Statistics of Pressure Fluctuations in Decaying, Isotropic Turbulence

We present results from a systematic direct-numerical simulation study of pressure fluctuations in an unforced, incompressible, homogeneous, and isotropic, three-dimensional turbulent fluid. At cascade completion, isosurfaces of low pressure are found to be organised as slender filaments, whereas the predominant isostructures appear sheet-like. We exhibit several new results, including plots of probability distributions of the spatial pressure-difference, the pressure-gradient norm, and the eigenvalues of the pressure-hessian tensor. Plots of the temporal evolution of the mean pressure-gradient norm, and the mean eigenvalues of the pressure-hessian tensor are also exhibited. We find the statistically preferred orientations between the eigenvectors of the pressure-hessian tensor, the pressure-gradient, the eigenvectors of the strain-rate tensor, the vorticity, and the velocity. Statistical properties of the non-local part of the pressure-hessian tensor are also exhibited, for the first time. We present numerical tests (in the viscous case) of some conjectures of Ohkitani [Phys. Fluids A {\bf 5}, 2570 (1993)] and Ohkitani and Kishiba [Phys. Fluids {\bf 7}, 411 (1995)] concerning the pressure-hessian and the strain-rate tensors, for the unforced, incompressible, three-dimensional Euler equations.Comment: 10 pages, 29 figures, Accepted for publication in Physical Review

Coupled attribute analysis on numerical data

The usual representation of quantitative data is to formalize it as an information table, which assumes the independence of attributes. In real-world data, attributes are more or less interacted and coupled via explicit or implicit relationships. Limited research has been conducted on analyzing such attribute interactions, which only describe a local picture of attribute couplings in an implicit way. This paper proposes a framework of the coupled attribute analysis to capture the global dependency of continuous attributes. Such global couplings integrate the intra-coupled interaction within an attribute (i.e. The correlations between attributes and their own powers) and inter-coupled interaction among different attributes (i.e. The correlations between attributes and the powers of others) to form a coupled representation for numerical objects by the Taylor-like expansion. This work makes one step forward towards explicitly addressing the global interactions of continuous attributes, verified by the applications in data structure analysis, data clustering, and data classification. Substantial experiments on 13 UCI data sets demonstrate that the coupled representation can effectively capture the global couplings of attributes and outperforms the traditional way, supported by statistical analysis

Terminal Proterozoic cyanobacterial blooms and phosphogenesis documented by the Doushantuo granular phosphorites II: Microbial diversity and C isotopes

An unprecedented period of phosphogenesis, along with massive deposition of black shales, major perturbations in the global carbon cycle and the rise of atmospheric oxygen, occurred in the terminal Proterozoic in the aftermath of the Marinoan glaciation. Although causal links between these processes have been postulated, evidence remains challenging. Correlated in situ micro-analyses of granular phosphorites from the Ediacaran Doushantuo Formation in Yichang, South China, suggested that cyanobacteria and associated extracellular polymeric substances (EPS) might have promoted aggregated granule growth and subsequent phosphatization (She et al., 2013). Here, we present new paleontological data for the Doushantuo phosphorites from Yichang, which, combined with Raman microspectroscopy and carbon isotope data, further document links between the biology of cyanobacteria and phosphogenesis. Mapping of microfossils in thin section shows that most phosphatic granules contain microfossils that are dominated by colonies of Myxococcoides, along with several filamentous genera generally considered to represent cyanobacterial sheaths. In addition, the phosphorites and associated rocks have δ13Corg values in the range of −26.0 to −29.7‰ VPDB, consistent with photoautotrophic carbon fixation with the Rubisco enzyme. Close association of phosphorites with the Marinoan tillites in stratigraphic level supports a genetic link between deglaciation and phosphogenesis, at least for the Doushantuo occurrence. Our new data suggest that major cyanobacterial blooms probably took place in the terminal Proterozoic, which might have resulted in rapid scavenging of bioavailable phosphorus and massive accumulations of organic matter (OM). Within a redox-stratified intra-shelf basin, the OM-bound phosphorus could have liberated by microbial sulfate reduction and other anaerobic metabolisms and subsequently concentrated by Fe-redox pumping below the chemocline. Upwelling of the bottom waters or upward fluctuation of the chemocline might have brought P-enriched waters to the photic zone, where it was again scavenged by cyanobacteria through their EPS to be subsequently precipitated as francolite. The feedbacks between enhanced continental weathering, cyanobacterial blooms, carbon burial, and accelerated phosphorus cycle thus controlled the marine biogeochemical changes, which led to further oxygenation of the atmosphere and oceans, ultimately paving the way for the rise of metazoans

