Abstract
Recent experiments have shown the existence of a very strong temperature overshoot behind a propagating second sound shock wave close to the heated surface. The ratio of the temperature overshoot to the shock wave amplitude depends strongly on the rest time between two consecutive heat pulses. These results can be reproduced by a simple theoretical model using only the Gorter-Mellink mutual interaction force and a vortex line density (VLD) evolution equation. The evolution equation is taken to be that proposed by Vinen as extended to include spatial dependence. The drift velocity of the VLD is assumed to have a specific form, and the initial VLD is chosen as a parameter. Experimental observations and existing physical considerations led to the formulation of the used theoretical model. The quantitative agreement between the theoretical calculations and experiments is fair for an overshoot ratio below about 3. At stronger heat pulses the agreement is only qualitative. The model describes well the mechanism of development of a hot layer close to the heated surface and the evolution of the counterflow velocity and temperature field behind the second sound shock wave and indicates possible improvements of the theoretical model.
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