The multivariate tool of Principal Component Analysis ( PCA ) is applied to 23 fields in the FCRAO CO Survey of the Outer Galaxy .
PCA enables the identification of line profile differences which are assumed to be generated from fluctuations within a turbulent velocity field .
The variation of these velocity differences with spatial scale within a molecular region is described by a singular power law , { \delta } v = cL ^ { \alpha } which can be used as a powerful diagnostic to turbulent motions .
For the ensemble of 23 fields , we find a mean value < \alpha > =0.62 \pm 0.11 .
From a recent calibration of this method using fractal Brownian motion simulations ( Brunt & Heyer 2001 ) , the measured velocity difference-size relationship corresponds to an energy spectrum , E ( k ) , which varies as k ^ { - \beta } , where \beta = 2.17 \pm 0.31 .
We compare our results to both decaying and forced hydrodynamic simulations of turbulence .
We conclude that energy must be continually injected into the regions to replenish that lost by dissipative processes such as shocks .
The absence of large , widely distributed shocks within the targeted fields suggests that the energy is injected at spatial scales less than several pc .