  We systematise the study of dynamic multiscaling of time-dependent structure
functions in different models of passive-scalar and fluid turbulence. We show
that, by suitably normalising these structure functions, we can eliminate their
dependence on the origin of time at which we start our measurements and that
these normalised structure functions yield the same linear bridge relations
that relate the dynamic-multiscaling and equal-time exponents for statistically
steady turbulence. We show analytically, for both the Kraichnan Model of
passive-scalar turbulence and its shell model analogue, and numerically, for
the GOY shell model of fluid turbulence and a shell model for passive-scalar
turbulence, that these exponents and bridge relations are the same for
statistically steady and decaying turbulence. Thus we provide strong evidence
for dynamic universality, i.e., dynamic-multiscaling exponents do not depend on
whether the turbulence decays or is statistically steady.
