SPIN UP, SPIN DOWN AND PROPAGATION OF TURBULENT FRONTS IN SUPERFLUIDS

Transcription

1 SPIN UP, SPIN DOWN AND PROPAGATION OF TURBULENT FRONTS IN SUPERFLUIDS Vladimir Eltsov Low Temperature Laboratory, Aalto University ROTA group: Rob de Graaf, Petri Heikkinen, Jaakko Hosio, Risto Hänninen, Matti Krusius In collaboration with: Victor L vov, Weizmann Institute David Schmoranzer, Charles University Grigori Volovik, Aalto University Paul Walmsley, Manchester University

2 SPIN-UP AND SPIN-DOWN IN SUPERFLUIDS Problem of coupling of different subsystems: Normal fluid viscosity η Container (reference frame)

3 SPIN-UP AND SPIN-DOWN IN SUPERFLUIDS Problem of coupling of different subsystems: Normal component viscosity η Superfluid component (quantized vortices) Container (reference frame)

4 SPIN-UP AND SPIN-DOWN IN SUPERFLUIDS Problem of coupling of different subsystems: Normal component mutual friction α viscosity η Container (reference frame) Superfluid component (quantized vortices) pinning/surface friction

5 SPIN-UP AND SPIN-DOWN IN SUPERFLUIDS Problem of coupling of different subsystems: Normal component mutual friction α viscosity η Container (reference frame) Superfluid component (quantized vortices) pinning/surface friction Additional complications: Laminar or turbulent?

6 SPIN-UP AND SPIN-DOWN IN SUPERFLUIDS Problem of coupling of different subsystems: Normal component mutual friction α viscosity η Container (reference frame) Superfluid component (quantized vortices) pinning/surface friction Additional complications: Laminar or turbulent? Homogeneous or inhomogeneous along the rotation axis?

7 SPIN-UP AND SPIN-DOWN IN SUPERFLUIDS Problem of coupling of different subsystems: Normal component mutual friction α viscosity η Container (reference frame) Superfluid component (quantized vortices) pinning/surface friction Additional complications: Laminar or turbulent? Homogeneous or inhomogeneous along the rotation axis? For spin-up: formation of quantized vortices?

8 SPIN-UP AND SPIN-DOWN IN SUPERFLUID 4He Series of works by J.S. Tsakadze and S.J. Tsakadze One of the latest and most advanced: P.W. Adams, M. Cieplack and W.I. Glaberson, PRB 32, 171 (1985). Levitating (superconducting) sample chamber Superconducting, contactless, computer-controlled drive

9 SPIN-UP AND SPIN-DOWN IN SUPERFLUID 4He Series of works by J.S. Tsakadze and S.J. Tsakadze One of the latest and most advanced: P.W. Adams, M. Cieplack and W.I. Glaberson, PRB 32, 171 (1985). smooth walls, T = 1.3 K rad/s viscous-like rough walls, T = 1.3 K rad/s viscous-like strong pinning

10 SIMPLE MODEL OF SPIN-UP AND SPIN-DOWN Assumptions: Normal component is in equilibrium rotation v n = r. Superfluid vorticity is homogeneous ω s = v s = 2 s (t), v s = s r. Then coarse-grained equations of superfluid hydrodynamics v s t + (v s )v s + µ = α ω s (v s v n ) + α ˆω s [ω s (v n v s )] are simplified to d s dt = 2 α s ( s ).

11 SIMPLE MODEL OF SPIN-UP AND SPIN-DOWN Assumptions: Normal component is in equilibrium rotation v n = r. Superfluid vorticity is homogeneous ω s = v s = 2 s (t), v s = s r. Then coarse-grained equations of superfluid hydrodynamics v s t + (v s )v s + µ = α ω s (v s v n ) + α ˆω s [ω s (v n v s )] are simplified to d s dt = 2 α s ( s ). Spin-up to = 0 : s (t) = ε 0 ε + (1 ε)exp( t/τ ), s(0) = ε 0. τ (T ) = [2α(T ) 0 ] 1

