163 research outputs found
Cataracts and Visual Decline – A Conversation with Rahul T. Pandit, MD, Blanton Eye institute, Houston Methodist Hospital
No full textStudies Of Spiral Turbulence And Its Control In Models Of Cardiac Tissue
No full textThere is a growing consensus that life-threatening cardiac arrhythmias like ventricular tachycardia (VT) or ventricular fibrillation (VF) arise because of the formation of spiral waves of electrical activation in cardiac tissue; unbroken spiral waves are associated with VT and broken ones with VF. Several experimental studies have shown that inhomogeneities in cardiac tissue can have dramatic effects on such spiral waves. In this thesis we try to understand these experimental results by carrying out detailed and systematic studies of the interaction of spiral waves with different types of inhomogeneities in mathematical models for cardiac tissue.
In Chapter 1 we begin with a general introduction to cardiac arrhythmias, the cardiac conduction system, and the connection between electrical activation waves in cardiac tissue and cardiac arrhythmias. As we have noted above, VT and VF are believed to be associated with spiral waves of electrical activation on cardiac tissue; such spiral waves form because cardiac tissue is an excitable medium. Thus we give an overview of excitable media, in which sub-threshold perturbations decay but super-threshold perturbations lead to an action potential that consists of a rapid stage of depolarization of cardiac cells followed by a slow phase of repolarization. During this repolarization phase the cells are refractory. We then give an overview of earlier studies of the effects of inhomogeneities in cardiac tissue; and we end with a brief description of the principal problems we study here.
Chapter 2 describes the models we use in our work. We start with a general introduction to the cable equation and then discuss the Hodgkin-Huxley-formalism for the transport of ions across a cell membrane through voltage-gated ion channels. We then describe in detail the three models that we use for cardiac tissue, which are, in order of increasing complexity, the Panfilov model, the Luo Rudy Phase I (LRI) model, and the reduced Priebe Beuckelmann (RPB)model. We then give the numerical schemes we use for solving these model equations and the initial conditions that lead to the formation of spiral waves. For all these models we give representative results from our simulations and compare the states with spiral turbulence.
In Chapter 3 we investigate the effects of conduction inhomogeneities (obstacles) in the three models introduced in Chapter 2. We outline first the experimental results that have provided the motivation for our study. We then discuss how we introduce obstacles in our simulations of the Panffilov, LRI, and RPB models for cardiac tissue. Next we present the results of our numerical studies of the effects, on spiral-wave dynamics, of the sizes, shapes, and positions of the obstacles. Our Principal result is that spiral-wave dynamics in these models depends sensitively on the position of the obstacle. We find, in particular, that, merely by changing the position of a conduction inhomogeneity, we may convert spiral turbulence (the analogue in our models of VF) to a single rotating spiral (the analogue of VT) anchored to the obstacle or vice versa; even more exciting is the possibility that, at the boundary between these two types of behaviour, we find a quiescent state Q with no spiral waves. Thus our study obtains all the possible qualitative behaviours found in experiments, namely, (1) VF might persist even in the presence of an obstacle, (2) it might be suppressed partially and become VT, or (3) it might be eliminated completely.
In Chapter 4 we extend our work on conduction inhomogeneities (Chapter 3) to ionic inhomogeneities. Unlike conduction inhomogeneities, ionic inhomogeneities allow the conduction of activation waves. We find, nevertheless, that they too can lead to the anchoring of spiral waves or even the complete elimination of spiral-wave turbulence. Since spiral waves can enter the region in which there is an ionic inhomogeneity, their behaviours in the presence of such an inhomogeneity are richer than those with conduction inhomogeneities. We find, in particular, that a single spiral wave anchored at an ionic inhomogeneity can show temporal evolution that may be periodic, quasiperiodic, or even chaotic. In the last case the spiral wave shows a chaotic pattern inside the ionic inhomogeneity and a regular one outside it.