Universal statistics of non-linear energy transfer in turbulent models

A class of shell models for turbulent energy transfer at varying the inter-shell separation, $\lambda$, is investigated. Intermittent corrections in the continuous limit of infinitely close shells ($\lambda \rightarrow 1$) have been measured. Although the model becomes, in this limit, non-intermittent, we found universal aspects of the velocity statistics which can be interpreted in the framework of log-poisson distributions, as proposed by She and Waymire (1995, Phys. Rev. Lett. 74, 262). We suggest that non-universal aspects of intermittency can be adsorbed in the parameters describing statistics and properties of the most singular structure. On the other hand, universal aspects can be found by looking at corrections to the monofractal scaling of the most singular structure. Connections with similar results reported in other shell models investigations and in real turbulent flows are discussed.Comment: 4 pages, 2 figures available upon request to [email protected]

Bifractality of the Devil's staircase appearing in the Burgers equation with Brownian initial velocity

It is shown that the inverse Lagrangian map for the solution of the Burgers equation (in the inviscid limit) with Brownian initial velocity presents a bifractality (phase transition) similar to that of the Devil's staircase for the standard triadic Cantor set. Both heuristic and rigorous derivations are given. It is explained why artifacts can easily mask this phenomenon in numerical simulations.Comment: 12 pages, LaTe

A new scaling property of turbulent flows

We discuss a possible theoretical interpretation of the self scaling property of turbulent flows (Extended Self Similarity). Our interpretation predicts that, even in cases when ESS is not observed, a generalized self scaling, must be observed. This prediction is checked on a number of laboratory experiments and direct numerical simulations.Comment: Plain Latex, 1 figure available upon request to [email protected]

Developed turbulence: From full simulations to full mode reductions

Developed Navier-Stokes turbulence is simulated with varying wavevector mode reductions. The flatness and the skewness of the velocity derivative depend on the degree of mode reduction. They show a crossover towards the value of the full numerical simulation when the viscous subrange starts to be resolved. The intermittency corrections of the scaling exponents of the pth order velocity structure functions seem to depend mainly on the proper resolution of the inertial subrange. Universal scaling properties (i.e., independent of the degree of mode reduction) are found for the relative scaling exponents rho which were recently defined by Benzi et al.Comment: 4 pages, 5 eps-figures, replaces version from August 5th, 199

On the stationarity of linearly forced turbulence in finite domains

A simple scheme of forcing turbulence away from decay was introduced by Lundgren some time ago, the `linear forcing', which amounts to a force term linear in the velocity field with a constant coefficient. The evolution of linearly forced turbulence towards a stationary final state, as indicated by direct numerical simulations (DNS), is examined from a theoretical point of view based on symmetry arguments. In order to follow closely the DNS the flow is assumed to live in a cubic domain with periodic boundary conditions. The simplicity of the linear forcing scheme allows one to re-write the problem as one of decaying turbulence with a decreasing viscosity. Scaling symmetry considerations suggest that the system evolves to a stationary state, evolution that may be understood as the gradual breaking of a larger approximate symmetry to a smaller exact symmetry. The same arguments show that the finiteness of the domain is intimately related to the evolution of the system to a stationary state at late times, as well as the consistency of this state with a high degree of isotropy imposed by the symmetries of the domain itself. The fluctuations observed in the DNS for all quantities in the stationary state can be associated with deviations from isotropy. Indeed, self-preserving isotropic turbulence models are used to study evolution from a direct dynamical point of view, emphasizing the naturalness of the Taylor microscale as a self-similarity scale in this system. In this context the stationary state emerges as a stable fixed point. Self-preservation seems to be the reason behind a noted similarity of the third order structure function between the linearly forced and freely decaying turbulence, where again the finiteness of the domain plays an significant role.Comment: 15 pages, 7 figures, changes in the discussion at the end of section VI, formula (60) correcte