No Arabic abstract
Using experimental transverse velocities data for very high Reynolds number turbulence, we suggest a model describing both formation of intermittency and asymmetry of turbulence. The model, called bump-model is a modification of ramp-model suggested earlier, S.I. Vainshtein and K.R. Sreenivasan, Phys. Rev. Lett., 73, 3085 (1994). The connection between asymmetry and intermittency makes it possible to study the latter with relatively low moments.
We revisit the issue of Lagrangian irreversibility in the context of recent results [Xu, et al., PNAS, 111, 7558 (2014)] on flight-crash events in turbulent flows and show how extreme events in the Eulerian dissipation statistics are related to the statistics of power-fluctuations for tracer trajectories. Surprisingly, we find that particle trajectories in intense dissipation zones are dominated by energy gains sharper than energy losses, contrary to flight-crashes, through a pressure-gradient driven take-off phenomenon. Our conclusions are rationalised by analysing data from simulations of three-dimensional intermittent turbulence, as well as from non-intermittent decimated flows. Lagrangian irreversibility is found to persist even in the latter case, wherein fluctuations of the dissipation rate are shown to be relatively mild and to follow probability distribution functions with exponential tails.
Using high Reynolds number experimental data, we search for most dissipative, most intense structures. These structures possess a scaling predicted by log-Poisson model for the dissipation field $epsilon_r$. The probability distribution function for the exponents $alpha$, $epsilon_rsim e^{alpha a}$, has been constructed, and compared with Poisson distribution. These new experimental data suggest that the most intense structures have co-dimension less than 2. The log-Poisson statistics is compared with log-binomial which follows from the random $beta$-model.
We employ the horizontal visibility algorithm to map the velocity and acceleration time series in turbulent flows with different Reynolds numbers, onto complex networks. The universal nature of velocity fluctuations in high Reynolds turbulent Helium flow is found to be inherited in the corresponding network topology. The degree distributions of the acceleration series are shown to have stretched exponential forms with the Reynolds number dependent fitting parameter. Furthermore, for acceleration time series, we find a transitional behavior in terms of the Reynolds number in all network features which is in agreement with recent empirical studies.
The notion of self-similar energy cascades and multifractality has long since been connected with fully developed, homogeneous and isotropic turbulence. We introduce a number of amendments to the standard methods for analysing the multifractal properties of the energy dissipation field of a turbulent flow. We conjecture that the scaling assumption for the moments of the energy dissipation rate is valid within the transition range to dissipation introduced by Castaing et al.(Physica D (46), 177 (1990)). The multifractal spectral functions appear to be universal well within the error margins and exhibit some as yet undiscussed features. Furthermore, this universality is also present in the neither homogeneous nor isotropic flows in the wake very close to a cylinder or the off-centre region of a free jet.
The concept of inverse statistics in turbulence has attracted much attention in the recent years. It is argued that the scaling exponents of the direct structure functions and the inverse structure functions satisfy an inversion formula. This proposition has already been verified by numerical data using the shell model. However, no direct evidence was reported for experimental three dimensional turbulence. We propose to test the inversion formula using experimental data of three dimensional fully developed turbulence by considering the energy dissipation rates in stead of the usual efforts on the structure functions. The moments of the exit distances are shown to exhibit nice multifractality. The inversion formula between the direct and inverse exponents is then verified.