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Register a new userFully Developed Turbulence in the view of Horizontal Visibility Graphs
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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.
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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 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.
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.
We investigate the statistical properties, based on numerical simulations and analytical calculations, of a recently proposed stochastic model for the velocity field of an incompressible, homogeneous, isotropic and fully developed turbulent flow. A key step in the construction of this model is the introduction of some aspects of the vorticity stretching mechanism that governs the dynamics of fluid particles along their trajectory. An additional further phenomenological step aimed at including the long range correlated nature of turbulence makes this model depending on a single free parameter $gamma$ that can be estimated from experimental measurements. We confirm the realism of the model regarding the geometry of the velocity gradient tensor, the power-law behaviour of the moments of velocity increments (i.e. the structure functions), including the intermittent corrections, and the existence of energy transfers across scales. We quantify the dependence of these basic properties of turbulent flows on the free parameter $gamma$ and derive analytically the spectrum of exponents of the structure functions in a simplified non dissipative case. A perturbative expansion in power of $gamma$ shows that energy transfers, at leading order, indeed take place, justifying the dissipative nature of this random field.
We investigate the conditional vorticity budget of fully developed three-dimensional homogeneous isotropic turbulence with respect to coherent and incoherent flow contributions. The Coherent Vorticity Extraction based on orthogonal wavelets allows to decompose the vorticity field into coherent and incoherent contributions, of which the latter are noise-like. The impact of the vortex structures observed in fully developed turbulence on statistical balance equations is quantified considering the conditional vorticity budget. The connection between the basic structures present in the flow and their statistical implications is thereby assessed. The results are compared to those obtained for large- and small-scale contributions using a Fourier decomposition, which reveals pronounced differences.
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