arXiv subjects

Itamar Procaccia

Publications and source records attributed to Itamar Procaccia.

At least 199 records · Page 11Linked to original sources

arXiv2006

Random and Correlated Roughening in Slow Fracture by Damage Nucleation

We address the role of the nature of material disorder in determining the roughness of cracks which grow by damage nucleation and coalescence ahead of the crack tip. We highlight the role of quenched and annealed disorders in relation to the length scales $d$ and $ξ_c$ associated with the disorder and the damage nucleation respectively. In two related models, one with quenched disorder in which $d \simeq ξ_c $, the other with annealed disorder in which $d \ll ξ_c$, we find qualitatively different roughening properties for the resulting cracks in 2-dimensions. The first model results in random cracks with an asymptotic roughening exponent $ζ\approx 0.5$. The second model shows correlated roughening with $ζ\approx 0.66$. The reasons for the qualitative difference are rationalized and explained.

cond-mat.mtrl-sci↗

arXiv2006

Turbulent Drag Reduction by Flexible and Rodlike Polymers: Crossover Effects at Small Concentrations

Drag reduction by polymers is bounded between two universal asymptotes, the von-Kármán log-law of the law and the Maximum Drag Reduction (MDR) asymptote. It is theoretically understood why the MDR asymptote is universal, independent of whether the polymers are flexible or rodlike. The cross-over behavior from the Newtonian von-Kármán log-law to the MDR is however not universal, showing different characteristics for flexible and rodlike polymers. In this paper we provide a theory for this cross-over phenomenology.

nlin.CD↗

arXiv2005

Disentangling Scaling Properties in Anisotropic Fracture

Structure functions of rough fracture surfaces in isotropic materials exhibit complicated scaling properties due to the broken isotropy in the fracture plane generated by a preferred propagation direction. Decomposing the structure functions into the even order irreducible representations of the SO(2) symmetry group (indexed by $m=0,2,4...$) results in a lucid and quickly convergent description. The scaling exponent of the isotropic sector ($m=0$) dominates at small length scales. One can reconstruct the anisotropic structure functions using only the isotropic and the first non vanishing anisotropic sector ($m=2$) (or at most the next one ($m=4$)). The scaling exponent of the isotropic sector should be observed in a proposed, yet unperformed, experiment.

cond-mat.mtrl-sci↗

arXiv2005

The Universality Class of Diffusion Limited Aggregation and Viscous Fingering

We investigate whether fractal viscous fingering and diffusion limited aggregates are in the same scaling universality class. We bring together the largest available viscous fingering patterns and a novel technique for obtaining the conformal map from the unit circle to an arbitrary singly connected domain in two dimensions. These two Laplacian fractals appear different to the eye; in addition, viscous fingering is grown in parallel and the aggregates by a serial algorithm. Nevertheless, the data strongly indicate that these two fractal growth patterns are in the same universality class.

cond-mat.dis-nn↗

arXiv2005

Drag Reduction by Bubble Oscillations

Drag reduction in stationary turbulent flows by bubbles is sensitive to the dynamics of bubble oscillations. Without this dynamical effect the bubbles only renormalize the fluid density and viscosity, an effect that by itself can only lead to a small percentage of drag reduction. We show in this paper that the dynamics of bubbles and their effect on the compressibility of the mixture can lead to a much higher drag reduction.

nlin.CD↗

arXiv2005

Statistical Physics of Fracture Surfaces Morphology

Experiments on fracture surface morphologies offer increasing amounts of data that can be analyzed using methods of statistical physics. One finds scaling exponents associated with correlation and structure functions, indicating a rich phenomenology of anomalous scaling. We argue that traditional models of fracture fail to reproduce this rich phenomenology and new ideas and concepts are called for. We present some recent models that introduce the effects of deviations from homogeneous linear elasticity theory on the morphology of fracture surfaces, succeeding to reproduce the multiscaling phenomenology at least in 1+1 dimensions. For surfaces in 2+1 dimensions we introduce novel methods of analysis based on projecting the data on the irreducible representations of the SO(2) symmetry group. It appears that this approach organizes effectively the rich scaling properties. We end up with the proposition of new experiments in which the rotational symmetry is not broken, such that the scaling properties should be particularly simple.

cond-mat.mtrl-sci↗

arXiv2005

Fracture Surfaces as Multiscaling Graphs

Fracture paths in quasi-two-dimenisonal (2D) media (e.g thin layers of materials, paper) are analyzed as self-affine graphs $h(x)$ of height $h$ as a function of length $x$. We show that these are multiscaling, in the sense that $n^{th}$ order moments of the height fluctuations across any distance $\ell$ scale with a characteristic exponent that depends nonlinearly on the order of the moment. Having demonstrated this, one rules out a widely held conjecture that fracture in 2D belongs to the universality class of directed polymers in random media. In fact, 2D fracture does not belong to any of the known kinetic roughening models. The presence of multiscaling offers a stringent test for any theoretical model; we show that a recently introduced model of quasi-static fracture passes this test.

