  We analyze the evolution of shock waves in high-resolution 3D radiative MHD
simulations of the quiet Sun and their synthetic emission characteristics. The
simulations model the dynamics of a 12.8x12.8x15.2 Mm quiet-Sun region
(including a 5.2 Mm layer of the upper convection zone and a 10 Mm atmosphere
from the photosphere to corona) with an initially uniform vertical magnetic
field of 10 G, naturally driven by convective flows. We synthesize the Mg II
and C II spectral lines observed by the IRIS satellite and EUV emission
observed by the SDO/AIA telescope. Synthetic observations are obtained using
the RH1.5D radiative transfer code and temperature response functions at both
the numerical and instrumental resolutions. We found that the Doppler velocity
jumps of the C II 1334.5 A IRIS line and a relative enhancement of the emission
in the 335 A SDO/AIA channel are the best proxies for the enthalpy deposited by
shock waves into the corona (with Kendall's $\tau$ correlation coefficients of
0.59 and 0.38, respectively). The synthetic emission of the lines and extreme
ultraviolet passbands are correlated with each other during the shock wave
propagation. All studied shocks are mostly hydrodynamic (i.e., the magnetic
energy carried by horizontal fields is $\leq{}$2.6% of the enthalpy for all
events) and have Mach numbers > 1.0-1.2 in the low corona. The study reveals
the possibility of diagnosing energy transport by shock waves into the solar
corona, as well as their other properties, by using IRIS and SDO/AIA sensing
observations.
