tailieunhanh - Mesoscopic Non-Equilibrium Thermodynamics Part 10

Tham khảo tài liệu 'mesoscopic non-equilibrium thermodynamics part 10', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Hydrodynamical Models of Superfluid Turbulence 261 is the speed of the vortex density wave which was found in Jou et al. 2007 . If we try to read the relation 119 in terms of the second sound we note that the vortex vibrations modify this second sound speed through the two contributions V22V0peL and V2O the latter due to the presence of the vortex density waves and the former due to the reciprocal existence of two waves. The correction for the speed of the second sound is not important because V2 is of the order of 20 m s near 1 7 K whereas for L0 106cm 2 the speed of vortex density waves would be of the order 0 25 cm s much lower than V2 Jou et al. 2007 . To obtain approximate solutions of equations 116 and 117 we assume that the quantities N1 N2 N3 and N4 are coefficients small enough to assume them as perturbations of the physical system. This is reasonable at high-frequencies since we have assumed that w N1 w N2 and K max AqiVL . Therefore let assume that the speed of the wave has the following expression w w w Ỗ 121 kr for which substituting it in the equations 116 and 117 we obtain at the lowest order the relation 119 for the speed w. From the next order follows that Ỗ 0 that is the perturbations due to the coefficients N1 N2 N3 and N4 do not modify the speed of the wave while they modify the coefficients ks related to the attenuation in the form which in the parallel case is k _ N2 w2 V2 w peLNV N1W N3V0 N4X0 k 2w3 122 and in the orthogonal case is k N2 w2 V22 N1w2 123 ks 2w3 123 From a comparison between the two relations of ks 122 and 123 one may note that fc k PeL V2 X0 N4 N3X0 124 Anyway the modification of the attenuation coefficients due to Ni will be small because w2 V is small and the coefficients Ni are also small in the considered situation. This is in contrast with what happens at low frequency or when the vortex tangle is assumed as perfectly rigid not affected by the second sound in which case the relative motion of the normal fluid with respect