Defibrillation is the control of arrhythmias such as VF. Most often defibrillation is effected electrically by administering a shock, either externally or via an internally implanted defibrillator. The development of low-amplitude defibrillation schemes, which minimise the deleterious effects of the applied shock, is a major challenge in the treatment of cardiac arrhythmias. Numerical studies of models for cardiac tissue provide us with convenient means of studying the elimination of spiral-wave turbulence by the application of external electrical stimuli; this is the numerical analogue of defibrillation. Over the years some low-amplitude defibrillation schemes have been suggested on the basis of such numerical studies. In Chapter 5 we discuss two such schemes that have been shown to suppress spiral-wave turbulence in two-dimensional models for cardiac tissue and also scroll-wave turbulence in three-dimensional models. One of these schemes uses local electrical pacing, typically in the centre of the simulation domain; the other applies the external electrical stimuli over a mesh. We study the efficacy of these schemes in the presence of conduction inhomogeneities. We find, in particular, that the local-pacing scheme, though effective in a homogeneous simulation domain, fails to control spiral turbulence in the presence of an obstacle and, indeed, might even facilitate spiral-wave break up. By contrast, the second scheme, which uses a mesh, succeeds in eliminating spiral-wave turbulence even in the presence of an obstacle. We end with some concluding remarks about the possible experimental implications of our study in Chapter 6
Particles and Fields in Superfluids: Insights from the Two-dimensional Gross-Pitaevskii Equation
No full textWe study the dynamics of active particles in two-dimensional superfluids at temperature , for a variety of initial configurations, by carrying out extensive direct-numerical-simulations of the two-dimensional, Galerkin-truncated Gross-Pitaevskii equation. Our study elucidates the interplay of particles and fields, in both simple and turbulent flows. We show that particle collisions can be inelastic, if the repulsive interactions between particles is weak, and elastic otherwise. We show that assemblies of many particles and vortices yield turbulent spatiotemporal evolutions
Numerical Studies of Problems in Turbulence : 1) Fluid Films with Polymer Additives; 2) Fluid Films with Inertial and Elliptical Particles; 3) Scaled Vorticity Moments in Three- and Two-dimensional Turbulence
No full textIn this thesis we study a variety of problems in fluid turbulence, principally in two dimensions. A summary of the main results of our studies is given below; we indicate the Chapters in which we present these.
In Chapter 1, we provide an overview of several problems in turbulence with special emphasis on background material for the problems we study in this thesis. In particular, we give (a) natural and laboratory examples of fluid turbulence, (b) and introductory accounts of the equations of hydrodynamics, without and with polymer additives, Eulerian and Lagrangian frameworks, and the equations of motion of inertial particles in fluid flows. We end with a summary of the problems we study in subsequent Chapters of this thesis.
In Chapter 2, we carry out the most extensive and high-resolution direct numerical simulation, attempted so far, of homogeneous, isotropic turbulence in two-dimensional fluid films with air-drag-induced friction and with polymer additives. Our study reveals that the polymers (a) reduce the total fluid energy, enstrophy, and palinstrophy, (b) modify the fluid energy spectrum both in inverse- and forward-cascade regimes, (c) reduce small-scale intermittency, (d) suppress regions of large vorticity and strain rate, and (e) stretch in strain-dominated regions. We compare our results with earlier experimental studies and propose new experiments.
In Chapter 3, we perform a direct numerical simulation (DNS) of the forced, incompressible two-dimensional Navier-Stokes equation coupled with the FENE-P equations for the polymer- conformation tensor. The forcing is such that, without polymers and at low Reynolds numbers Re, the lm attains a steady state that is a square lattice of vortices and anti-vortices. We nd that, as we increase the Weissenberg number (Wi), this lattice undergoes a series of nonequilibrium phase transitions, first to spatially distorted, but temporally steady, crystals and then to a sequence of crystals that oscillate in time, periodically, at low Wi, and quasiperiodically, for slightly larger Wi. Finally, the system becomes disordered and displays spatiotepmoral chaos and elastic turbulence. We then obtain the nonequilibrium phase diagram for this system, in the Wi − Re plane, and show that (a) the boundary between the crystalline and turbulent phases has a complicated, fractal-type character and (b) the Okubo-Weiss parameter provides us with a natural measure for characterizing the phases and transitions in this diagram.
