Mixing in turbulent jets: scalar measures and isosurface geometry

Experiments have been conducted to investigate mixing and the geometry of scalar isosurfaces in turbulent jets. Specifically, we have obtained high-resolution, high-signal-to-noise-ratio images of the jet-fluid concentration in the far field of round, liquid-phase, turbulent jets, in the Reynolds number range 4.5 × 10^3 ≤ Re ≤ 18 × 10^3, using laser-induced-fluorescence imaging techniques. Analysis of these data indicates that this Reynolds-number range spans a mixing transition in the far field of turbulent jets. This is manifested in the probability-density function of the scalar field, as well as in measures of the scalar isosurfaces. Classical as well as fractal measures of these isosurfaces have been computed, from small to large spatial scales, and are found to be functions of both scalar threshold and Reynolds number. The coverage of level sets of jet-fluid concentration in the two-dimensional images is found to possess a scale-dependent-fractal dimension that increases continuously with increasing scale, from near unity, at the smallest scales, to 2, at the largest scales. The geometry of the scalar isosurfaces is, therefore, more complex than power-law fractal, exhibiting an increasing complexity with increasing scale. This behaviour necessitates a scale-dependent generalization of power-law-fractal geometry. A connection between scale-dependent-fractal geometry and the distribution of scales is established and used to compute the distribution of spatial scales in the flow

Multiscaling properties on sequences of turbulent plumes images

A multifractal analysis on a finite-range-scale of the plume concentration images at different experimental conditions (the height of the source Ho), where the measure is the grey value of the image (from 0 to 255), was applied to study its structure through time. The multifractal spectrum showed the characteristic inverse U-shape and a similar evolution in all Ho. The variation of the Hölder exponent (¿a) presented different amplitudes at different moments and increased with time. The symmetry of the spectrum (¿f) decreased with time achieving negative values (from left hand asymmetry evolving to right asymmetry). We show the different behaviour of axial velocity (W) with ¿a and ¿f. There is a linear relation of entrainment coefficient (ae) and the entropy dimension (a1). Therefore, the multifractal spectrum and the derived parameters can be used as markers of plume evolution as well as to study the effect of experimental conditions.Postprint (published version

Turbulence, Complexity, and Solar Flares

The issue of predicting solar flares is one of the most fundamental in physics, addressing issues of plasma physics, high-energy physics, and modelling of complex systems. It also poses societal consequences, with our ever-increasing need for accurate space weather forecasts. Solar flares arise naturally as a competition between an input (flux emergence and rearrangement) in the photosphere and an output (electrical current build up and resistive dissipation) in the corona. Although initially localised, this redistribution affects neighbouring regions and an avalanche occurs resulting in large scale eruptions of plasma, particles, and magnetic field. As flares are powered from the stressed field rooted in the photosphere, a study of the photospheric magnetic complexity can be used to both predict activity and understand the physics of the magnetic field. The magnetic energy spectrum and multifractal spectrum are highlighted as two possible approaches to this.Comment: 2 figure

A fractal fragmentation model for rockfalls

The final publication is available at Springer via http://dx.doi.org/10.1007/s10346-016-0773-8The impact-induced rock mass fragmentation in a rockfall is analyzed by comparing the in situ block size distribution (IBSD) of the rock mass detached from the cliff face and the resultant rockfall block size distribution (RBSD) of the rockfall fragments on the slope. The analysis of several inventoried rockfall events suggests that the volumes of the rockfall fragments can be characterized by a power law distribution. We propose the application of a three-parameter rockfall fractal fragmentation model (RFFM) for the transformation of the IBSD into the RBSD. A discrete fracture network model is used to simulate the discontinuity pattern of the detached rock mass and to generate the IBSD. Each block of the IBSD of the detached rock mass is an initiator. A survival rate is included to express the proportion of the unbroken blocks after the impact on the ground surface. The model was calibrated using the volume distribution of a rockfall event in Vilanova de Banat in the Cadí Sierra, Eastern Pyrenees, Spain. The RBSD was obtained directly in the field, by measuring the rock block fragments deposited on the slope. The IBSD and the RBSD were fitted by exponential and power law functions, respectively. The results show that the proposed fractal model can successfully generate the RBSD from the IBSD and indicate the model parameter values for the case study.Peer ReviewedPostprint (author's final draft

Traffic measurement and analysis

Measurement and analysis of real traffic is important to gain knowledge about the characteristics of the traffic. Without measurement, it is impossible to build realistic traffic models. It is recent that data traffic was found to have self-similar properties. In this thesis work traffic captured on the network at SICS and on the Supernet, is shown to have this fractal-like behaviour. The traffic is also examined with respect to which protocols and packet sizes are present and in what proportions. In the SICS trace most packets are small, TCP is shown to be the predominant transport protocol and NNTP the most common application. In contrast to this, large UDP packets sent between not well-known ports dominates the Supernet traffic. Finally, characteristics of the client side of the WWW traffic are examined more closely. In order to extract useful information from the packet trace, web browsers use of TCP and HTTP is investigated including new features in HTTP/1.1 such as persistent connections and pipelining. Empirical probability distributions are derived describing session lengths, time between user clicks and the amount of data transferred due to a single user click. These probability distributions make up a simple model of WWW-sessions