12 SIMPLE MODEL OF SPIN-UP AND SPIN-DOWN Assumptions: Normal component is in equilibrium rotation v n = r. Superfluid vorticity is homogeneous ω s = v s = 2 s (t), v s = s r. Then coarse-grained equations of superfluid hydrodynamics v s t + (v s )v s + µ = α ω s (v s v n ) + α ˆω s [ω s (v n v s )] are simplified to d s dt = 2 α s ( s ). Spin-up to = 0 : s (t) = ε 0 ε + (1 ε)exp( t/τ ), s(0) = ε 0. Spin-down to = 0: s (t) = t/τ, s (0) = 0. τ (T ) = τ (T ) = [2α(T ) 0 ] 1

13 SIMPLE MODEL OF SPIN-UP AND SPIN-DOWN Assumptions: Normal component is in equilibrium rotation v n = r. Superfluid vorticity is homogeneous ω s = v s = 2 s (t), v s = s r. Then coarse-grained equations of superfluid hydrodynamics v s t + (v s )v s + µ = α ω s (v s v n ) + α ˆω s [ω s (v n v s )] are simplified to d s dt = 2 α s ( s ). Spin-up to = 0 : s (t) = ε 0 ε + (1 ε)exp( t/τ ), s(0) = ε 0. Spin-down to = 0: s (t) = t/τ, s (0) = 0. τ (T ) = τ (T ) = [2α(T ) 0 ] 1 Coupled normal-superfluid dynamics was also solved (for small Rossby numbers), e.g. Reisenegger, JLTP 92, 77 (1993); van Eysden and Melatos, MNRAS 409, 1253 (2010).

14 quartz cell EXPERIMENTAL SETUP Rotating cryostat: NMR sample ( 6 110mm) NMR pick-up coils Velocity up to 3rad/s Heat leak to sample < 30pW to heat exchanger

15 quartz cell EXPERIMENTAL SETUP Rotating cryostat: NMR sample ( 6 110mm) NMR pick-up coils black-body radiator Velocity up to 3rad/s Heat leak to sample < 30pW orifice 0.75mm quartz tuning forks orifice 0.3mm to heat exchanger

16 quartz cell EXPERIMENTAL SETUP Rotating cryostat: Velocity up to 3rad/s NMR sample ( 6 110mm) 3 3 He-B He-A NMR pick-up coils Heat leak to sample < 30pW orifice 0.75mm quartz tuning forks black-body radiator orifice 0.3mm to heat exchanger

17 NMR MEASUREMENTS OF THE FLOW PROFILES Counterflow peak in the cw NMR spectrum depends primarily on v n v s : Absorption, arb.un bar, 0.22T, rad/s Calibrated in the c vortex-free state f - f Larmor, khz v v s = 0 R v n = r r

18 NMR MEASUREMENTS OF THE FLOW PROFILES Counterflow peak in the cw NMR spectrum depends primarily on v n v s : Absorption, arb.un. CF absorption, arb.un bar, 0.22T, rad/s Calibrated in the c vortex-free state f - f Larmor, khz s, rad/s f CF - f Larmor, khz v v v n = 0 v s = 0 R v n = r r Used to find s during spin-up and spin-down v n = r v s = s r r

19 OBSERVATION OF THE SPIN-DOWN The laminar dependence s = 0 /(1+t/τ ) and the solid-body velocity profile: s, rad/s exper. T = 0.24 T c fit: 0 = 1.47 rad/s τ = 106 s time, s CF absorption calibration spin-down T = 0.21 T c f CF - f Larmor, khz

20 OBSERVATION OF THE SPIN-DOWN The laminar dependence s = 0 /(1+t/τ ) and the solid-body velocity profile: s, rad/s exper. T = 0.24 T c fit: 0 = 1.47 rad/s τ = 106 s time, s CF absorption calibration spin-down T = 0.21 T c f CF - f Larmor, khz spin-down T = 0.21 T c s, rad/s fit: 0 = 0.96 rad/s τ = 737 s Long-time relaxation can be probed with spin-ups time, s

