We investigate the self-induced turbulence of high repetition rate laser filaments over a wide range of average powers (1 mW to 100 W) and its sensitivity to external atmospheric turbulence. Although both externally-imposed and self-generated turbulences can have comparable magnitudes, they act on different temporal and spatial scales. While the former drives the shot-to-shot motion at the millisecond time scale, the latter acts on the 0.5 s scale. As a consequence, their effects are decoupled, preventing beam stabilization by the thermally-induced low-density channel produced by the laser filaments.