Small-scale turbulent fluctuations beyond Taylor's frozen-flow hypothesis

Spatiotemporal statistics of optical turbulence beyond Taylor's frozen turbulence hypothesis

Currently, limitations in modeling the temporal behavior of light propagating through atmospheric turbulence stem from the Taylor's frozen turbulence hypothesis (TFTH). Indeed, under certain conditions it has been reported to be unreliable, often leading to inaccurate predictions. On the other hand, in fluid dynamics an alternative has been validated: the random sweeping hypothesis. Nevertheless, its applicability to optical turbulence has remained unexplored. This work introduces the first, to the best of our knowledge, controlled experiment testing this hypothesis on the spatiotemporal properties from image wander. The existence of two characteristic times is observed, one associated with TFTH decorrelation and a second potentially linked to the sweeping hypothesis.

Coherence of Velocity Fluctuations in Turbulent Flows

We investigate the spatiotemporal quantity of coherence for turbulent velocity fluctuations at spatial distances of the order or larger than the integral length scale l_{0}. Using controlled laboratory experiments, an exponential decay as a function of distance is observed with a decay rate that depends on the flow properties. The same law is observed in two different flows, indicating that it can be a generic property of turbulent flows.

Applicability of Taylor's hypothesis in thermally driven turbulence

In this paper, we show that, in the presence of large-scale circulation (LSC), Taylor's hypothesis can be invoked to deduce the energy spectrum in thermal convection using real-space probes, a popular experimental tool. We perform numerical simulation of turbulent convection in a cube and observe that the velocity field follows Kolmogorov's spectrum (k^-5/3). We also record the velocity time series using real-space probes near the lateral walls. The corresponding frequency spectrum exhibits Kolmogorov's spectrum (f^-5/3), thus validating Taylor's hypothesis with the steady LSC playing the role of a mean velocity field. The aforementioned findings based on real-space probes provide valuable inputs for experimental measurements used for studying the spectrum of convective turbulence.

Logarithmic spatial variations and universal f-1 power spectra of temperature fluctuations in turbulent Rayleigh-Bénard convection

We report measurements of the temperature variance σ(2)(z,r) and frequency power spectrum P(f,z,r) (z is the distance from the sample bottom and r the radial coordinate) in turbulent Rayleigh-Bénard convection (RBC) for Rayleigh numbers Ra = 1.6 × 10(13) and 1.1 × 10(15) and for a Prandtl number Pr ≃ 0.8 for a sample with a height L = 224 cm and aspect ratio D/L=0.50 (D is the diameter). For z/L ≲ 0.1 σ(2)(z,r) was consistent with a logarithmic dependence on z, and there was a universal (independent of Ra, r, and z) normalized spectrum which, for 0.02 ≲ fτ(0) ≲ 0.2, had the form P(fτ(0)) = P(0)(fτ(0))(-1) with P(0) = 0.208 ± 0.008 a universal constant. Here τ(0) = sqrt[2R] where R is the radius of curvature of the temperature autocorrelation function C(τ) at τ = 0. For z/L ≃ 0.5 the measurements yielded P(fτ(0))∼(fτ(0))(-α) with α in the range from 3/2 to 5/3. All the results are similar to those for velocity fluctuations in shear flows at sufficiently large Reynolds numbers, suggesting the possibility of an analogy between the flows that is yet to be determined in detail.

Scaling behavior in turbulent Rayleigh-Bénard convection revealed by conditional structure functions

We show that the nature of the scaling behavior can be revealed by studying the conditional structure functions evaluated at given values of the locally averaged thermal dissipation rate. These conditional structure functions have power-law dependence on the value of the locally averaged thermal dissipation rate, and such dependence for the Bolgiano-Obukhov scaling is different from the other scaling behaviors. Our analysis of experimental measurements verifies the power-law dependence and reveals the Bolgiano-Obukhov scaling behavior at the center of the bottom plate of the convection cell.

Transition to the ultimate state of turbulent Rayleigh-Bénard convection

Measurements of the Nusselt number Nu and of a Reynolds number Re(eff) for Rayleigh-Bénard convection (RBC) over the Rayleigh-number range 10(12)≲Ra≲10(15) and for Prandtl numbers Pr near 0.8 are presented. The aspect ratio Γ≡D/L of a cylindrical sample was 0.50. For Ra≲10(13) the data yielded Nu∝Ra(γ(eff)) with γ(eff)≃0.31 and Re(eff)∝Ra(ζ(eff)) with ζ(eff)≃0.43, consistent with classical turbulent RBC. After a transition region for 10(13)≲Ra≲5×10(14), where multistability occurred, we found γ(eff)≃0.38 and ζ(eff)=ζ≃0.50, in agreement with the results of Grossmann and Lohse for the large-Ra asymptotic state with turbulent boundary layers which was first predicted by Kraichnan.

Anomalous scaling for Lagrangian velocity structure functions in fully developed turbulence

A hierarchical structure model is developed for anomalous scaling of the Lagrangian velocity structure functions in fully developed turbulence. This model is an extension of the Eulerian hierarchical structure model of She and Leveque [Phys. Rev. Lett. 72, 366 (1994)] to the Lagrangian velocity structure functions, where the straining and sweeping hypotheses are used to build up the relationship between the singular scalings of Lagrangian and Eulerian intermittent structures. The Lagrangian scaling exponents obtained from the straining hypothesis are in good agreement with the experimental results of the Bodenschatz group.

Kraichnan's random sweeping hypothesis in homogeneous turbulent convection

We report an experimental study of the temperature space-time cross-correlation function, C{T}(r,τ), in the central region of turbulent Rayleigh-Bénard convection. The measured C{T}(r,τ) is found to have the scaling form C{T}(r{E},0), where r{E}=[r² +(Vτ)²]¹/² with V being the rms velocity at the center of the convection cell. The experiment confirms the theory by He et al. [Phys. Rev. E 73, 055303(R) (2006)] and demonstrates its applications to homogenous turbulent flows, where the mean flow velocity is zero and Kraichnan's random sweeping hypothesis holds approximately.