21 THE SPIN-DOWN TIME P = 29 bar τ experiment α from Bevan et al 1997 (extrapolation) T c /T Spin-down in 3 He-B is laminar at least up to Re α = 1 α α 10 3 PRL 105, (2010)

22 THE SPIN-DOWN TIME P = 29 bar τ experiment α from Bevan et al 1997 (extrapolation) T c /T Spin-down in 3 He-B is laminar at least up to Re α = 1 α α Compare with: 10 3 PRL 105, (2010) For other types of flow in 3 He-B transition to turbulence at Re α In classical fluids impulsive spin-down to rest is turbulent.

23 SPIN-DOWN IN THE SIMULATIONS With ideal symmetric starting conditions spin-down follows analytic solution.

24 SPIN-DOWN IN THE SIMULATIONS With ideal symmetric starting conditions spin-down follows analytic solution. Perturbation? Inclination of the cylinder η = 2 (in the experiment η 1 ). t = 0 6mm 6mm 0 = 0.5rad/s, T = 0.22T c

25 SPIN-DOWN IN THE SIMULATIONS With ideal symmetric starting conditions spin-down follows analytic solution. Perturbation? Inclination of the cylinder η = 2 (in the experiment η 1 ). t = 0 t = 100s t = 1000s 6mm 6mm 0 = 0.5rad/s, T = 0.22T c

26 SPIN-DOWN IN THE SIMULATIONS With ideal symmetric starting conditions spin-down follows analytic solution. Perturbation? Inclination of the cylinder η = 2 (in the experiment η 1 ) polarization p 2 z simulation and fit to the laminar model: L(t) L(0) = t/τ with τ = 239s τ laminar = 1/(2α 0 ) = 231s t Simulation demonstrates laminar behaviour. 0 = 0.5rad/s, T = 0.22T c

27 WHEN SPIN-DOWN BECOMES TURBULENT? This is a problem which is not yet fully understood. In simulations both turbulent boundary layer and Kelvin waves exsist, but they do not change the character of the process at these temperature T and perturbation η. Number of reconnections Total reconnections: = 0.5rad/s T = 0.22T c α = Distance from axis, mm

28 WHEN SPIN-DOWN BECOMES TURBULENT? Transition is seen in simulations with increase of η at constant T. L(t)/L(0) 1.5 η = 45 : turbulent 1 η = 2 : laminar t

29 WHEN SPIN-DOWN BECOMES TURBULENT? Transition is seen in simulations with increase of η at constant T. L(t)/L(0) 1.5 η = 45 : turbulent 1 η = 2 : laminar t What happens when T 0 and Re α? log η turbulent Is there scaling similar to classical liquid in a circular pipe? η c Re 1 laminar [Hof et al, PRL 91, (2003)] log Re α

30 Caroli, de Gennes, Matricon 1964 BOUND FERMION STATES IN THE VORTEX CORE Radial quantum number n (n max a/ξ). Anomalous (crossing zero) branch n = 0. y n = 0 ε n (p z = 0, µ) n max 1 a x hω 0 µ/p F a Andreev reflection y b hole particle x Angular momentum µ = b p, quantized. µ/ h = { m + 1/2, s-wave superconductors m, superfluid 3 He Minigap ω 0 a p F 1 h 2 E F h.

31 n = 0 hω 0 MUTUAL FRICTION FROM BOUND FERMIONS µ/p F a Angular momentum µ = r p. Vortex motion r r (v L v n )t leads to pumping of q.p. along anomalous branch (spectral flow). Relaxation (τ) towards equilibrium distribution via interaction with bulk q.p. results in force ω 0 τ (T ) with D = ρκ 1 + ω0 2 tanh τ2 2T, F N = D(v n v L ) + D ẑ (v n v L ) D = ρκ [ ] 1 ω2 0 τ2 (T ) 1 + ω0 2 tanh ρ n κ τ2 2T

