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Tree methods , and the detection of vortical structures in the vortex filament method

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 method. Biot-Savart Integral. Model reconnections algorithmically ‘cut and paste’. Mutual friction.

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Tree methods , and the detection of vortical structures in the vortex filament method

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  1. Tree methods, and the detection of vortical structures in the vortex filament method Andrew Baggaley, Carlo Barenghi, Jason Laurie, Lucy Sherwin, Yuri Sergeev.

  2. Vortex filament method Biot-Savart Integral Model reconnections algorithmically ‘cut and paste’

  3. Mutual friction Counterflow Turbulence 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.

  4. Tree algorithms • Introduced by Barnes & Hut, (Nature, 1986). • De-facto method for astrophysical simulations where gravity is important (e.g. galaxy formation). • Relatively easy to implement numerically. • Acceptable loss of accuracy when compared to full BS integral (AWB & Barenghi, JLTP, 2011). • Significant improvement in speed of code O(NlogN) vs O(N2)

  5. Sensitivity to reconnection algorithm

  6. 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.

  7. Generation of bundles at finite temperatures Vortex Locking - Morris, Koplik & Rouson, PRL, 2008 Gaussian normal fluid vortex – Samuels, PRB, 1993

  8. Reconnections:Bundles remain intact Alamri, Youd& Barenghi, PRL, 2008

  9. 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?

  10. Detecting structures

  11. The importance of vortex bundles AWB, PoF, 2012

  12. A surprising result • 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 polarisedcomponent, and a random component. • Random component advected as a passive scalar explaining scaling. Roche et al., EPL, 2007

  13. 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.

  14. Decomposition of the tangle AWB, Laurie & Barenghi, PRL, 2012

  15. Numerical results Left, frequency spectra (red polarised ; black total), right energy spectrum, upper random component, lower polarised component. AWB, Laurie & Barenghi, PRL, 2012

  16. Thermally vs Mechanically Driven Multi-scale flow, summation of random Fourier modes with imposed Kolmogorov spectrum. AWB, Sherwin, Barenghi, Sergeev, PRB, 2012.

  17. Generation of bundles via shear flow

  18. Kelvin-Helmholtz rollup

  19. The End

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