Superfluid Turbulence in the Low Temperature Regime

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SUPERFLUID TURBULENCE IN THE LOW TEMPERATIRE REGIME The two most common approaches to study of superfluid turbulence are the HVBK theory and the classical theory of vortex filaments. There are many shortcomings in these models that make them unrealistic and ad hoc. The main objective of our proposal is to use a third approach based on certain forms of nonlinear Schroedinger equation (NLS) for two closely related purposes: to provide microscopically realistic parameters for HVBK theory and the classical theory of vortex filaments and to elucidate superfluid turbulence using new variants of the NLS that are more faithful to real helium II. More specifically we plan: (1) use NLS equations to study the process of vortex line reconnection in sufficient detail to characterize quantitatively the accompanying radiation of sound and Kelvin waves. The results will allow us to define reconnection rules that could be used when classical theory is applied to superfluid turbulence. (2) Use NLS theory to simulate superfluid turbulence in the low temperature regime to study the transition between weak and strong turbulence states in the superfluid. (3) Analyze dissipative NLS models that include damping from the mutual friction between superfluid and normal fluid. (4) Study and classify attractors, bifurcation sequences, and routes to chaos in solutions of forced and dissipative NLS equations. Our main goal is, however, to elucidate superfluid turbulence in the low temperature regime in which experiments are currently in the planning stage. Superfluid turbulence has been studied experimentally for many years and has by now become a major branch of cryogenic physics. In addition to the intrinsic intellectual challenges of the subject, there are several reasons for this. Helium is used as a coolant for superconducting magnets and for infrared detectors, to name just two of several engineering applications. The flow commonly becomes turbulent in these contexts. The subject also has implications beyond the field of helium research, such as in the study of high temperature superconductivity, systems of magnetic spins, melting transitions of crystals, and the origin of glitches in neutron star rotations. Superfluid turbulence may also provide insights into classical fluid turbulence, especially at high Reynolds numbers, where the vorticity has an intermittent, fractal character.