We present a series of numerical simulations aimed at understanding the nature and origin of turbulence in coronal loops in the framework of the Parker model for coronal heating. A coronal loop is studied via reduced magnetohydrodynamic (MHD) simulations in Cartesian geometry. A uniform and strong magnetic field threads the volume between the two photospheric planes, where a velocity field in the form of a one-dimensional shear flow pattern is present. Initially, the magnetic field that develops in the coronal loop is a simple map of the photospheric velocity field. This initial configuration is unstable to a multiple tearing instability that develops islands with X and O points in the plane orthogonal to the axial field. Once the nonlinear stage sets in the system evolution is characterized by a regime of MHD turbulence dominated by magnetic energy. A well-developed power law in energy spectra is observed and the magnetic field never returns to the simple initial state mapping the photospheric flow. The formation of X and O points in the planes orthogonal to the axial field allows the continued and repeated formation and dissipation of small-scale current sheets where the plasma is heated. We conclude that the observed turbulent dynamics are not induced by the complexity of the pattern that the magnetic field-line footpoints follow but they rather stem from the inherent nonlinear nature of the system.