Turbulence in Jupiter's atmosphere was investigated with archival and ongoing observations from the Hubble Space Telescope. Data sets that include one full rotation (360° longitude coverage) were used to produce complete maps of the planet's upper cloud layer. The global maps were analyzed to generate the passive tracer power spectrum of cloud features for single rotation observations, while successive rotations produced pairs of maps such that zonal winds were calculated. An atmosphere's dimensionality and dynamics are reflected in the slopes of such turbulent power spectra. Many of the retrieved passive tracer power spectra have a shallow spectral index over wave numbers k∼1 - 30 and transition to the well-known Kolmogorov k-5/3 relation at smaller scales between wave numbers k∼30 - 1,000. The transition scale is similar to the number of jets in Jupiter's zonal wind profile and is related to the Rhines scale and the beta effect induced anisotropy scale. We also report on differences found in anticyclonic and cyclonic shear region power spectra and how they correlate to latitudinal changes in the zonal wind profile. We found that properties of Jupiter's power spectra are consistent with quasi-geostrophic turbulence for shallow fluids.