cond-mat.mtrl-sci↗

arXiv2005

Phenomenology of Wall Bounded Newtonian Turbulence

We construct a simple analytic model for wall-bounded turbulence, containing only four adjustable parameters. Two of these parameters characterize the viscous dissipation of the components of the Reynolds stress-tensor and other two parameters characterize their nonlinear relaxation. The model offers an analytic description of the profiles of the mean velocity and the correlation functions of velocity fluctuations in the entire boundary region, from the viscous sub-layer, through the buffer layer and further into the log-layer. As a first approximation, we employ the traditional return-to-isotropy hypothesis, which yields a very simple distribution of the turbulent kinetic energy between the velocity components in the log-layer: the streamwise component contains a half of the total energy whereas the wall-normal and the cross-stream components contain a quarter each. In addition, the model predicts a very simple relation between the von-Kármán slope $κ$ and the turbulent velocity in the log-law region $v^+$ (in wall units): $v^+=6 κ$. These predictions are in excellent agreement with DNS data and with recent laboratory experiments.

nlin.CD↗

arXiv2005

Estimating von-Karman's constant from Homogeneous Turbulence

A celebrated universal aspect of wall-bounded turbulent flows is the von Karman log-law-of-the-wall, describing how the mean velocity in the streamwise direction depends on the distance from the wall. Although the log-law is known for more than 75 years, the von Karman constant governing the slope of the log-law was not determined theoretically. In this Letter we show that the von-Karman constant can be estimated from homogeneous turbulent data, i.e. without information from wall-bounded flows.

nlin.CD↗

arXiv2005

Identification and Calculation of the Universal Maximum Drag Reduction Asymptote by Polymers in Wall Bounded Turbulence

Drag reduction by polymers in wall turbulence is bounded from above by a universal maximal drag reduction (MDR) velocity profile that is a log-law, estimated experimentally by Virk as $V^+(y^+)\approx 11.7 \log y^+ -17$. Here $V^+(y)$ and $y^+$ are the mean streamwise velocity and the distance from the wall in "wall" units. In this Letter we propose that this MDR profile is an edge solution of the Navier-Stokes equations (with an effective viscosity profile) beyond which no turbulent solutions exist. This insight rationalizes the universality of the MDR and provides a maximum principle which allows an ab-initio calculation of the parameters in this law without any viscoelastic experimental input.

nlin.CD↗

arXiv2005

Non-universality in Micro-branching Instabilities in Rapid Fracture: the Role of Material Properties

In spite of the apparent similarity of micro-branching instabilities in different brittle materials, we propose that the physics determining the typical length- and time-scales characterizing the post-instability patterns differ greatly from material to material. We offer a scaling theory connecting the pattern characteristics to material properties (like molecular weight) in brittle plastics like PMMA, and stress the fundamental differences with patterns in glass which are crucially influenced by 3-dimensional dynamics. In both cases the present ab-initio theoretical models are still too far from reality, disregarding some fundamental physics of the phenomena.

cond-mat.mtrl-sci↗

arXiv2005

Additive Equivalence in Turbulent Drag Reduction by Flexible and Rodlike Polymers

We address the "Additive Equivalence" discovered by Virk and coworkers: drag reduction affected by flexible and rigid rodlike polymers added to turbulent wall-bounded flows is limited from above by a very similar Maximum Drag Reduction (MDR) asymptote. Considering the equations of motion of rodlike polymers in wall-bounded turbulent ensembles, we show that although the microscopic mechanism of attaining the MDR is very different, the macroscopic theory is isomorphic, rationalizing the interesting experimental observations.

nlin.CD↗

arXiv2004

Void Formation and Roughening in Slow Fracture

Slow crack propagation in ductile, and in certain brittle materials, appears to take place via the nucleation of voids ahead of the crack tip due to plastic yields, followed by the coalescence of these voids. Post mortem analysis of the resulting fracture surfaces of ductile and brittle materials on the $μ$m-mm and the nm scales respectively, reveals self-affine cracks with anomalous scaling exponent $ζ\approx 0.8$ in 3-dimensions and $ζ\approx 0.65$ in 2-dimensions. In this paper we present an analytic theory based on the method of iterated conformal maps aimed at modelling the void formation and the fracture growth, culminating in estimates of the roughening exponents in 2-dimensions. In the simplest realization of the model we allow one void ahead of the crack, and address the robustness of the roughening exponent. Next we develop the theory further, to include two voids ahead of the crack. This development necessitates generalizing the method of iterated conformal maps to include doubly connected regions (maps from the annulus rather than the unit circle). While mathematically and numerically feasible, we find that the employment of the stress field as computed from elasticity theory becomes questionable when more than one void is explicitly inserted into the material. Thus further progress in this line of research calls for improved treatment of the plastic dynamics.

