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Carlo F. Barenghi

Publications and source records attributed to Carlo F. Barenghi.

64 records · Page 4Linked to original sources
arXiv2004

Torsional Oscillations of a Rotating Column of $^3$He-B

We have analysed the axisymmetric and non-axisymmetric modes of a continuum of vortices in a rotating superfluid. We have investigated how changing the temperature affects the growth rate of the disturbances. We find that, in the long axial wavelength limit the condition q=alpha/(1-alpha')=1, where alpha and alpha' are temperature-dependent mutual friction parameters, is the crossover between damped and propagating Kelvin waves. Thus at temperatures for which q>1, perturbations on the vortices are unlikely to cause vortex reconnections and turbulence. These results are in agreement with the recent discovery of Finne et al (2003} of an intrinsic condition for the onset of quantum turbulence in $^3$He-B.

cond-mat.soft↗
arXiv2004

Vortex nucleation by collapsing bubbles in Bose-Einstein condensates

The nucleation of vortex rings accompanies the collapse of ultrasound bubbles in superfluids. Using the Gross-Pitaevskii equation for a uniform condensate we elucidate the various stages of the collapse of a stationary spherically symmetric bubble and establish conditions necessary for vortex nucleation. The minimum radius of the stationary bubble, whose collapse leads to vortex nucleation, was found to be about 28 healing lengths. The time after which the nucleation becomes possible is determined as a function of bubble's radius. We show that vortex nucleation takes place in moving bubbles of even smaller radius if the motion made them sufficiently oblate.

cond-mat.soft↗
arXiv2003

Instability of vortex array and transitions to turbulent states in rotating helium II

We consider superfluid helium inside a container which rotates at constant angular velocity and investigate numerically the stability of the array of quantized vortices in the presence of an imposed axial counterflow. This problem was studied experimentally by Swanson {\it et al.}, who reported evidence of instabilities at increasing axial flow but were not able to explain their nature. We find that Kelvin waves on individual vortices become unstable and grow in amplitude, until the amplitude of the waves becomes large enough that vortex reconnections take place and the vortex array is destabilized. The eventual nonlinear saturation of the instability consists of a turbulent tangle of quantized vortices which is strongly polarized. The computed results compare well with the experiments. Finally we suggest a theoretical explanation for the second instability which was observed at higher values of the axial flow.

cond-mat.soft↗
arXiv2002

Polarization of superfluid turbulence

We show that normal fluid eddies in turbulent helium II polarize the tangle of quantized vortex lines present in the flow, thus inducing superfluid vorticity patterns similar to the driving normal fluid eddies. We also show that the polarization is effective over the entire inertial range. The results help explain the surprising analogies between classical and superfluid turbulence which have been observed recently.

cond-mat↗
arXiv2002

Hydromagnetic Taylor--Couette flow: numerical formulation and comparison with experiment

Taylor--Couette flow in the presence of a magnetic field is a problem belonging to classical hydromagnetics and deserves to be more widely studied than it has been to date. In the nonlinear regime the literature is scarce. We develop a formulation suitable for solution of the full three dimensional nonlinear hydromagnetic equations in cylindrical geometry, which is motived by the formulation for the magnetic field. It is suitable for study at finite magnetic Prandtl numbers and in the small Prandtl number limit, relevant to laboratory liquid metals. The method is used to determine the onset of axisymmetric Taylor vortices, and finite amplitude solutions. Our results compare well with existing linear and nonlinear hydrodynamic calculations and with hydromagnetic experiments.

astro-ph↗
arXiv2002

Hydromagnetic Taylor--Couette flow: wavy modes

We investigate magnetic Taylor--Couette flow in the presence of an imposed axial magnetic field. First we calculate nonlinear steady axisymmetric solutions and determine how their strength depends on the applied magnetic field. Then we perturb these solutions to find the critical Reynolds numbers for the appearance of wavy modes, and the related wavespeeds, at increasing magnetic field strength. We find that values of imposed magnetic field which alter only slightly the transition from circular--Couette flow to Taylor--vortex flow, can shift the transition from Taylor--vortex flow to wavy modes by a substantial amount. The results are compared against onset in the absence of a magnetic field.

astro-ph↗
arXiv2002

Magnetic instability in a sheared azimuthal flow

We study the magneto-rotational instability of an incompressible flow which rotates with angular velocity Omega(r)=a+b/r^2 where r is the radius and $a$ and b are constants. We find that an applied magnetic field destabilises the flow, in agreement with the results of Rudiger & Zhang 2001. We extend the investigation in the region of parameter space which is Rayleigh stable. We also study the instability at values of magnetic Prandtl number which are much larger and smaller than Rudiger & Zhang. Large magnetic Prandtl numbers are motivated by their possible relevance in the central region of galaxies (Kulsrud & Anderson 1992). In this regime we find that increasing the magnetic Prandtl number greatly enhances the instability; the stability boundary drops below the Rayleigh line and tends toward the solid body rotation line. Very small magnetic Prandtl numbers are motivated by the current MHD dynamo experiments performed using liquid sodium and gallium. Our finding in this regime confirms Rudiger & Zhang's conjecture that the linear magneto-rotational instability and the nonlinear hydrodynamical instability (Richard & Zahn 1999) take place at Reynolds numbers of the same order of magnitude.

astro-ph↗
arXiv2002

A Taylor-Couette Dynamo

Recent experiments have shown that it is possible to study a fundamental astrophysical process such as dynamo action in controlled laboratory conditions using simple MHD flows. In this paper we explore the possibility that Taylor-Couette flow, already proposed as a model of the magneto-rotational instability of accretion discs, can sustain generation of magnetic field. Firstly, by solving the kinematic dynamo problem, we identify the region of parameter space where the magnetic field's growth rate is higher. Secondly, by solving simultaneously the coupled nonlinear equations which govern velocity field and magnetic field, we find a self-consistent nonlinearly saturated dynamo.

astro-ph↗
arXiv2002

Competition between rotation and turbulence in superfluid He$^4$

Two types of vortex states have been much studied in superfluid $^4$He. The first is the vortex array in a rotating container. The second is the vortex tangle in turbulent flow. An experiment attempt to combine these two states by rotating a counterflow was attempted years ago. The data suggest the existence of different flow regimes separated by instabilities, but a theoretical interpretation is still missing. We present work in which we use the vortex filament model to numerically investigate rotating counterflow. We show evidence of a new state of polarized turbulence.

cond-mat.soft↗