32 n = 0 hω 0 MUTUAL FRICTION FROM BOUND FERMIONS µ/p F a Angular momentum µ = r p. Vortex motion r r (v L v n )t leads to pumping of q.p. along anomalous branch (spectral flow). Relaxation (τ) towards equilibrium distribution via interaction with bulk q.p. results in force ω 0 τ (T ) with D = ρκ 1 + ω0 2 tanh τ2 2T, F N = D(v n v L ) + D ẑ (v n v L ) D = ρκ [ ] 1 ω2 0 τ2 (T ) 1 + ω0 2 tanh ρ n κ τ2 2T Simon memorial prize 2011: Nikolai Kopnin Sergey Iordanskii

33 n = 0 hω 0 MUTUAL FRICTION FROM BOUND FERMIONS µ/p F a Angular momentum µ = r p. Vortex motion r r (v L v n )t leads to pumping of q.p. along anomalous branch (spectral flow). Relaxation (τ) towards equilibrium distribution via interaction with bulk q.p. results in force ω 0 τ (T ) with D = ρκ 1 + ω0 2 tanh τ2 2T, F N = D(v n v L ) + D ẑ (v n v L ) D = ρκ [ ] 1 ω2 0 τ2 (T ) 1 + ω0 2 tanh ρ n κ τ2 2T Simon memorial prize 2011: Nikolai Kopnin Sergey Iordanskii Re α = 1 α α = 1 D /κρ s D/κρ s = ω 0 τ T T c : ω 0 2 /E F 0 Re α 0 T 0 : τ τ n exp T Re α

34 n = 0 hω 0 MUTUAL FRICTION FROM BOUND FERMIONS µ/p F a Angular momentum µ = r p. Vortex motion r r (v L v n )t leads to pumping of q.p. along anomalous branch (spectral flow). Relaxation (τ) towards equilibrium distribution via interaction with bulk q.p. results in force ω 0 τ (T ) with D = ρκ 1 + ω0 2 tanh τ2 2T, F N = D(v n v L ) + D ẑ (v n v L ) D = ρκ [ ] 1 ω2 0 τ2 (T ) 1 + ω0 2 tanh ρ n κ τ2 2T Simon memorial prize 2011: Nikolai Kopnin Sergey Iordanskii Re α = 1 α α = 1 D /κρ s D/κρ s = ω 0 τ T T c : ω 0 2 /E F 0 Re α 0 T 0 : τ τ n exp T Re α T T c : α can be ignored α exp( /T )

35 COMPARISON WITH THE EXPERIMENT Theory agrees with the measurements fairly well: D/κρ s D /κρ s 1 Bevan et al bar T/T c One fitting parameter: scale of ω 0 τ

36 APPLICATION OF SPIN-DOWN TO MUTUAL FRICTION MEASUREMENTS Simulations: Output α 10-2 y = x Input α

37 APPLICATION OF SPIN-DOWN TO MUTUAL FRICTION MEASUREMENTS Simulations: Measurements: bar Output α 10-2 y = x 10-1 exp( /T) α Input α 10-2 Bevan et al spin down T c /T

38 APPLICATION OF SPIN-DOWN TO MUTUAL FRICTION MEASUREMENTS Simulations: Measurements: bar Output α 10-2 y = x 10-1 exp( /T) α Input α Open questions in T 0 limit: 10-2 Finite τ (walls, kinks) and thus finite α? Bevan et al spin down Core states "overflow" and v L -dependent α? Interaction with Kelvin waves? T c /T

39 SPIN-DOWN IN A TWO-PHASE SAMPLE Spin-down is different when AB phase boundary is present in the sample. A B Two B-phase vortices are connected to an A-phase vortex through the interface

40 SPIN-DOWN IN A TWO-PHASE SAMPLE Spin-down is different when AB phase boundary is present in the sample. Not solid-body: A B Two B-phase vortices are connected to an A-phase vortex through the interface CF absorption s, rad/s calibration spin-down T = 0.21 T c f CF - f Larmor, khz AB Much faster: B only T = 0.21 T c time, s Turbulence or other process?

