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We investigate the power spectra of outflow-driven turbulence through high-resolution threedimensional isothermal numerical simulations where the turbulence is driven locally in real space by a simple spherical outflow model. The resulting turbulent flow saturates at an average Mach number of ~2.5 and is analysed through density and velocity power spectra, including an investigation of the evolution of the solenoidal and compressional components.We obtain a shallow density power spectrum with a slope of ~-1.2 attributed to the presence of a network of localized dense filamentary structures formed by strong shock interactions. The total velocity power spectrum slope is found to be ~-2.0, representative of the Burgers shock-dominated turbulence model. The density-weighted velocity power spectrum slope is measured as~-1.6, slightly less than the expected Kolmogorov scaling value (slope of -5/3) found in previous works. The discrepancy may be caused by the nature of our real-space-driving model, and we suggest that there is no universal scaling law for supersonic compressible turbulence. We find that on average, solenoidal modes slightly dominate in our turbulence model as the interaction between strong curved compressible shocks generates solenoidal modes, and compressible modes decay faster. [ABSTRACT FROM AUTHOR]