Dissipation layers in Rayleigh-Bénard convection: a unifying view

Lagrangian coherent sets in turbulent Rayleigh-Bénard convection

Coherent circulation rolls and their relevance for the turbulent heat transfer in a two-dimensional Rayleigh-Bénard convection model are analyzed. The flow is in a closed cell of aspect ratio four at a Rayleigh number Ra=10^{6} and at a Prandtl number Pr=10. Three different Lagrangian analysis techniques based on graph Laplacians (distance spectral trajectory clustering, time-averaged diffusion maps, and finite-element based dynamic Laplacian discretization) are used to monitor the turbulent fields along trajectories of massless Lagrangian particles in the evolving turbulent convection flow. The three methods are compared to each other and the obtained coherent sets are related to results from an analysis in the Eulerian frame of reference. We show that the results of these methods agree with each other and that Lagrangian and Eulerian coherent sets form basically a disjoint union of the flow domain. Additionally, a windowed time averaging of variable interval length is performed to study the degree of coherence as a function of this additional coarse graining which removes small-scale fluctuations that cause trajectories to disperse quickly. Finally, the coherent set framework is extended to study heat transport.

Statistics of velocity and temperature fluctuations in two-dimensional Rayleigh-Bénard convection

We investigate fluctuations of the velocity and temperature fields in two-dimensional (2D) Rayleigh-Bénard (RB) convection by means of direct numerical simulations (DNS) over the Rayleigh number range 10^{6}≤Ra≤10^{10} and for a fixed Prandtl number Pr=5.3 and aspect ratio Γ=1. Our results show that there exists a counter-gradient turbulent transport of energy from fluctuations to the mean flow both locally and globally, implying that the Reynolds stress is one of the driving mechanisms of the large-scale circulation in 2D turbulent RB convection besides the buoyancy of thermal plumes. We also find that the viscous boundary layer (BL) thicknesses near the horizontal conducting plates and near the vertical sidewalls, δ_{u} and δ_{v}, are almost the same for a given Ra, and they scale with the Rayleigh and Reynolds numbers as ∼Ra^{-0.26±0.03} and ∼Re^{-0.43±0.04}. Furthermore, the thermal BL thickness δ_{θ} defined based on the root-mean-square (rms) temperature profiles is found to agree with Prandtl-Blasius predictions from the scaling point of view. In addition, the probability density functions of turbulent energy ɛ_{u^{'}} and thermal ɛ_{θ^{'}} dissipation rates, calculated, respectively, within the viscous and thermal BLs, are found to be always non-log-normal and obey approximately a Bramwell-Holdsworth-Pinton distribution first introduced to characterize rare fluctuations in a confined turbulent flow and critical phenomena.

Vertically Bounded Double Diffusive Convection in the Finger Regime: Comparing No-Slip versus Free-Slip Boundary Conditions

Vertically bounded fingering double diffusive convection is numerically investigated, focusing on the influences of different velocity boundary conditions, i.e., the no-slip condition, which is inevitable in the lab-scale experimental researches, and the free-slip condition, which is an approximation for the interfaces in many natural environments, such as the oceans. For both boundary conditions the flow is dominated by fingers and the global responses follow the same scaling laws, with enhanced prefactors for the free-slip cases. Therefore, the laboratory experiments with the no-slip boundaries serve as a good model for the finger layers in the ocean. Moreover, in the free-slip case, although the tangential shear stress is eliminated at the boundaries, the local dissipation rate in the near-wall region may exceed the value found in the no-slip cases, which is caused by the stronger vertical motions of horizontally focused fingers and sheet structures near the free-slip boundaries. This counterintuitive result might be relevant for properly estimating and modeling the mixing and entrainment phenomena at free surfaces and interfaces widespread in oceans and geophysical flows.

Closed-loop approach to thermodynamics

We present the closed-loop approach to linear nonequilibrium thermodynamics considering a generic heat engine dissipatively connected to two temperature baths. The system is usually quite generally characterized by two parameters: the output power P and the conversion efficiency η, to which we add a third one, the working frequency ω. We establish that a detailed understanding of the effects of the dissipative coupling on the energy conversion process requires only knowing two quantities: the system's feedback factor β and its open-loop gain A_{0}, which product A_{0}β characterizes the interplay between the efficiency, the output power, and the operating rate of the system. By raising the abstract hermodynamic analysis to a higher level, the feedback loop approach provides a versatile and economical, hence fairly efficient, tool for the study of any conversion engine operation for which a feedback factor can be defined.

Inhibited pattern formation by asymmetrical high-voltage excitation in nematic fluids

In contrast to the predictions of the standard theory of electroconvection (EC), our experiments showed that the action of superposed ac and dc voltages rather inhibits pattern formation than favors the emergence of instabilities; the patternless region may extend to much higher voltages than the individual ac or dc thresholds. The pattern formation induced by such asymmetrical voltage was explored in a nematic liquid crystal in a wide frequency range. The findings could be qualitatively explained for the conductive EC, but represent a challenging problem for the dielectric EC.

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., Péclet number Pe, Nusselt number Nu, and rms value of the temperature fluctuations θ(rms). We complement the analytical work with direct numerical simulations, and show that Nu ∼ Ra(γ) with γ ≈ (0.30-0.32), Pe ∼ Ra(η) with η ≈ (0.57-0.61), and θ(rms) ∼ const. The Nusselt number is observed to be an intricate function of Pe, θ(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) ∼ k(-13/3), which is in a very good agreement with our numerical results. The entropy spectrum E(θ)(k), however, exhibits dual branches consisting of k(-2) and k(0) spectra; the k(-2) branch corresponds to the Fourier modes θ[over ̂](0,0,2n), which are approximately -1/(2 nπ). The scaling relations for Prandtl number beyond 10(2) match with those for infinite Prandtl number.