41 AXIALLY HOMOGENEOUS SPIN-UP Homogeneous spin-up is observed when many vortices (dynamic remnants) are pre-exsisting. Such spin-up shows laminar-like features, but relaxation s, rad/s fit s = ε = τ = 279s ε 0 ε + (1 ε)exp( t/τ ) exper. T = 0.21T c 0 = 1.1rad/s time, s time is often longer than expected.

42 AXIALLY HOMOGENEOUS SPIN-UP Homogeneous spin-up is observed when many vortices (dynamic remnants) are pre-exsisting. Such spin-up shows laminar-like features, but relaxation s, rad/s fit s = ε = τ = 279s ε 0 ε + (1 ε)exp( t/τ ) exper. T = 0.21T c 0 = 1.1rad/s time, s τ 0 time is often longer than expected spin-down α T c /T Vortex formation process intervenes?

43 AXIALLY HOMOGENEOUS SPIN-UP Homogeneous spin-up is observed when many vortices (dynamic remnants) are pre-exsisting. Such spin-up shows laminar-like features, but relaxation s, rad/s fit s = ε = τ = 279s ε 0 ε + (1 ε)exp( t/τ ) exper. T = 0.21T c 0 = 1.1rad/s time, s τ 0 time is often longer than expected α 1/2 spin-down α T c /T Vortex formation process intervenes?

44 VORTEX FRONT IN ROTATING He-B Axially non-uniform spin-up of superfluid in a long column: z 3 V V Expansion of vorticity reduces free energy Excess free energy πρ s 2 R 4 /4 per unit v n v s height R

45 VORTEX FRONT IN ROTATING He-B Axially non-uniform spin-up of superfluid in a long column: z 3 Expansion of vorticity Mutual friction dissipation V V reduces free energy coefficient α, velocity scale R, Excess free energy πρ s 2 R 4 /4 per unit expansion velocity v n v s height V α R R Friction α 0 when T 0 Vortex expansion becomes turbulent. Finite dissipation and expansion velocity V α R. Example of a steady-state turbulent state.

46 4 PROPAGATING TURBULENT FRONT IN He Turbulent state in the counterflow experiment is often established via propagation of a vortex front: Originally observed by K. Mendelssohn and W.A. Steele in Experimentally studied by Peshkov and Tkachenko (1961), van Sciver (1979), van Beelen et al ( ) and others. Theoretical explanations by Tough et al (1995), Nemirovskii (2010).

47 Scaled CF peak absorption 0 1 FRONT PROPAGATION AT LOW TEMPERATURES 1 0 Time, s bottom top = 1.2rad/s T = 0.38T c α = 0.19 T = 0.25T c α =

48 Scaled CF peak absorption 0 1 FRONT PROPAGATION AT LOW TEMPERATURES Time, s bottom top = 1.2rad/s T = 0.38T c α = 0.19 T = 0.25T c α = T = 0.22T c α = T = 0.20T c α =

49 PROPAGATION VELOCITY P = 29bar turbulent laminar V const α R V α R 0.6 V/( R) 10-2 exp( /T ) =1.97T c exper. α meas. α(t) model V/( R) T c /T T/T c PRL 99, (2007)

50 BOTTLENECK EFFECT Suggested by L'vov, Nazarenko and Rudenko [PRB 76, (2007)] for polarized systems where reconnections are suppressed and Kelvin waves are the main energy transfer mechanism at sub-intervortex scales. Energy density k?/?, Kelvin-wave cascade increase to keep the same flux k 5/3, Kolmogorov cascade k

51 BOTTLENECK EFFECT Suggested by L'vov, Nazarenko and Rudenko [PRB 76, (2007)] for polarized systems where reconnections are suppressed and Kelvin waves are the main energy transfer mechanism at sub-intervortex scales. Energy density k?/?, Kelvin-wave cascade increase to keep the same flux k 5/3, Kolmogorov cascade k quantum crossover scale

