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The evolution and decay of the turbulent spectrum injected by a supernova explosion in the local environment is studied through an analytical solution of the dynamic equation. The results, when compared with HST high resolution absorption line data, are consistent with an explosion that occurred a few times $10^5$ years ago and a turbulent outer scale $\sim 10^{18}$~cm. The study implies that the Galactic ISM must have a high porosity parameter Q to account for the observed degree of turbulence.
