eddies.

Formation of the "superconducting" core in turbulent thermal convection.

A sinusoidal temperature perturbation is superimposed on the bottom plate of a cylindrical convection cell, and its decay is measured at the cell midheight. Rayleigh numbers up to Ra=10(13) and aspect ratios 1 and 4 are considered. The technique allows a dynamic measurement of the height of the layer interposed between the superconducting core and the boundary. This deduced height is in good agreement with results from recent numerical simulations.

Fluctuations of temperature gradients in turbulent thermal convection.

Broad theoretical arguments are proposed to show, formally, that the magnitude G of the temperature gradients in turbulent thermal convection at high Rayleigh numbers obeys the same advection-diffusion equation that governs the temperature fluctuation T , except that the velocity field in the new equation is substantially smoothed. This smoothed field leads to a -1 scaling of the spectrum of G in the same range of scales for which the spectral exponent of T lies between -7/5 and -5/3 . This result is confirmed by measurements in a confined container with cryogenic helium gas as the working fluid for Rayleigh number Ra=1.5x 10(11) . Also confirmed is the logarithmic form of the autocorrelation function of G . The anomalous scaling of dissipation-like quantities of T and G are identical in the inertial range, showing that the analogy between the two fields is quite deep.

Critical fluctuation of wind reversals in convective turbulence.

The irregular reversals of wind direction in convective turbulence are found to have fluctuating intervals that can be related, under certain circumstances, to critical behavior. In particular, by focusing on its temporal evolution, the net magnetization of a two-dimensional Ising lattice of finite size is observed to fluctuate in the same way. Detrended fluctuation analysis of the wind reversal time series results in a scaling behavior that agrees remarkably well with that of the Ising problem. The specific properties found here, as well as the lack of an external tuning parameter, also suggest that the wind reversal phenomenon exhibits signs of self-organized criticality.

"Clusterization" and intermittency of temperature fluctuations in turbulent convection.

Temperature time traces are obtained in turbulent thermal convection at high Rayleigh numbers. Measurements are made in the midplane of the apparatus, near the sidewall but outside the boundary layer. A telegraph approximation for temperature traces is generated by setting the fluctuation amplitude to 1 or 0 depending on whether or not it exceeds the mean value. Unlike the standard diagnostics of intermittency, the telegraph approximation allows one to distinguish the tendency of events to cluster (clusterization) from their large-scale variability in amplitude. A qualitative conclusion is that amplitude intermittency might mitigate clusterization effects.

Temperature structure functions in the Bolgiano regime of thermal convection.

We measure temperature fluctuations in the Rayleigh-Bénard apparatus, which is a closed cylindrical container with the bottom wall heated and the top wall cooled. The aspect ratio, which is the diameter-to-height ratio of the apparatus, is unity. The Rayleigh number is 1.5 x 10(11). The working fluid is cryogenic helium gas. We compute temperature structure functions up to order 16, and use extended self-similarity to obtain scaling exponents in the Bolgiano regime. In contrast to passive scalars, the scaling exponents tend not to saturate with the order of the structure function, suggesting the absence of ramplike structures in temperature traces of convective motion.

Mean wind and its reversal in thermal convection.

Properties of the mean wind in thermal convection, especially the abrupt reversal of its direction at high Rayleigh numbers, are studied. Measurements made in a closed cylindrical container of aspect ratio 1 are analyzed, and both the long-term and short-term behaviors of the direction reversals are discussed. A first look at the data suggests a Brownian-type process in action, but a closer look suggests the existence of hierarchical features with time scales extending roughly over a decade and a half. A physical model consistent with experimental observations is presented, and the origin of the cutoff scales is discussed. It appears that the generation of the wind as well as the reversal of its direction can be understood in terms of the imbalance between buoyancy effects and friction.

Energy spectrum of grid-generated He II turbulence.

A grid of bars towed through a sample of He II produces both superfluid turbulence and classical hydrodynamic turbulence. The two velocity fields-in the normal fluid and in the superfluid-have been observed to have the same energy spectral density over a large range of scales. Here, we introduce a characteristic scale l(q)=2 pi(epsilon/kappa(3))(-1/4), where epsilon is the rate of turbulent energy dissipation per unit volume, and note that the energy spectrum in superfluid turbulence depends also on the quantum of circulation kappa, for wave numbers k>k(q) identical with 2 pi/l(q). We propose that the spectral density in this range is of the form straight phi(k)=C epsilon kappa(-1)k(-3), where C is the three-dimensional Kolmogorov constant in classical turbulence. This form is consistent with recent experiments in the temperature range 1.2 K

Four regimes of decaying grid turbulence in a finite channel.

Attenuation of second sound in helium II has been used to observe up to 6 orders of magnitude of decaying vorticity displaying four distinctly different regimes of decaying grid turbulence in a finite channel. A purely classical spectral model for homogeneous and isotropic turbulence describes most of the decay of helium II vorticity in the temperature range 1.2