An exact relation between Eulerian and Lagrangian velocity increment statistics

We present a formal connection between Lagrangian and Eulerian velocity increment distributions which is applicable to a wide range of turbulent systems ranging from turbulence in incompressible fluids to magnetohydrodynamic turbulence. For the case of the inverse cascade regime of two-dimensional turbulence we numerically estimate the transition probabilities involved in this connection. In this context we are able to directly identify the processes leading to strongly non-Gaussian statistics for the Lagrangian velocity increments.Comment: 5 pages, 3 figure

Diffusion of passive scalar in a finite-scale random flow

We consider a solvable model of the decay of scalar variance in a single-scale random velocity field. We show that if there is a separation between the flow scale k_flow^{-1} and the box size k_box^{-1}, the decay rate lambda ~ (k_box/k_flow)^2 is determined by the turbulent diffusion of the box-scale mode. Exponential decay at the rate lambda is preceded by a transient powerlike decay (the total scalar variance ~ t^{-5/2} if the Corrsin invariant is zero, t^{-3/2} otherwise) that lasts a time t~1/\lambda. Spectra are sharply peaked at k=k_box. The box-scale peak acts as a slowly decaying source to a secondary peak at the flow scale. The variance spectrum at scales intermediate between the two peaks (k_box0). The mixing of the flow-scale modes by the random flow produces, for the case of large Peclet number, a k^{-1+delta} spectrum at k>>k_flow, where delta ~ lambda is a small correction. Our solution thus elucidates the spectral make up of the ``strange mode,'' combining small-scale structure and a decay law set by the largest scales.Comment: revtex4, 8 pages, 4 figures; final published versio

Spectra and Diffusion in a Round Turbulent Jet

In a round turbulent jet at room temperature, measurement of the shear correlation coefficient as a function of frequency (through band-pass filters) has given a rather direct verification of Kolmogoroff's local-isotropy hypothesis. One-dimensional power spectra of velocity and temperature fluctuations, measured in unheated and heated jets, respectively, have been contrasted. Under the same conditions, the two corresponding transverse correlation functions have been measured and compared. Finally, measurements have been made of the mean thermal wakes behind local (line) heat sources in the unheated turbulent jet, and the order of magnitude of the temperature fluctuations has been determined

Diffusion of Heat from a Line Source in Isotropic Turbulence

An experimental and analytical study has been made of some features of the turbulent heat diffusion behind a line heated wire stretched perpendicular to a flowing isotropic turbulence. The mean temperature distributions have been measured with systematic variations in wind speed, size of turbulence-producing grid, and downstream location of heat source. The nature of the temperature fluctuation field has been studied. A comparison of Lagrangian and Eulerian analyses for diffusion in a nondecaying turbulence yields an expression for turbulent-heat-transfer coefficient in terms of turbulence velocity and a Lagrangian "scale." the ratio of Eulerian to Lagrangian microscale has been determined theoretically by generalization of a result of Heisenberg and with arbitrary constants taken from independent sources, shows rough agreement with experimental results. A convenient form has been deduced for the criterion of interchangeability of instantaneous space and time derivatives in a flowing turbulence

Spectrums and Diffusion in a Round Turbulent Jet

In a round turbulent jet at room temperature, measurement of the shear correlation coefficient as a function of frequency (through bandpass filters) has given a rather direct verification of Kolmogoroff's local-isotropy hypothesis. One-dimensional power spectrums of velocity and temperature fluctuations, measured in unheated and heated jets, respectively, have been contrasted. Under the same conditions, the two corresponding transverse correlation functions have been measured and compared. Finally, measurements have been made of the mean thermal wakes behind local (line) heat sources in the unheated turbulent jet, and the order of magnitude of the temperature fluctuations has been determined. (author

Further Experiments on the Flow and Heat Transfer in a Heated Turbulent Air Jet

Measurements have been made of the mean total-head and temperature fields in a round turbulent jet with various initial temperatures. The results show that the jet spreads more rapidly as its density becomes lower than that of the receiving medium, even when the difference is not sufficiently great to cause measurable deviations from the constant-density, dimensionless, dynamic-pressure profile function. Rough analytical considerations have given the same relative spread. The effective "turbulent Prandtl number" for a section of the fully developed jet was found to be equal to the true (laminar) Prandtl number within the accuracy of measurement. (author

Further Experiments on the Flow and Heat Transfer in a Heated Turbulent Air Jet

Measurements have been made of the mean-total-head and mean-temperature fields in a round turbulent jet with various initial temperatures. The results show that the jet spreads more rapidly as its density becomes lower than that of the receiving medium, even when the difference is not sufficiently great to cause dynamic-pressure function. Rough analytical considerations have given the same relative spread. The effective "turbulent Prandtl number" for a section of the fully developed jet was found to be equal to the true (laminar) Prandtl number within the accuracy measurement

Kolmogorov Similarity Hypotheses for Scalar Fields: Sampling Intermittent Turbulent Mixing in the Ocean and Galaxy

Kolmogorov's three universal similarity hypotheses are extrapolated to describe scalar fields like temperature mixed by turbulence. By the analogous Kolmogorov third hypothesis for scalars, temperature dissipation rates chi averaged over lengths r > L_K should be lognormally distributed with intermittency factors I that increase with increasing turbulence energy length scales L_O as I_chi-r = m_T ln(L_O/r). Tests of Kolmogorovian velocity and scalar universal similarity hypotheses for very large ranges of turbulence length and time scales are provided by data from the ocean and the Galactic interstellar medium. The universal constant for turbulent mixing intermittency m_T is estimated from oceanic data to be 0.44+-0.01, which is remarkably close to estimates for Kolmogorov's turbulence intermittency constant m_u of 0.45+-0.05 from Galactic as well as atmospheric data. Extreme intermittency complicates the oceanic sampling problem, and may lead to quantitative and qualitative undersampling errors in estimates of mean oceanic dissipation rates and fluxes. Intermittency of turbulence and mixing in the interstellar medium may be a factor in the formation of stars.Comment: 23 pages original of Proc. Roy. Soc. article, 8 figures; in "Turbulence and Stochastic Processes: Kolmogorov's ideas 50 years on", London The Royal Society, 1991, J.C.R. Hunt, O.M. Phillips, D. Williams Eds., pages 1-240, vol. 434 (no. 1890) Proc. Roy. Soc. Lond. A, PDF fil

Intermittency in two-dimensional Ekman-Navier-Stokes turbulence

We study the statistics of the vorticity field in two-dimensional Navier-Stokes turbulence with a linear Ekman friction. We show that the small-scale vorticity fluctuations are intermittent, as conjectured by Nam et al. [Phys. Rev. Lett. vol.84 (2000) 5134]. The small-scale statistics of vorticity fluctuations coincides with the one of a passive scalar with finite lifetime transported by the velocity field itself.Comment: 4 pages, 7 figure