  Renormalization enables a systematic scale-by-scale analysis of multiscale
systems. In this paper, we employ \textit{renormalization group} (RG) to the
shell model of turbulence and show that the RG equation is satisfied by $
|u_n|^2 =K_\mathrm{Ko} \epsilon^{2/3} k_n^{-2/3}$ and $ \nu_n = \nu_*
\sqrt{K_\mathrm{Ko}} \epsilon^{1/3} k_n^{-4/3}$, where $k_n, u_n $ are the
wavenumber and velocity of shell $ n $; $\nu_*, K_\mathrm{Ko}$ are RG and
Kolmogorov's constants; and $ \epsilon $ is the energy dissipation rate. We
find that $\nu_* \approx 0.5$ and $K_\mathrm{Ko} \approx 1.7$, consistent with
earlier RG works on Navier-Stokes equation. We verify the theoretical
predictions using numerical simulations.
