Superfluid spherical Couette flow

Peralta, C.; Melatos, A.; Giacobello, Matteo; Ooi, Andrew

doi:10.1088/1742-6596/150/3/032081

Cited by 9 publications

(22 citation statements)

References 9 publications

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“…A crucial question in statistical theories of thermal superfluid turbulence (Peralta et al 2006(Peralta et al , 2008Andersson et al 2007;Sidery et al 2008) is whether the average (macroscopic) effects of mutual friction could be modelled by an isotropic (Gorter and Mellink) or rectilinear-array-type (Hall & Vinen 1956) laws. The present results suggest that (in homogeneous isotropic turbulence) neither approach is absolutely correct.…”

Section: Resultsmentioning

confidence: 99%

“…Finally, a further coarse-graining of our model would correspond to theories of the HallVinen (Hall & Vinen 1956) and Bekharevich-Khalatnikov (Leggett 2006) type, i.e. to statistical theories of thermal superfluid turbulence (Henderson & Barenghi 2004;Peralta et al 2005Peralta et al , 2006Peralta et al , 2008Andersson, Sidery & Comer 2007;Sidery, Andersson & Comer 2008;Melatos & Peralta 2010). The mathematical difficulties involved in this coarse-graining are great, and our results could guide the relevant analyses.…”

Section: Introductionmentioning

confidence: 85%

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Spreading of superfluid vorticity clouds in normal-fluid turbulence

Kivotides

2010

J. Fluid Mech.

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In this paper, we formulate a self-consistent model of thermal superfluid dynamics. By solving it, we analyse the problem of superfluid vorticity cloud propagation in normal-fluid turbulence. We show that superfluid cloud expansion is driven by pattern-forming superfluid vortex instabilities taking place in the interface layer between the cloud's bulk and the outer undisturbed normal-fluid turbulence. The radius of the cloud increases linearly with time. Mutual friction transfers energy from the normal-fluid turbulence to the superfluid cloud, whilst damping the smallest normal-fluid turbulence motions. This damping action is much weaker than viscous dissipation effects in a corresponding pure normal-fluid turbulence. The energy spectrum of superfluid turbulence presents the k −3 scaling that characterizes the spiral superfluid vorticity patterns of normal vortex tube-superfluid vortex interactions. The corresponding k −2 pressure spectrum signifies the singular nature of superfluid vorticity. These two scalings coincide in wavenumber space with the Kolmogorov regime in the normal-fluid turbulence. We compute a fractal dimension d f ≈ 1.652 for superfluid vorticity. Due to simpler underlying superfluid vortex dynamics in relation to the strongly nonlinear classical vortex dynamics, this fractal dimension is smaller than the corresponding dimension of vortex tube centrelines in classical turbulence.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 85%

Spreading of superfluid vorticity clouds in normal-fluid turbulence

Kivotides

2010

J. Fluid Mech.

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“…Noise in these pulses is probably indicative of irregularities in the pulsar rotation rate. Short-term fluctuations are often interpreted as having been caused by a sudden increase in the angular velocity of the pulsars associated with "starquakes", and a detailed description of the analogy between pulsars and phenomena in SCF can be found in [21]. The rotation of the Earth itself, as measured by space geodetic techniques, is also subject to fluctuations of order 0.1 ms on a variety of timescales, ranging from days to decades and longer [22].…”

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confidence: 99%

Wave number selection in the presence of noise: Experimental results

Zhilenko

Krivonosova

Gritsevich

et al. 2018

Chaos: An Interdisciplinary Journal of Nonlinear Science

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In this study, we consider how the wave number selection in spherical Couette flow, in the transition to azimuthal waves after the first instability, occurs in the presence of noise. The outer sphere was held stationary, while the inner sphere rotational speed was increased linearly from a subcritical flow to a supercritical one. In a supercritical flow, one of two possible flow states, each with different azimuthal wave numbers, can appear depending upon the initial and final Reynolds numbers and the acceleration value. Noise perturbations were added by introducing small disturbances into the rotational speed signal. With an increasing noise amplitude, a change in the dominant wave number from m to m ± 1 was found to occur at the same initial and final Reynolds numbers and acceleration values. The flow velocity measurements were conducted by using laser Doppler anemometry. Using these results, the role of noise as well as the behaviour of the amplitudes of the competing modes in their stages of damping and growth were determined.

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“…Gilman & Fox (1997) have generalized the problem of barotropic instability on a sphere to its hydromagnetic analogue by demonstrating that the differential rotation of the solar photosphere is unstable when a non-uniform toroidal magnetic field is added. Peralta et al (2009) have presented numerical simulations of a superfluid Stewartson layer in the outer core of a differentially rotating neutron star. The nonlinear instability of Stewartson layers can even relate to Keplerian accretion disks, as discussed in § 2.…”

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confidence: 99%

Linear stability analysis of a shear layer induced by differential coaxial rotation within a cylindrical enclosure

Montabone

Sheard

2013

J. Fluid Mech.

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The generation of distinct polygonal configurations via the instability of a Stewartson shear layer is numerically investigated. The shear layer is induced using a rotating cylindrical tank with differentially forced disks located at the top and bottom boundaries. The incompressible Navier–Stokes equations are solved on a two-dimensional semi-meridional plane. Axisymmetric base flows are consistently found to reach a steady state for a wide range of flow conditions, and details of the vertical structure are revealed. An axially invariant two-dimensional flow is ascertained for small $\vert \mathit{Ro}\vert $, which substantiates the Taylor–Proudman theorem. Sufficient increases in $\vert \mathit{Ro}\vert $ forcing develops flow features that break this quasi-two-dimensionality. The onset of this breaking occurs earlier with increasing $\vert \mathit{Ro}\vert $ for $\mathit{Ro}\gt 0$ compared with $\mathit{Ro}\lt 0$. The thickness scaling of the vertical Stewartson layers are in agreement with previous analytical results. Growth rates of the most unstable azimuthal wavenumber from a global linear stability analysis are obtained. The threshold between axisymmetric and non-axisymmetric flow follows a power law, and both positive- and negative-$\mathit{Ro}$ regimes are found to adopt the same threshold for instability, namely $\vert \mathit{Ro}\vert \geq 18. 1{E}^{0. 767} $. This relationship corresponds to a constant critical internal Reynolds number of ${\mathit{Re}}_{i, c} \simeq 22. 5$. A review of reported critical internal Reynolds number and their characteristic length scales yields a consistent instability onset given by $\vert \mathit{Ro}\vert / {E}^{3/ 4} = 15. 4{\unicode{x2013}} 16. 6$; here we find $\vert \mathit{Ro}\vert / {E}^{3/ 4} = 15. 8$. At the onset of linear instability, the initially circular shear layer deforms, resulting in a polygonal structure consistent with barotropic instability. Dominant azimuthal wavenumbers range from $3$ to $7$ at the onset of instability for the parameter space explored. Empirical relationships for the preferential wavenumber have been obtained. Additional instability modes have been discovered that favour higher wavenumbers, and these exhibit structures localized to the disk–tank interfaces.

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Superfluid spherical Couette flow

Cited by 9 publications

References 9 publications

Spreading of superfluid vorticity clouds in normal-fluid turbulence

Spreading of superfluid vorticity clouds in normal-fluid turbulence

Wave number selection in the presence of noise: Experimental results

Linear stability analysis of a shear layer induced by differential coaxial rotation within a cylindrical enclosure

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