52 BOTTLENECK EFFECT Suggested by L'vov, Nazarenko and Rudenko [PRB 76, (2007)] for polarized systems where reconnections are suppressed and Kelvin waves are the main energy transfer mechanism at sub-intervortex scales. distorted spectra Energy density k?/?, Kelvin-wave cascade increase to keep the same flux dissipation decreases k 5/3, Kolmogorov cascade k quantum crossover scale

53 BOTTLENECK EFFECT Suggested by L'vov, Nazarenko and Rudenko [PRB 76, (2007)] for polarized systems where reconnections are suppressed and Kelvin waves are the main energy transfer mechanism at sub-intervortex scales. distorted spectra Energy density k?/?, Kelvin-wave cascade increase to keep the same flux dissipation decreases k 5/3, Kolmogorov cascade k quantum crossover scale At sufficiently large mutual friction no energy reaches the crossover scale bottleneck disappears.

54 THERMAL POWER MEASUREMENTS are based on temperature increase across calibrated thermal impedance. heater thermometer impedance (orifice 0.2mm) assumed T = 0 Calibration interpretation ballistic quasiparticle transport through a hole: Effective area 0.02mm 2 and -dependent Andreev reflection. Residual heat leak 13 30pW, strongly -dependent.

55 THERMAL POWER MEASUREMENTS are based on temperature increase across calibrated thermal impedance. heater thermometer impedance (orifice 0.2mm) assumed T = 0 Power, pw Calibration interpretation ballistic quasiparticle transport through a hole: Effective area 0.02mm 2 and -dependent Andreev reflection. 0.5 Residual heat leak 13 30pW, strongly -dependent. Sensitivity 0.1pW and thermal time constant 25s. 1 meas pw applied T = 0.21 T c = 1rad/s time,s

56 TRIGGERING FRONT WITH AB INTERFACE INSTABILITY 3 He-B < cab (T, H H=HAB ) 3 He-A barrier magnet with current I b PRL 89, (2002)

57 TRIGGERING FRONT WITH AB INTERFACE INSTABILITY 3 He-B = cab (T, H H=HAB ) 3 He-A barrier magnet with current I b PRL 89, (2002)

58 TRIGGERING FRONT WITH AB INTERFACE INSTABILITY Vortex injection at = const: Decreasing I b until cab drops to. Increasing I b until A phase forms. 3 He-B 43mm = cab (T, H H=HAB ) 3 He-A barrier magnet with current I b PRL 89, (2002)

59 THERMAL SIGNAL FROM THE FRONT PROPAGATION A phase formation at = 1.2 rad/s 21 Power, pw A phase formation t - t trig, s

60 THERMAL SIGNAL FROM THE FRONT PROPAGATION A phase formation at = 1.2 rad/s 21 Power, pw A phase formation t - t trig, s

61 THERMAL SIGNAL FROM THE FRONT PROPAGATION A phase formation at = 1.2 rad/s Integrated energy: nJ Total original energy: 1.01nJ Power, pw 20 Front arrives to the end of the sample (from NMR) Only 24% of the energy is released by the end of front motion Vortex state behind the front 19 A phase formation is far from the equilibrium. Following relaxation has laminar t - t trig, s time scale.

62 Power, pw THERMAL SIGNAL FROM THE FRONT PROPAGATION A phase formation at = 1.2 rad/s Integrated energy: Front arrives to the end of the sample (from NMR) A phase formation t - t trig, s These properties are universal and observed for different and trigger. Power, pw t - t trig, s 0.75nJ Total original energy: 1.01nJ Only 24% of the energy is released by the end of front motion Vortex state behind the front is far from the equilibrium. Following relaxation has laminar time scale. = 1.0rad/s A form AB instab t - t detect, s

63 INTERPRETATION OF THE THERMAL SIGNAL Model: Turbulent front which creates fraction ε of equlibrium amount of vortices followed by relaxation via laminar spin-up with time τ. Power, pw exper. = 1.2 rad/s fit ε = 0.35, τ = 496 s t - t trig, s

