  The \minerva experiment reports double-differential cross-section
measurements for $\nu_{\mu}$-carbon interactions with three-momentum transfer
$|\vec{q}| < 1.2$ GeV obtained with medium energy exposures in the NuMI beam.
These measurements are performed as a function of the three-momentum transfer
and an energy transfer estimator called the available energy defined as the
energy that would be visible in the detector. The double differential cross
sections are compared to the GENIE and NuWro predictions along with the
modified version of GENIE which incorporates new models for better agreement
with earlier measurements from MINERvA. In these measurements, the
quasi-elastic, resonance, and multi-nucleon knockout processes appear at
different kinematics in this two-dimensional space. The results can be used to
improve models for neutrino interactions needed by neutrino oscillation
experiments.
