Transverse sound in differentially moving superfluid helium

There exists a transverse sound mode in superfluid helium, in addition to the first and second sound modes. In this mode, the velocity of the normal component oscillates in the direction perpendicular to the wave vector; hence, it is named the transverse mode. We analyze this mode at arbitrary values of the relative velocity of the normal and superfluid components. In general, temperature, pressure, and superfluid velocity also oscillate. The general relations between the amplitudes of the oscillating variables in the transverse mode are found in a general direction of the wave vector with respect to the relative velocity of the normal fluid and superfluid. We estimate the attenuation of the transverse mode in phonon pulses and discuss the possibility of detecting it experimentally.