In grid turbulence, not so far behind the grid, an average flow can be observed with a close to sinusoidal velocity profile, corresponding to the wakes behind the grid bars. The kinetic energy of this mean flow decays rapidly and a close to isotropic flow is observed further downstream. We show how these wakes behind the grid bars influence the downstream turbulence. In particular, we investigate the decay rate of kinetic energy, the behavior of the normalized dissipation rate, and the sensitivity of the flow on initial conditions. We show that the initial value of the ratio of the length scale of the turbulence to the mesh-size determines the precise decay of the mean-flow and the generation of the turbulent kinetic energy. We further show how a simple turbulence model can estimate the degree of nonequilibrium and inhomogeneity of grid turbulence and how this model can be extended to take into account disequilibrium observed in direct numerical simulations of decaying isotropic turbulence.