DECAYING KOLMOGOROV TURBULENCE IN A MODEL OF SUPERFLOW

Superfluid turbulence is studied using numerical simulations of the no nlinear Schrodinger equation (NLSE), which is the correct equation of motion for superflows at low temperatures. This equation depends on tw o parameters: the sound velocity and the coherence length. It naturall y contains nonsingular quantized vortex lines. The NLSE mass, momentum , and energy conservation relations are derived in hydrodynamic form. The total energy is decomposed into an incompressible kinetic part, an d other parts that correspond to acoustic excitations. The correspondi ng energy spectra are defined and computed numerically in the case of the two-dimensional vortex solution. A preparation method, generating initial data reproducing the vorticity dynamics of any three-dimension al flow with Clebsch representation is given and is applied to the Tay lor-Green (TG) vortex. The NLSE TG vortex is studied with resolutions up to 512(3). The energetics of the flow is found to be remarkably sim ilar to that of the viscous TG vortex. The rate of the (irreversible) transfer of kinetic energy into other energy components is comparable, both in magnitude and time scale, to the energy dissipation of the vi scous flow. This transfer rate depends weakly on the coherence length. At the moment of maximum energy dissipation, the energy spectrum foll ows a power law compatible with Kolmogorov's -5/3 value. Physical-spac e visualizations show that the vorticity dynamics of the superflow is similar to that of the viscous flow in which vortex reconnection event s play a major role. It is argued that there may be some amount of uni versality of reconnection processes, because of topological constraint s. Some preliminary support for this conjecture is given in the specia l case of secondary instabilities of round jets. The experimental impl ications of the close analogy between superfluid and viscous decaying turbulence are discussed. (C) 1997 American Institute of Physics.