Theory of Second Sound Absorption in Rotating Helium

Abstract

1. H. Hall and W. Vinen, Proc. Roy. Soc. (London) A238, 204 (1956). 2. H. Hall and W. Vinen, Proc. Roy. Soc. (London) A238, 215 (1956). 3. L. Onsager, Suppl. Nuovo cimento 2, 249 (1949). 4. R. Feynman, Progress in Low-Temperature Physics, edited by C. J. Gorter (North-Holland Publishing Company, Amsterdam, 1955), Vol. 1, Chap. II, p. 36. 5 Additional dynamic complications for rotating systems (Coriolis effects) are neglected as higher order in Ω for absorption (quadratic). 6 Recalling that temperature waves support no first-order pressure fluctuations, we recognize that second-order processes assume primary importance. 7 Local density deviations from the ambient contribute positively to the potential energy, regardless of sign (consider the potential energy content of ordinary sound) 8 In contrast to the normally adiabatic nature of second sound, involving no actual conversion between phases. 9 Uupon conversion from superfluid, for example, there results a small portion of normal fluid travelling in the wrong direction, with consequent frictional retardation and degeneration of kinetic energy. The reverse process presents greater subtleties. 10 Note that whether in "closing' the normal component enters regions of greater or less wave energy remains immaterial, as either process produces irreversible energy transfer (thus the absolute value signs). Such a consideration also enters integration of Eq. (4). following. 11 Note independence on domain size upon normalization for density calculation. 12 The present result remains valid only for conditions wherein the wavelength greatly exceeds the domain size (λ >>a). A re-evaluation would be necessary for the opposite extreme, and in fact, for high enough frequencies (λ << a), the effect may conceivably disappear.