In Chapter 4, our study is devoted to heavy, inertial particles in two-dimensional (2D) tur- bulent, but statistically steady, flows that are homogeneous and isotropic. The inertial particles are distributed uniformly in our simulation domain when St = 0; they start to cluster as St increases; this clustering tendency reaches a maximum at St 1 and decreases thereafter. We then obtain PDFs of and show that their left tails, which come from extensional regions, do not depend sensitively on St; in contrast, their right tails, from the vortical regions of the flow, are consistent with the exponential form ∼ exp ‰− + Ž; and we nd that the scale + decreases with St until St _0:1 and then saturates at a value _0:75. Our persistence-type studies yield the following results, when we consider forcing that leads to an energy spectrum that is dominated by a forward-cascade regime: In strain-dominated or extensional regions of the flow, wend that the cumulative PDF of the persistence time decays exponentially; this decay yields a time scale T−, which increases rapidly with St, at low values of St, but more slowly after St _0:75. By contrast, in vortical regions of the flow, this cumulative PDF displays a tail that has power-law and exponential parts; the power-law part yields the persistence exponent _ and the exponential tail gives a time scale T−; _ increases with St, whereas T− decreases with St; _ and T− reach saturation values as St increases. From the cumulative PDF of the particle mean-square displacement r2, we obtain the time scale Ttrans at which there is a crossover from ballistic to diffusive behavior; we _nd that Ttrans increases with St. The PDFs of v2, the square of the particle velocity, and v2 ejected, the square of the velocity of a particle just as it is ejected from a region with _ > 0 (vortical region) to one that has _ < 0 (extensional region), do not show a significant dependence on St; the tails of these PDFs are characterized by power-law decays with exponents _1 and _5~3, respectively. Our next set of results deal with statistical properties of special combinations of the acceleration a =dv~dt and the velocity v. For instance, the curvature of the trajectory is _ =aÙ~v2, where the subscript Ù denotes the component perpendicular to the particle trajectory; we obtain PDFs of _ and _nd there from that particles in regions of elongational flow have, on average, trajectories with a lower curvature than particles in vortical regions; this . We also determine how the number of number of points NI , at which a ×v changes sign along a particle trajectory, as time increases; we _nd that the increase of NI with time and decrease as St increases. Our ninth set of results show that the characteristic decay time T_ for decreases with St.
In Chapter 5, we study the statistical properties of orientation and rotation dynamics of elliptical tracer particles in two-dimensional, homogeneous and isotropic turbulence by direct numerical simulations. We consider both the cases in which the turbulent flow is generated by forcing at large and intermediate length scales. We show that the two cases are qualitatively different. For the large-scale forcing, the spatial distribution of particle orientations forms large- scale structures, which are absent for the intermediate-scale forcing. The alignment with the local directions of the flow is much weaker in the latter case than in the former. For the intermediate- scale forcing, the statistics of rotation rates depends weakly on the Reynolds number and on the aspect ratio of particles. In contrast with what is observed in three-dimensional turbulence, in two dimensions the mean-square rotation rate decreases as the aspect ratio increases.
In Chapter 6, we study the issue of intermittency in numerical solutions of the 3D Navier-Stokes equations on a periodic box [0; L]3. This is addressed through four sets of numerical simulations that calculate a new set of variables defined by Dm(t) = where All four simulations unexpectedly show that the Dm are ordered for m =1 ….,9 such that Dm+1 <Dm. Moreover, the Dm squeeze together such that Dm+1/Dm 1 as m increases. The values of D1 lie far above the values of the rest of the Dm, giving rise to a suggestion that a depletion of nonlinearity is occuring which could be the cause of Navier{Stokes regularity. The first simulation, by R. Kerr, is of very anisotropic decaying turbulence ; the second and third, which have been carried out by me, are of decaying isotropic turbulence from random initial conditions and forced isotropic turbulence at fixed Grashof number, respectively ; the fourth, by D. Donzis, is of very-high-Reynolds-number forced, stationary, isotropic turbulence at resolutions up to 40963 collocation points. For the sake of completeness and for a comparison of the data from all these four simulations, all the results are presented; however, in the Sections that deal with the simulations, I indicate who carried out the calculations reported there. I also present an extension of this work to two-dimensional fluid turbulence; this has not been submitted for publication so far.
We hope our in silico studies of 2D and 3D turbulence will stimulate new experimental, numerical, and theoretical studies
Particles and Fields in Superfluid Turbulence : Numerical and Theoretical Studies
No full textIn this thesis we study a variety of problems in superfluid turbulence, princi-pally in two dimensions. A summary of the main results of our studies is given below; we indicate the Chapters in which we present these.
In Chapter 1, we provide an overview of several problems in superfluid turbulence with special emphasis on background material for the problems we study in this thesis. In particular, we give: (a) a brief introduction of fluid turbulence; (b) an overview of superfluidity and the phenomenological two-fluid model; (c) a brief overview of experiments on superfluid turbulence; (d) an introductory accounts of the phenomenological models used in the study of superfluid turbulence. We end with a summary of the problems we study in subsequent Chapters of this thesis.
