Quantized Vortex Dynamics and Superfluid Turbulence

Carlo F. Barenghi (auth.), C. F. Barenghi, R. J. Donnelly, W. F. Vinen (eds.)3540422269, 9783540422266

This book is primarily concerned with turbulence in superfluid helium. Quantized vorticity has traditionally generated great interest among physicists but there are now also important engineering applications, such as liquid helium cooling of superconducting magnets. Presently much research is done on the relationship between superfluid turbulence and classical turbulence, as intense turbulence can be generated in liquid helium due to its small kinematic viscosity. There is also a close relationship between superfluid behaviour and quantized vorticity in liquid helium and in atomic Bose–Einstein condensates. Putting special emphasis on the interplay between the different disciplines involved, this readable account of recent research will appeal not only to established researchers but also to newcomers and graduate students wishing to enter the field.

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Table of contents :
Introduction to Superfluid Vortices and Turbulence….Pages 3-14
An Introduction to Experiments on Superfluid Turbulence….Pages 17-35
The Experimental Evidence for Vortex Nucleation in 4 He….Pages 36-50
Applications of Superfluid Helium in Large-Scale Superconducting Systems….Pages 51-65
The Temperature Dependent Drag Crisis on a Sphere in Flowing Helium II….Pages 66-72
Experiments on Quantized Turbulence at mK Temperatures….Pages 73-79
Grid-Generated He II Turbulence in a Finite Channel – Experiment….Pages 80-86
Intermittent Switching Between Turbulent and Potential Flow Around a Sphere in He II at mK Temperatures….Pages 87-94
Vortex Filament Methods for Superfluids….Pages 97-113
Introduction to HVBK Dynamics….Pages 114-130
Magnus Force, Aharonov-Bohm Effect, and Berry Phase in Superfluids….Pages 131-137
Using the HVBK Model to Investigate the Couette Flow of Helium II….Pages 138-145
An Introduction to the Theory of Superfluid Turbulence….Pages 149-161
Numerical Methods for Coupled Normal-Fluid and Superfluid Flows in Helium II….Pages 162-176
From Vortex Reconnections to Quantum Turbulence….Pages 177-183
Vortices and Stability in Superfluid Boundary Layers….Pages 184-190
Grid Generated He II Turbulence in a Finite Channel—Theoretical Interpretation….Pages 191-197
Vortex Tangle Dynamics Without Mutual Friction in Superfluid 4 He….Pages 198-204
Applications of the Gaussian Model of the Vortex Tangle in the Superfluid Turbulent He II….Pages 205-211
Stochastic Dynamics of a Vortex Loop. Thermal Equilibrium….Pages 212-218
Stochastic Dynamics of a Vortex Loop. Large-Scale Stirring Force….Pages 219-225
Nonequilibrium Vortex Dynamics in Superfluid Phase Transitions and Superfluid Turbulence….Pages 226-232
The Nonlinear Schrödinger Equation as a Model of Superfluidity….Pages 235-257
Vortex Nucleation and Limit Speed for a Flow Passing Nonlinearly Around a Disk in the Nonlinear Schrödinger Equation….Pages 258-267
Vortices in Nonlocal Condensate Models of Superfluid Helium….Pages 268-275
Ginzburg-Landau Description of Vortex Nucleation in a Rotating Superfluid….Pages 276-282
Weak Turbulence Theory for the Gross-Pitaevskii Equation….Pages 283-289
Dissipative Vortex Dynamics and Magnus Force….Pages 290-296
Transition to Dissipation in Two- and Three-Dimensional Superflows….Pages 297-304
Motion of Objects Through Dilute Bose-Einstein Condensates….Pages 307-319
Stability of a Vortex in a Rotating Trapped Bose-Einstein Condensate * ….Pages 320-326
Kinetics of Strongly Non-equilibrium Bose-Einstein Condensation….Pages 327-333
Quantum Nucleation of Phase Slips in Bose—Einstein Condensates….Pages 334-341
Vortex Reconnection in Normal and Superfluids….Pages 345-357
Helicity in Hydro and MHD Reconnection….Pages 358-365
Tropicity and Complexity Measures for Vortex Tangles….Pages 366-372
The Geometry of Magnetic and Vortex Reconnection….Pages 373-380
Current-Sheet Formation near a Hyperbolic Magnetic Neutral Line….Pages 381-388
Nonlocality in Turbulence….Pages 389-395
Quantized Vorticity in Superfluid 3 He-A: Structure and Dynamics….Pages 399-420
Vortices in Metastable 4 He Films….Pages 421-427
Quantum Hall E.ect Breakdown Steps and Possible Analogies with Classical and Super.uid Hydrodynamics….Pages 428-437
Atomic Bose Condensate with a Spin Structure: The Use of Bloch State….Pages 438-444
Quantum Dynamics of Vortex-Antivortex Pairs in a Circular Box….Pages 445-452