Abstract
We show that in He II a counterflow without any local center-of-mass motion cannot be maintained, except for special symmetries of the flow field (e.g., plane axial or spherical symmetry) and for second-sound waves with small amplitudes. Our considerations are based on assuming constant values of the density and of the ratio of entropy to normal mass. Hence convection by center-of-mass velocities has to be taken into account for general three-dimensional and in particular for turbulent motions even if the total or the average local momentum vanishes.
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