In Chapter 2, we present a systematic, direct numerical simulation of the two-dimensional, Fourier-truncated, Gross-Pitaevskii equation to study the turbulent evolutions of its solutions for a variety of initial conditions and a wide range of parameters. We find that the time evolution of this system can be classified into four regimes with qualitatively different statistical properties. First, there are transients that depend on the initial conditions. In the second regime, power- law scaling regions, in the energy and the occupation-number spectra, appear and start to develop; the exponents of these power laws and the extents of the scaling regions change with time and depend on the initial condition. In the third regime, the spectra drop rapidly for modes with wave numbers k > kc and partial thermalization takes place for modes with k < kc ; the self-truncation wave number kc(t) depends on the initial conditions and it grows either as a power of t or as log t. Finally, in the fourth regime, complete thermalization is achieved and, if we account for finite-size effects carefully, correlation functions and spectra are consistent with their nontrivial Berezinskii-Kosterlitz-Thouless forms. Our work is a natural generalization of recent studies of thermalization in the Euler and other hydrodynamical equations; it combines ideas from fluid dynamics and turbulence, on the one hand, and equilibrium and nonequilibrium statistical mechanics on the other.
In Chapter 3, we present the first calculation of the mutual-friction coefficients α and α (which are parameters in the Hall-Vinen-Bekharevich-Khalatnikov two-fluid model that we study in chapter 5) as a function of temperature in a homogeneous Bose gas in two-dimensions by using the Galerkin-truncated Gross-Pitaevskii equation, with very special initial conditions, which we obtain by using the advective, real, Ginzburg-Landau equation (ARGLE) and an equilibration procedure that uses a stochastic Ginzburg-Landau equation (SGLE). We also calculate the normal-fluid density as a function of temperature.
In Chapter 4, we elucidate the interplay of particles and fields in superfluids, in both simple and turbulent flows. We carry out extensive direct numerical simulations (DNSs) of this interplay for the two-dimensional (2D) Gross-Pitaevskii (GP) equation. We obtain the following results: (1) the motion of a particle can be chaotic even if the superfluid shows no sign of turbulence; (2) vortex motion depends sensitively on particle charateristics; (3) there is an effective, superfluid-mediated, attractive interaction between particles; (4) we introduce a short-range repulsion between particles, with range rSR, and study two- and many-particle collisions; in the case of two-particle, head-on collisions, we find that, at low values of rSR, the particle collisions are inelastic with coefficient of restitution e = 0; and, as we in-crease rSR, e becomes nonzero at a critical point, and finally attains values close to 1; (5) assemblies of particles and vortices show rich, turbulent, spatio-temporal evolution.
In Chapter 5, we present results from our direct numerical simulations (DNSs) of the Hall-Vinen-Bekharevich-Khalatnikov (HVBK) two-fluid model in two dimensions. We have designed these DNSs to study the statistical properties of inverse and forward cascades in the HVBK model. We obtain several interesting results that have not been anticipated hitherto: (1) Both normal-fluid and superfluid energy spectra, En(k) and Es(k), respectively, show inverse- and forward-cascade regimes; the former is characterized by a power law Es(k) En(k) kα whose exponent is consistent with α 5/3. (2) The forward-cascade power law depends on (a) the friction coefficient, as in 2D fluid turbulence, and, in addition, on (b) the coefficient B of mutual friction, which couples normal and superfluid compo-nents. (3) As B increases, the normal and superfluid velocities, un and us, re-spectively, get locked to each other, and, therefore, Es(k) En(k), especially in the inverse-cascade regime. (4) We quantify this locking tendency by calculating the probability distribution functions (PDFs) P(cos(θ)) and P(γ), where the angle θ ≡ (un • us)/( |un||us|) and the amplitude ratio γ = |un|/|us |; the former has a peak at cos(θ) = 1; and the latter exhibits a peak at γ = 1 and power-law tails on both sides of this peak. (4) This locking increases as we increase B, but the power-law exponents for the tails of P(γ) are universal, in so far as they do not depend on B, ρn/ρ, and the details of the energy-injection method. (5) We characterize the energy and enstrophy cascades by computing the energy and enstrophy fluxes and the mutual-friction transfer functions for all wave-number scales k.
In Chapter 6, we examine the multiscaling of structure functions in three-dimensional superfluid turbulence by using a shell-model for the three-dimensional HVBK equations. Our HVBK shell model is based on the GOY shell model. In particular, we examine the dependence of multiscaling on the normal-fluid fraction and the mutual-friction coefficients.
