  We consider the intermittent behavior of superfluid turbulence in $^4$He. Due
to the similarity in the nonlinear structure of the two-fluid model of
superfluidity and the Euler and Navier-Stokes equations one expects the scaling
exponents of the structure functions to be the same as in classical turbulence
for temperatures close to the superfluid transition $T_\lambda$ and also for
$T\ll T_\lambda$. This is not the case when mutual friction becomes important.
Using shell model simulations, we propose that for an intermediate regime of
temperatures, such that the density of normal and superfluid components are
comparable to each other, there exists a range of scales in which the effective
exponents indicate stronger intermittency. We offer a bridge relation between
these effective and the classical scaling exponents. Since this effect occurs
at accessible temperatures and Reynolds numbers, we propose that experiments
should be conducted to further assess the validity and implications of this
prediction.
