Vortex Nucleation in Superfluids

I discuss what a superfluid is, why it's relevant, and what causes vortex nucleation in a superfluid. Along the way I discuss which fluid analogies are useful for understanding nucleation and which are not. Finally, I discuss how to predict vortex nucleation number from a hydrofoil dragged through a superfluid.

Transcript

1. VORTEX NUCLEATION IN SUPERFLUIDS SETH MUSSER
2. INTRODUCTION OVERVIEW ▸ What is a superfluid? ▸ Why is it relevant? ▸ What governs vortex nucleation, and what are good fluid analogies to aid understanding? ▸ How can we predict the number of vortices nucleated by hydrofoils?
3. WHAT IS A SUPERFLUID? 1) A FLUID WITH ZERO VISCOSITY (INTERNAL FRICTION) A. Leitner Michigan State ‣ Helium-I to Helium-II superfluid transition. Zero viscosity demonstrated with pipe flow.
4. WHAT IS A SUPERFLUID? 2) CAN’T SUPPORT ROTATION P. Engels, JILA ‣ Density field of a superfluid bath stirred with lasers. ‣ Depleted regions are point-like vortices with circulation 2ℏ/m
5. RELEVANCE WHY DO WE CARE? ▸ Superfluids are similar to superconductors, both flows without resistance ▸ Superconductors also suffer from (magnetic field) vortices, making them develop resistance ▸ Stretch goal: could lead to more efficient MRIs, Maglevs, etc. F.S. Wells, Institute for Superconducting and Electronic Materials B
6. INTRODUCTION NUMERICS ▸ A superfluid has a condensate wave function (r,t) that obeys the Gross-Pitaevskii equation, a non-linear Schrödinger equation: ▸ i∂t(r,t) = (-2 + V(r,t) + ||2) (r,t) ▸ Numerically integrate with split-step Fourier method. FFT to Fourier space to turn differentiation into multiplication, then transform back to apply non-linear piece. Subtleties brushed over, but very fast, especially on a GPU.
7. INTRODUCTION HOW TO SIMULATE (HYDROFOIL POTENTIAL)
8. VORTEX NUCLEATION CREATING VORTICES TO STUDY ▸ In air or water hydrofoils nucleate a starting vortex ▸ Vortex nucleated has a specific circulation =ULsin() (at least for 2D flows) ▸ So does this mean a foil dragged through superfluid should nucleate n=ULsin()/(2ℏ/m) vortices? D.J. Acheson, Oxford W.T.M. Irvine, University of Chicago
9. VORTEX NUCLEATION NOT SO FAST ▸ Mechanism for nucleation of starting vortex in water or air is totally dependent on viscosity ▸ Boundary layers, where velocity adjusts to zero are crucial ▸ Do we still get nucleation in a superfluid, even though it is inviscid? D.J. Acheson, Oxford
10. VORTEX NUCLEATION NUCLEATION STILL OCCURS (EVEN WITH ZERO VISCOSITY!)
11. VORTEX NUCLEATION NUCLEATION NUMBERS FOR POINTS IN PHASE SPACE
12. VORTEX NUCLEATION NUCLEATION TO AVOID SHOCKS ▸ Superfluids can’t nucleate a (viscosity produced) starting vortex ▸ However, a shock like that seen in transonic flow over an airplane wing would violate inviscid flow ▸ Superfluids nucleate to avoid these shocks by decreasing local fluid velocity below local sound velocity Russell Croman
13. VORTEX NUCLEATION AIRPLANE WING SHOCK
14. PREDICTING VORTEX NUMBER VELOCITY DISTRIBUTION AROUND WING ▸ Superfluid nucleation governed by local speeds exceeding sound speed ▸ Knowing local speeds should tell us when we’re going to nucleate ▸ Turns out speeds are predicted almost exactly by incompressible inviscid flow
15. PREDICTING VORTEX NUMBER AGREEMENT WITH IDEAL THEORY
16. PREDICTING VORTEX NUMBER VELOCITY DISTRIBUTION AROUND WING ▸ Use ideal fluid speeds at tail and a regularization argument to deal with singularity ▸ Allows us to predict nucleation from tail up to a fitting parameter C ▸ Good agreement with measurements
17. PREDICTING VORTEX NUMBER AGREEMENT WITH DATA
18. PREDICTING VORTEX NUMBER STALLING BEHAVIOR (DUE TO INCREASING SPEED AT TOP)
19. PREDICTING VORTEX NUMBER ADDED STALLING BEHAVIOR WITH PREDICTIONS
20. CONCLUSION OVERVIEW ▸ What is a superfluid? ▸ Why is it relevant? ▸ What governs vortex nucleation, and what are good fluid analogies to aid understanding? ▸ How can we predict the number of vortices nucleated by hydrofoils?