We hope our in silico studies of 2D and 3D superfluid turbulence will stimulate new experimental, numerical, and theoretical studies
Mutual-Friction Coefficients in Two-Dimensional Superfluids: From the Gross-Pitaevskii equation to the Hall-Vinen-Bekharevich-Khalatnikov Two-fluid Model
No full textWe start from the two-dimensional Gross-Pitaevskii equation (GPE) and develop algorithms for the ab-initio determination of the temperature (T) dependence of the mutual-friction coefficients, α and α, and the normal-fluid density Pn, which appear as parameters in the Hall-Vinen-Bekharevich-Khalatnikov (HVBK) two-fluid model for a superfluid. In the second part of our study, we elucidate the statistical properties of two-dimensional, homogeneous, isotropic superfluid turbulence in the simplified HVBK model, with values for the mutual-friction coefficients that are comparable to those we obtain from the first part of our study
Surfactant protein D inhibits HIV-1 infection of target cells via interference with gp120-CD4 interaction and modulates pro-inflammatory cytokine production
No full text© 2014 Pandit et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.Surfactant Protein SP-D, a member of the collectin family, is a pattern recognition protein, secreted by mucosal epithelial cells and has an important role in innate immunity against various pathogens. In this study, we confirm that native human SP-D and a recombinant fragment of human SP-D (rhSP-D) bind to gp120 of HIV-1 and significantly inhibit viral replication in vitro in a calcium and dose-dependent manner. We show, for the first time, that SP-D and rhSP-D act as potent inhibitors of HIV-1 entry in to target cells and block the interaction between CD4 and gp120 in a dose-dependent manner. The rhSP-D-mediated inhibition of viral replication was examined using three clinical isolates of HIV-1 and three target cells: Jurkat T cells, U937 monocytic cells and PBMCs. HIV-1 induced cytokine storm in the three target cells was significantly suppressed by rhSP-D. Phosphorylation of key kinases p38, Erk1/2 and AKT, which contribute to HIV-1 induced immune activation, was significantly reduced in vitro in the presence of rhSP-D. Notably, anti-HIV-1 activity of rhSP-D was retained in the presence of biological fluids such as cervico-vaginal lavage and seminal plasma. Our study illustrates the multi-faceted role of human SPD against HIV-1 and potential of rhSP-D for immunotherapy to inhibit viral entry and immune activation in acute HIV infection. © 2014 Pandit et al.The work (Project no. 2011-16850) was supported by Medical Innovation Fund of Indian Council of Medical Research, New Delhi, India (www.icmr.nic.in/)
Steady state properties of discrete and continuous models of nonequilibrium phenomena
No full textThe understanding of nonequilibrium phenomena, of fundamental importance in statistical
physics, has great implications for many physical, chemical, and biological systems. Such
phenomena are observed almost everywhere in the natural world. These phenomena are
characterized by complicated spatiotemporal evolution. To explore nonequilibrium phenomena
we often study simple model systems that embody their essential characteristics. In this thesis,
we report the results of our investigations of the statistically steady state properties of three
one-dimensional models: multispecies asymmetric simple exclusion processes, the Kuramoto-
Sivashinsky equation, and the Burgers equation. The thesis is divided into two parts: Part I
and Part II.
In Chapters 2–5 of Part I, we present our results for multispecies exclusion models, principally
the phase diagrams and statistical properties of their nonequilibrium steady state (NESS). We
list below abstracts of these chapters.
• In Chapter 2, we consider a multispecies ASEP (mASEP) on a one-dimensional lattice
with semipermeable boundaries in contact with particle reservoirs. The mASEP involves
¹2 ¸1º species of particles: species of positive charges and their negative counterparts
as well as vacancies. At the boundaries, a species can replace or be replaced by its
negative counterpart. We derive the exact nonequilibrium phase diagram for the system
in the long time limit. We find two new phenomena in certain regions of the phase
diagram: dynamical expulsion when the density of a species becomes zero throughout
the system, and dynamical localization when the density of a species is nonzero only
within an interval far from the boundaries. We give a complete explanation of the
macroscopic features of the phase diagram using what we call nested fat shocks.
• In Chapter 3, we study an asymmetric exclusion process with two species and vacancies
on an open one-dimensional lattice called the left-permeable ASEP (LPASEP). The left
boundary is permeable for the vacancies but the right boundary is not. We find a matrix
product solution for the stationary state and the exact stationary phase diagram for the
densities and currents. By calculating the density of each species at the boundaries,
we find further structure in the stationary phases. In particular, we find that the slower
species can reach and accumulate at the far boundary, even in phases where the bulk
density of these particles approaches zero.