cond-mat.mtrl-sci↗

arXiv2004

Branching Instabilities in Rapid Fracture: Dynamics and Geometry

We propose a theoretical model for branching instabilities in 2-dimensional fracture, offering predictions for when crack branching occurs, how multiple cracks develop, and what is the geometry of multiple branches. The model is based on equations of motion for crack tips which depend only on the time dependent stress intensity factors. The latter are obtained by invoking an approximate relation between static and dynamic stress intensity factors, together with an essentially exact calculation of the static ones. The results of this model are in good agreement with a sizeable quantity of experimental data.

cond-mat.mtrl-sci↗

arXiv2004

Drag Reduction by Microbubbles in Turbulent Flows: the Limit of Minute Bubbles

Drag reduction by microbubbles is a promising engineering method for improving ship performance. A fundamental theory of the phenomenon is lacking however, making actual design quite uphazard. We offer here a theory of drag reduction by microbubbles in the limit of very small bubbles, when the effect of the bubbles is mainly to normalize the density and the viscosity of the carrier fluid. The theory culminates with a prediction of the degree of drag reduction given the concentration profile of the bubbles. Comparisons with experiments are discussed and the road ahead is sketched.

nlin.CD↗

arXiv2004

The Polymer Stress Tensor in Turbulent Shear Flows

The interaction of polymers with turbulent shear flows is examined. We focus on the structure of the elastic stress tensor, which is proportional to the polymer conformation tensor. We examine this object in turbulent flows of increasing complexity. First is isotropic turbulence, then anisotropic (but homogenous) shear turbulence and finally wall bounded turbulence. The main result of this paper is that for all these flows the polymer stress tensor attains a universal structure in the limit of large Deborah number $\De\gg 1$. We present analytic results for the suppression of the coil-stretch transition at large Deborah numbers. Above the transition the turbulent velocity fluctuations are strongly correlated with the polymer's elongation: there appear high-quality "hydro-elastic" waves in which turbulent kinetic energy turns into polymer potential energy and vice versa. These waves determine the trace of the elastic stress tensor but practically do not modify its universal structure. We demonstrate that the influence of the polymers on the balance of energy and momentum can be accurately described by an effective polymer viscosity that is proportional to to the cross-stream component of the elastic stress tensor. This component is smaller than the stream-wise component by a factor proportional to $\De ^2 $. Finally we tie our results to wall bounded turbulence and clarify some puzzling facts observed in the problem of drag reduction by polymers.

nlin.CD↗

arXiv2004

Anisotropy in Turbulent Flows and in Turbulent Transport

We discuss the problem of anisotropy and intermittency in statistical theory of high Reynolds-number turbulence (and turbulent transport). We present a detailed description of the new tools that allow effective data analysis and systematic theoretical studies such as to separate isotropic from anisotropic aspects of turbulent statistical fluctuations. Employing the invariance of the equations of fluid mechanics to all rotations, we show how to decompose the (tensorial) statistical objects in terms of the irreducible representation of the SO(3) symmetry group. For the case of turbulent advection of passive scalar or vector fields, this decomposition allows rigorous statements to be made: (i) the scaling exponents are universal, (ii) the isotropic scaling exponents are always leading, (iii) the anisotropic scaling exponents form a discrete spectrum which is strictly increasing as a function of the anisotropic degree. Next we explain how to apply the SO(3) decomposition to the statistical Navier-Stokes theory. We show how to extract information about the scaling behavior in the isotropic sector. Doing so furnishes a systematic way to assess the universality of the scaling exponents in this sector, clarifying the anisotropic origin of the many measurements that claimed the opposite. A systematic analysis of Direct Numerical Simulations and of experiments provides a strong support to the proposition that also for the non-linear problem there exists foliation of the statistical theory into sectors of the symmetry group. The exponents appear universal in each sector, and again strictly increasing as a function of the anisotropic degreee.

nlin.CD↗

arXiv2004

Drag Reduction in Homogeneous Turbulence by Scale-Dependent Effective Viscosity

The phenomenon of drag reduction by polymer additives had been studied in simulations on the basis of non-Newtonian fluid mechanical models that take into account the field of polymer extension (conformation tensor) and its interaction with the velocity field. Drag reduction was found in both homogeneous and wall bounded turbulent flows. In the latter case it was shown recently that the notion of scale-dependent effective viscosity allows quantitative predictions of the characteristics of drag reduction in close correspondence with experiments. In this paper we demonstrate that also drag reduction in homogeneous turbulence is usefully discussed in terms of a scale-dependent viscosity. In other words, the essence of the phenomena under study can be recaptured by an "equivalent" equation of motion for the velocity field alone, with a judiciously chosen scale-dependent effective viscosity that succinctly summarizes the important aspects of the interaction between the polymer conformation tensor field and the velocity field. We will also clarify here the differences between drag reduction in homogeneous and wall bounded flows.

physics.flu-dyn↗