Tree methods, and the detection of vortical structures in the vortex
filament method
Andrew Baggaley, Carlo Barenghi, Jason Laurie, Lucy
Sherwin, Yuri Sergeev.
Vortex filament methodBiot-Savart Integral
Model reconnections algorithmically ‘cut and paste’
Mutual friction
Normal viscous fluid coupled to inviscid superfluid via mutual friction.
Superfluid component extracts energy from normal fluid component via Donelly-Glaberson instability, amplification of Kelvin waves.
Counterflow Turbulence
Tree algorithmso Introduced by Barnes &
Hut, (Nature, 1986).o De-facto method for
astrophysical simulations where gravity is important (e.g. galaxy formation).
o Relatively easy to implement numerically.
o Acceptable loss of accuracy when compared to full BS integral (AWB & Barenghi, JLTP, 2011).
o Significant improvement in speed of code O(NlogN) vs O(N2)
Sensitivity to reconnection algorithm
Coherent structures• In classical turbulence
vorticity is concentrated in vortical ‘worms’ (She & al, Nature, 1990 ; Goto, JFM, 2008)
• Are there vortex bundles in quantum turbulence ?
• Would allow a mechanism for vortex stretching, i.e. stretch the bundle.
Generation of bundles at finite temperatures
Vortex Locking - Morris, Koplik & Rouson, PRL, 2008Gaussian normal fluid vortex – Samuels, PRB, 1993
Reconnections:Bundles
remain intact
Alamri, Youd & Barenghi, PRL, 2008
Some questions…• What are the role of these structures
in QT?• Transfer energy? Allow vortex
stretching.• How can we detect these structures
(aside from our eyes)• How are structures generated?
Detecting structures
The importance of vortex bundles
AWB, PoF, 2012
A surprising result
Roche et al., EPL, 2007
• Fluctuations of vortex line density scale as .
• If we interpret L as a measure of the rms superfluid vorticity.
• Contradiction of the classical scaling of vorticity expected from K41.
• Roche & Barenghi (EPL, 2008) - vortex line density field is decomposed into a polarised component, and a random component.
• Random component advected as a passive scalar explaining scaling.
Quantum turbulence at finite temp.
Drive turbulence in superfluid component to a steady state with imposed normal ‘fluid turbulence’.
Decompose tangle into a polarised and random component.
Measure frequency spectrum of these 2 components, and their contribution to 3D energy spectrum.
Decomposition of the tangle
AWB, Laurie & Barenghi, PRL, 2012
Numerical results
AWB, Laurie & Barenghi, PRL, 2012
Left, frequency spectra (red polarised ; black total), right energy spectrum, upper random component, lower polarised component.
Thermally vs Mechanically Driven
Multi-scale flow, summation of random Fourier modes with imposed Kolmogorov spectrum.
AWB, Sherwin, Barenghi, Sergeev, PRB, 2012.
Generation of bundles via shear flow
Kelvin-Helmholtz rollup
The End