• In Chapter 4, we study a multispecies generalization of the model in Chapter 3. We
determine all phases in the phase diagram using an exact projection to the LPASEP
solved earlier. In most phases, we observe the phenomenon of dynamical expulsion of
one or more species. We explain the density profiles in each phase using interacting
shocks. This explanation is corroborated by simulations.
• In Chapter 5, we investigate a multispecies generalization of the single-species asymmetric
simple exclusion process defined on an open one-dimensional, finite lattice connected
to particle reservoirs. At the boundaries, a species can be replaced with any other species.
We devise an exact projection scheme to find the phase diagram in terms of densities
and currents of all species. In most of the phases, one or more species are absent in the
system due to dynamical expulsion. We observe shocks as well in some regions of the
phase diagram. We explain the density profiles using a generalized shock structure that
is substantiated by numerical simulations.
In Chapters 7 and 8 of Part II, we study the statistical properties of turbulent, but statistically
steady, states of the Kuramoto-Sivashinsky and the Burgers equations in one dimension. Our
main results are summarized below.
• In Chapter 7, we investigate the long time and large system size properties of the onedimensional
Kuramoto-Sivashinsky equation. Tracy-Widom and Baik-Rains distributions
appear as universal limit distributions for height fluctuations in the one-dimensional
Kardar-Parisi-Zhang (KPZ) stochastic partial differential equation (PDE). We obtain the
same universal distributions in the spatiotemporally chaotic, nonequilibrium, but statistically
steady state of KS deterministic PDE, by carrying out extensive pseudospectral
direct numerical simulations to obtain the spatiotemporal evolution of the KS height
profile h(x,t) for different initial conditions. We establish, therefore, that the statistical
properties of the one-dimensional (1D) KS PDE in this state are in the 1D KPZ
universality class.
• In Chapter 8, we study the statistical properties of decaying turbulence in the onedimensional
Burgers equation, in the vanishing-viscosity limit; we start with random
initial conditions, whose energy spectra have simple functional dependences on the
wavenumber k:
E_0(k) = A \mathcal{E}(k) exp[ - 2 k^2 / k^2_c ] ,
where A is a positive real number, and k_c is a cutoff wavenumber. The simplest case is
the single-power law \mathcal{E}(k) = k^{n}. We focus here on the case of the Gaussian laws which
are characterized by E_0(k) = exp[ - 2 (k-k_c)^2 / k^2_c +2 k^2 / k^2_c]; in addition, we consider
initial spectra which are combinations of either two or four single-power law spectral
regions. For all these initial conditions, we systematize (a) the temporal decay of the total
energy, (b) the rich temporal evolution of the energy spectrum, and (c) the spatiotemporal
evolution of the velocity field. We present our results in the context of earlier studies of
this problem
Decay of magnetohydrodynamic turbulence from power-law initial conditions
No full textWe derive relations for the decay of the kinetic and magnetic energies and the growth of the Taylor and integral scales in unforced, incompressible, homogeneous, and isotropic three-dimensional magnetohydrodynamic (3DMHD) turbulence with power-law initial energy spectra. We also derive bounds for the decay of the cross and magnetic helicities. We then present results from systematic numerical studies of such decay both within the context of a MHD shell model and direct numerical simulations of 3DMHD.We show explicitly that our results about the power-law decay of the energies hold for times t<t*, where t* is the time at which the integral scales become comparable to the system size. For t<t*, our numerical results are consistent with those predicted by the principle of "permanence of large eddies.
Decay of magnetohydrodynamic turbulence from power-law initial conditions
No full textWe derive relations for the decay of the kinetic and magnetic energies and the growth of the Taylor and integral scales in unforced, incompressible, homogeneous, and isotropic three-dimensional magnetohydrodynamic (3DMHD) turbulence with power-law initial energy spectra. We also derive bounds for the decay of the cross and magnetic helicities. We then present results from systematic numerical studies of such decay both within the context of a MHD shell model and direct numerical simulations of 3DMHD. We show explicitly that our results about the power-law decay of the energies hold for times t<t∗, where t∗ is the time at which the integral scales become comparable to the system size. For t<t∗, our numerical results are consistent with those predicted by the principle of "permanence of large eddies"
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