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.

Cancellation exponents in isotropic turbulence and magnetohydrodynamic turbulence

Small-scale characteristics of turbulence such as velocity gradients and vorticity fluctuate rapidly in magnitude and oscillate in sign. Much work exists on the characterization of magnitude variations, but far less on sign oscillations. While in homogeneous turbulence averages performed on large scales tend to zero because of the oscillatory character, those performed on increasingly smaller scales will vary with the averaging scale in some characteristic way. This characteristic variation at high Reynolds numbers is captured by the so-called cancellation exponent, which measures how local averages tend to cancel out as the averaging scale increases, in space or time. Past experimental work suggests that the exponents in turbulence depend on whether one considers quantities in full three-dimensional (3D) space or uses their one- or two-dimensional cuts. We compute cancellation exponents of vorticity and longitudinal as well as transverse velocity gradients in isotropic turbulence at Taylor-scale Reynolds numbers up to 1300 on 8192^{3} grids. The 2D cuts yield the same exponents as those for full 3D, while the 1D cuts yield smaller numbers, suggesting that the results in higher dimensions are more reliable. We make the case that the presence of vortical filaments in isotropic turbulence leads to this conclusion. This effect is particularly conspicuous in magnetohydrodynamic turbulence, where an increased degree of spatial coherence develops along the direction of an imposed magnetic field.

Asteroseismic detection of latitudinal differential rotation in 13 Sun-like stars

The differentially rotating outer layers of stars are thought to play a role in driving their magnetic activity, but the underlying mechanisms that generate and sustain differential rotation are poorly understood. We report the measurement using asteroseismology of latitudinal differential rotation in the convection zones of 40 Sun-like stars. For the most significant detections, the stars' equators rotate approximately twice as fast as their midlatitudes. The latitudinal shear inferred from asteroseismology is much larger than predictions from numerical simulations.

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.

Threat-related learning relies on distinct dorsal prefrontal cortex network connectivity

Conditioned changes in the emotional response to threat (e.g. aversive unconditioned stimulus; UCS) are mediated in part by the prefrontal cortex (PFC). Unpredictable threats elicit large emotional responses, while the response is diminished when the threat is predictable. A better understanding of how PFC connectivity to other brain regions varies with threat predictability would provide important insights into the neural processes that mediate conditioned diminution of the emotional response to threat. The present study examined brain connectivity during predictable and unpredictable threat exposure using a fear conditioning paradigm (previously published in Wood et al., 2012) in which unconditioned functional magnetic resonance imaging data were reanalyzed to assess effective connectivity. Granger causality analysis was performed using the time series data from 15 activated regions of interest after hemodynamic deconvolution, to determine regional effective connectivity. In addition, connectivity path weights were correlated with trait anxiety measures to assess the relationship between negative affect and brain connectivity. Results indicate the dorsomedial PFC (dmPFC) serves as a neural hub that influences activity in other brain regions when threats are unpredictable. In contrast, the dorsolateral PFC (dlPFC) serves as a neural hub that influences the activity of other brain regions when threats are predictable. These findings are consistent with the view that the dmPFC coordinates brain activity to take action, perhaps in a reactive manner, when an unpredicted threat is encountered, while the dlPFC coordinates brain regions to take action, in what may be a more proactive manner, to respond to predictable threats. Further, dlPFC connectivity to other brain regions (e.g. ventromedial PFC, amygdala, and insula) varied with negative affect (i.e. trait anxiety) when the UCS was predictable, suggesting that stronger connectivity may be required for emotion regulation in individuals with higher levels of negative affect.

Turbulent mixing and beyond: non-equilibrium processes from atomistic to astrophysical scales II

This Introduction summarizes and provides a perspective on the papers representing one of the key themes of the 'Turbulent mixing and beyond' programme--the hydrodynamic instabilities of the Rayleigh-Taylor (RT) and Richtmyer-Meshkov (RM) type and their applications in nature and technology. The collection is intended to present the reader a balanced overview of the theoretical, experimental and numerical studies of the subject and to assess what is firm in our knowledge of the RT and RM turbulent mixing.

Turbulent mixing and beyond

Turbulence is a supermixer. Turbulent mixing has immense consequences for physical phenomena spanning astrophysical to atomistic scales under both high- and low-energy-density conditions. It influences thermonuclear fusion in inertial and magnetic confinement systems; governs dynamics of supernovae, accretion disks and explosions; dominates stellar convection, planetary interiors and mantle-lithosphere tectonics; affects premixed and non-premixed combustion; controls standard turbulent flows (wall-bounded and free-subsonic, supersonic as well as hypersonic); as well as atmospheric and oceanic phenomena (which themselves have important effects on climate). In most of these circumstances, the mixing phenomena are driven by non-equilibrium dynamics. While each article in this collection dwells on a specific problem, the purpose here is to seek a few unified themes amongst diverse phenomena.

