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Spreading of superfluid vorticity clouds in normal-fluid turbulence

Published online by Cambridge University Press:  16 December 2010

DEMOSTHENES KIVOTIDES
DEMOSTHENES KIVOTIDES*
Affiliation:
Department of Chemical Engineering, University of California, Santa Barbara, CA 93117, USA
*
†Email address for correspondence: demos@engineering.ucsb.edu
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Abstract

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 df ≈ 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.

JFM classification

Complex Fluids: Quantum fluids Turbulent Flows: Turbulent Flows Vortex Flows: Vortex Flows

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Papers
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Journal of Fluid Mechanics , Volume 668 , 10 February 2011 , pp. 58 - 75
Copyright
Copyright © Cambridge University Press 2010

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