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Dynamics of a Simple Model for Turbulence of the Second Sound in Helium II

B. V. Chirikov·V. G. Davidovsky
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Abstract

The results of numerical experiments on chaotic ('turbulent') dynamics of the second sound in helium II are presented and discussed based on a very simple model proposed and theoretically studied recently by Khalatnikov and Kroyter. Using a powerful present-day techniques for the studying nonlinear phenomena, we confirm their results on the stationary oscillation in helium and its stability as well as on a qualitative picture of successive transitions to limit cycles and chaos. However, the experiments revealed also a much more complicated structure of the bifurcations than it was expected. The fractal structure of chaotic attractors was also studied including their noninteger dimension. Surprisingly, a very simple model used in all these studies not only qualitatively represents the behavior of helium in laboratory experiments but also allows for a correct order-of-magnitude estimate of the critical heat pumping into helium at bifurcations.

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B. V. Chirikov, V. G. Davidovsky. 2000-06-13. Dynamics of a Simple Model for Turbulence of the Second Sound in Helium II. https://arxiv.org/abs/nlin/0006018

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