Velocity statistics distinguish quantum turbulence from classical turbulence

By analyzing trajectories of solid hydrogen tracers, we find that the distributions of velocity in decaying quantum turbulence in superfluid 4He are strongly non-Gaussian with 1/v(3) power-law tails. These features differ from the near-Gaussian statistics of homogenous and isotropic turbulence of classical fluids. We examine the dynamics of many events of reconnection between quantized vortices and show by simple scaling arguments that they produce the observed power-law tails.

Taylor's frozen-flow hypothesis in Burgers turbulence

By detailed analytical treatment of the shock dynamics in the Burgers turbulence with large scale forcing we calculate the velocity structure functions between pairs of points displaced both in time and space. Our analytical treatment verifies the so-called Taylor's frozen-flow hypothesis without relying on any closure and under very general assumptions. We discuss the limitation of the hypothesis and show that it is valid up to time scales smaller than the correlation time scale of temporal velocity correlation function. We support the analytical calculation by performing numerical simulation of the periodically kicked Burgers equation.

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.

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.

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.

Intermittency and the passive nature of the magnitude of the magnetic field

It is shown that the statistical properties of the magnitude of the magnetic field in turbulent electrically conducting media resemble, in the inertial range, those of passive scalars in fully developed three-dimensional fluid turbulence. This conclusion, suggested by the data from the Advanced Composition Explorer, is supported by a brief analysis of the appropriate magnetohydrodynamic equations.

"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<T<2 K on the temporal decay of the vortex line density in the grid-generated He II turbulence.

Dynamical equations for high-order structure functions, and a comparison of a mean-field theory with experiments in three-dimensional turbulence

Two recent papers [V. Yakhot, Phys. Rev. E 63, 026307, (2001) and R. J. Hill, J. Fluid Mech. 434, 379, (2001)] derive, through two different approaches that have the Navier-Stokes equations as the common starting point, a set of dynamic equations for structure functions of arbitrary order in turbulence. These equations are not closed. Yakhot proposed a "mean-field theory" to close the equations for locally isotropic turbulence, and obtained scaling exponents of structure functions and expressions for the peak in the probability density function of transverse velocity increments, and for its behavior for intermediate amplitudes. At high Reynolds numbers, some relevant experimental data on pressure gradient and dissipation terms are presented that are needed to provide closure, as well as on other aspects predicted by the theory. Comparison between the theory and the data shows varying levels of agreement, and reveals gaps inherent to the implementation of the theory.

Laser wipers

We present a novel application of lasers for removing particle deposits on inaccessible optical windows. The particular example arises with respect to cryostats filled with liquid helium. We explain the observation in terms of the radiation force acting on the adhering particles. We estimate the radiation forces to be much larger than all other forces acting on the particle.

Anisotropic scaling contributions to high-order structure functions in high-reynolds-number turbulence

We make an attempt at obtaining the scaling exponents for the anisotropic components of structure functions of order 2 through 6. We avoid mixing these components with their isotropic counterparts for each order by using tensor components that are entirely anisotropic. We do this by considering terms of the isotropic sector corresponding to j=0 in the SO(3) decomposition of each tensor, and then constructing components that are explicitly zero in the isotropic sector. We use an interpolation formula to compensate for the large-scale encroachment of inertial-range scales. This allows us to examine the lowest order anisotropic scaling behavior. The resulting anisotropic exponents for a given tensorial order are larger than those known for the corresponding isotropic part. One conclusion that emerges is that the anisotropy effects diminish with decreasing scale, although much more slowly than previously thought.

Scaling structure of the velocity statistics in atmospheric boundary layers

The statistical objects characterizing turbulence in real turbulent flows differ from those of the ideal homogeneous isotropic model. They contain contributions from various two- and three-dimensional aspects, and from the superposition of inhomogeneous and anisotropic contributions. We employ the recently introduced decomposition of statistical tensor objects into irreducible representations of the SO(3) symmetry group (characterized by j and m indices, where j=0ellipsisinfinity,-j</=m</=j) to disentangle some of these contributions, separating the universal and the asymptotic from the specific aspects of the flow. The different j contributions transform differently under rotations, and so form a complete basis in which to represent the tensor objects under study. The experimental data are recorded with hot-wire probes placed at various heights in the atmospheric surface layer. Time series data from single probes and from pairs of probes are analyzed to compute the amplitudes and exponents of different contributions to the second order statistical objects characterized by j=0, 1, and 2. The analysis shows the need to make a careful distinction between long-lived quasi-two-dimensional turbulent motions (close to the ground) and relatively short-lived three-dimensional motions. We demonstrate that the leading scaling exponents in the three leading sectors (j=0, 1, and 2) appear to be different but universal, independent of the positions of the probe, the tensorial component considered, and the large scale properties. The measured values of the scaling exponent are zeta((j=0))(2)=0.68+/-0.01, zeta((j=1))(2)=1.0+/-0.15, and zeta((j=2))(2)=1.38+/-0.10. We present theoretical arguments for the values of these exponents using the Clebsch representation of the Euler equations; neglecting anomalous corrections, the values obtained are 2/3, 1, and 4/3, respectively. Some enigmas and questions for the future are sketched.