  We are concerned with the inviscid limit of the Navier-Stokes equations to
the Euler equations for compressible fluids in $\mathbb{R}^3$. Motivated by the
Kolmogorov hypothesis (1941) for incompressible flow, we introduce a
Kolmogorov-type hypothesis for barotropic flows, in which the density and the
sonic speed normally vary significantly. We then observe that the compressible
Kolmogorov-type hypothesis implies the uniform boundedness of some fractional
derivatives of the weighted velocity and sonic speed in the space variables in
$L^2$, which is independent of the viscosity coefficient $\mu>0$. It is shown
that this key observation yields the equicontinuity in both space and time of
the density in $L^\gamma$ and the momentum in $L^2$, as well as the uniform
bound of the density in $L^{q_1}$ and the velocity in $L^{q_2}$ independent of
$\mu>0$, for some fixed $q_1 >\gamma$ and $q_2 >2$, where $\gamma>1$ is the
adiabatic exponent. These results lead to the strong convergence of solutions
of the Navier-Stokes equations to a solution of the Euler equations for
barotropic fluids in $\mathbb{R}^3$. Not only do we offer a framework for
mathematical existence theories, but also we offer a framework for the
interpretation of numerical solutions through the identification of a function
space in which convergence should take place, with the bounds that are
independent of $\mu>0$, that is in the high Reynolds number limit.
