  Spectral analysis of the translational superfluid flow of a Bose liquid is
attempted. When cooling a dissipative flow of liquid helium 4 through a
capillary at the lambda temperature,a superfluid flow abruptly appears at the
lambda temperature. By a thought experiment in which the pressure difference
between two ends of a capillary slowly oscillates, the spectrum of fluidity
(the reciprocal of kinematic viscosity) just above the lambda temperature
($2.17 K<T<2.18 K$) is examined using a sum rule that incorporates the result
of linear response theory and fluid mechanics. According to Feynman's picture
on the many-body wave function of bosons, as the condensate grows in the flow,
the transverse motion in the flow becomes suppressed by the emergence of a gap,
originating from the Bose statistics, in the excitation spectrum. This
statistical gap induces a continuous change in the fluidity spectrum just above
the lambda temperature, which demonstrates the growth of a superfluid flow. For
this mechanism, the size distribution of the coherent wave function plays an
important role. As a byproduct, a new interpretation of the critical velocity
is proposed.
