Small-scale dynamo action has been obtained for a flow previously used to model fluid turbulence, where the sensitivity of the magnetic field parameters to the kinetic energy spectrum can be explored. We apply quantitative morphology diagnostics, based on the Minkowski functionals, to magnetic fields produced by the kinematic small-scale dynamo to show that magnetic structures are predominantly filamentary rather than sheet-like. Our results suggest that the thickness, width and length of the structures scale differently with magnetic Reynolds number as R −2/(1−s) m and R −0.55 m for the former two, whereas the latter is independent of Rm, with s the slope of the energy spectrum.PACS numbers: 07.55.Db, 02.40.Pc The fluctuation (or small-scale) dynamo is a turbulent dynamo mechanism where a random flow of electrically conducting fluid generates a random magnetic field with zero mean value (the other type of dynamo relies on deviations of the flow from mirror symmetry, and perhaps other symmetries, and produces mean magnetic fields). This dynamo mechanism appears to be responsible for the random magnetic fields in the interstellar medium [1] and in galaxy clusters [2,3,4]. A necessary condition for the small-scale dynamo is that the magnetic Reynolds number R m is large enough that the random velocity shear dominates over the effects of the fluid's electric resistivity. Here R m = ul/η where u and l are a typical velocity and length-scale respectively and η is the magnetic diffusivity. The critical magnetic Reynolds number, R m,cr , is 30-500, depending on the nature of the flow [5,6,7,9,10,11]. Numerical simulations of the nonlinear, saturated states of the small-scale dynamo have been reviewed in ref. [11], but more insight can be gained by a careful analysis of the kinematic regime where the magnetic field is still too weak to affect the flow. In particular, the turbulent inertial range is undeveloped for the modest values of the Reynolds number achievable in direct numerical simulations; therefore, numerical results are often ambiguous.Here we study the kinematic small-scale dynamo by solving numerically the induction equationfor the magnetic field B in a prescribed flow u(x, t). Unlike other numerical models of the small-scale dynamo, our choice of the velocity field allows us to control fully its energy spectrum and time variation. In particular, the flow has a well pronounced power-law spectral range with controllable spectral slope. We use a spectral model for u, specified in Eq. (2), which was developed as a Lagrangian model of turbulence and contains its essential features: it is three dimensional, time-dependent, multiscale and has transport properties (two-particle dispersion, etc.) which agree remarkably well with those of turbulent flows [13,14] in both experiments and numerical calculations. Therefore, our main results are comparable with numerical experiments [16,17] and to some extent with experimental results [15]. The velocity field u is given bywhere φ n = k n ·x+ω n t, N is the number of m...
We formulate a coarse-grained molecular-dynamics model of polymer chains in solution that includes hydrodynamic interactions, thermal fluctuations, nonlinear elasticity, and topology-preserving solvent mediated excluded volume interactions. The latter involve a combination of potential forces with explicit geometric detection and tracking of chain entanglements. By solving this model with numerical and computational methods, we study the physics of polymer knots in a strong extensional flow (Deborah number De=1.6 ). We show that knots slow down the stretching of individual polymers by obstructing via entanglements the "natural," unraveling, and flow-induced chain motions. Moreover, the steady-state polymer length and polymer-induced stress values are smaller in knotted chains than in topologically trivial chains. We indicate the molecular processes via which the rate of knot tightening affects the rheology of the solution.
By solving pertinent mathematical models with numerical and computational methods, we analyze the formation of superfluid vorticity structures in a turbulent normal fluid with an inertial range exhibiting Kolmogorov scaling. We demonstrate that mutual friction forcing causes quantum vortex instabilities whose signature is spiral vortical configurations. The spirals expand until they accidentally meet metastable, intense normal fluid vorticity tubes of similar curvature and vorticity orientation that trap them by driving them towards low mutual friction sites where superfluid bundles are formed. The bundle formation sites are located within the tube cores, but, due to tube curvature and many-tube interaction effects, are displaced by variable distances from the tube centerlines as they follow the contours of the latter. We analyze possible implications of these processes in fully developed thermal superfluid turbulence dynamics.
We propose an adjustable-parameter-free, entangled chain dynamics model of dense polymer solutions. The model includes the self-consistent dynamics of molecular chains and solvent by describing the former via coarse-grained polymer dynamics that incorporate hydrodynamic interaction effects, and the latter via the forced Stokes equation. Real chain elasticity is modeled via the inclusion of a Pincus regime in the polymer's force-extension curve. Excluded volume effects are taken into account via the combined action of coarse-grained intermolecular potentials and explicit geometric tracking of chain entanglements. We demonstrate that entanglements are responsible for a new (compared to phantom chain dynamics), slow relaxation mode whose characteristic time scale agrees very well with experiment. Similarly good agreement between theory and experiment is also obtained for the equilibrium chain size. We develop methods for the solution of the model in periodic flow domains and apply them to the computation of entangled polymer solutions in equilibrium. We show that the number of entanglements Π agrees well with the number of entanglements expected on the basis of tube theory, satisfactorily reproducing the latter's scaling of Π with the polymer volume fraction φ. Our model predicts diminishing chain size with concentration, thus vindicating Flory's suggestion of excluded volume effects screening in dense solutions. The predicted scaling of chain size with φ is consistent with the heuristic, Flory theory based value.
We have performed self-consistent computations of the interactions between a superfluid vortex-ring and a solid-particle for two different vortex-ring sizes and over a wide range of temperatures. In all cases, the particle and the vortex eventually separate. For temperature T = 0 K, larger rings tend to trap the particle more effectively than smaller rings. Trying to escape the vortex, the particle follows a spiraling trajectory that could be experimentally detected. The dominant dynamical process is the excitation and propagation of Kelvin waves along the vortices. For T > 0 K, particle-vortex collision induces particle-vibrations that are normal to the particle's direction of motion and might be experimentally detectable. In contrast to the T = 0 K case, smaller rings induce larger particle oscillation velocities. With increasing temperature, enhanced mutual friction damping of Kelvin waves leads to the damping of both the intensity and frequency of post-collision particle vibrations. Moreover, higher temperatures increase the relative impact of the Stokes drag force on particle motion.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.