64 VORTEX FRONT IN SIMULATIONS Deficit of vortices behind the front in simulations rapidly increases with decrease of T below 0.3 T c. s, rad/s T c 0.25 T c 0.22 T c = 1rad/s Turbulent front rotates with s / T c Reconnections per 0.5mm motion T c T c T c 0.20 T c z, mm Solid-body rotation with s < T = 0.25 T c

65 FRONT ROTATION IN THE EXPERIMENT Vortex arrangement is not axially symmetric and rotates NMR signal is periodically modified. M, arb.un. = 1.02 rad/s front arrives to coil time, s

66 FRONT ROTATION IN THE EXPERIMENT Vortex arrangement is not axially symmetric and rotates NMR signal is periodically modified. M, arb.un. = 1.02 rad/s front arrives to coil time, s Estimation for precession: cluster: s front: s /2 (in simulations 0.65 s ) M spectral ampl Frequency, Hz

67 COMPETITION OF ROTATING FRAMES Superfluid behind the front feels two rotating frames: Container via normal component. Parameter Re α = 1 α α Front s /2 via vortex line tension. Parameter Re λ = UR/λ. friction tension s s /2 ( U = R, λ = κ 4π 1 α. ln intervortex spacing core size ) Quasi-equilibrium vortex density behind the front: s = f (Re α,re λ ).

68 COMPETITION OF ROTATING FRAMES Superfluid behind the front feels two rotating frames: Container via normal component. Parameter Re α = 1 α α Front s /2 via vortex line tension. Parameter Re λ = UR/λ. friction tension s s /2 ( U = R, λ = κ 4π 1 α. ln intervortex spacing core size ) Quasi-equilibrium vortex density behind the front: s = f (Re α,re λ ). Simple interpolation: s = Re α /Re λ s/ behind the front model rotation in the front α

69 DEPENDENCE OF THE FRONT VELOCITY ON ROTATION Front velocity: V = α eff s R T c (α eff α for laminar flow) Coupled regime: s, V. Decoupled regime: s Re λ Re α, V 2. V/( R) T c , rad/s

70 DEPENDENCE OF THE FRONT VELOCITY ON ROTATION Front velocity: V = α eff s R. (α eff α for laminar flow) 0.17T c 0.5 bar Coupled regime: s, V. Decoupled regime: s Re λ Re α, V 2. V/( R) 0.20T c 29 bar , rad/s Pressure dependence is not clear at the moment. Effect of the core size? (Core is 3x smaller at the lower pressure.)

71 SUMMARY Spin-up and spin-down Are complicated processes in superfluids with interactions between various subsystems. In 3 He-B case with only one essential coupling, mutual friction between normal and superfluid components, can be studied. When coupling to the reference frame happens effectively over the whole volume spin-down and spin-up processes take very simple laminar form, which is confirmed experimentally in 3 He-B up to Re α Open questions: Is there transition to turbulence when Re α? Vortex formation during spin-up, especially in simulations? Ballistic normal component with Andreev reflections from the walls? Core-bound fermions and dissipation Propagating vortex front

72 Spin-up and spin-down SUMMARY Core-bound fermions and dissipation Bound fermion states in vortex cores play essential role in the dynamics of fermionic systems including superfluid 3 He-B. The effect of the bound fermions on the laminar dissipation is fairly well understood and has been experimentally verified in 3 He-B at temperatures down to 0.2 T c. Open questions: Non-vanishing and velocity-dependent friction in the T 0 limit? Interaction with Kelvin waves? Role in the turbulent dissipation? Propagating vortex front

73 Spin-up and spin-down SUMMARY Core-bound fermions and dissipation Propagating vortex front A remarkable example of non-classical spin-up of superfluid with turbulent dynamics which results in mutual friction-independent propagation velocity in the T 0 limit. Combination of measurements of the front propagation, precession and energy dissipation together with numerical simulations hints formation of a new quasi-equilibrium rotating state behind the front, which is decoupled from the rotating reference frame at low temperatures. Open questions: Alternative models? Dissipation mechanisms? Pressure dependence? And more...