The reconnecting vortex-tangle model is used to investigate the interaction of tangles of quantized vortices with second sound. This interaction can be expressed in terms of an effective line-length density, which depends on the direction of the second-sound wave. By comparing the effective line-length densities in various directions the tangle structure can be examined. Simulations were done for flow channels with square and circular cross sections as well as for slits. The results show that in all these cases the tangles are inhomogeneous in direction as well as in space. The calculated inhomogeneities are in agreement with experiment.
Penz, H. R., Aarts, R. G. K. M., & Waele, de, A. T. A. M. (1995). Numerical investigations on interactions between tangles of quantized vortices and second sound. Physical Review B: Condensed Matter, 51(17), 11973-11976. https://doi.org/10.1103/PhysRevB.51.11973