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In a systematic study, we compare the density statistics in high resolutionnumerical experiments of supersonic isothermal turbulence, driven by theusually adopted solenoidal (divergence-free) forcing and by compressive(curl-free) forcing. We find that for the same rms Mach number, compressiveforcing produces much stronger density enhancements and larger voids comparedto solenoidal forcing. Consequently, the Fourier spectra of densityfluctuations are significantly steeper. This result is confirmed using theDelta-variance analysis, which yields power-law exponents beta~3.4 forcompressive forcing and beta~2.8 for solenoidal forcing. We obtain fractaldimension estimates from the density spectra and Delta-variance scaling, and byusing the box counting, mass size and perimeter area methods applied to thevolumetric data, projections and slices of our turbulent density fields. Ourresults suggest that compressive forcing yields fractal dimensionssignificantly smaller compared to solenoidal forcing. However, the actualvalues depend sensitively on the adopted method, with the most reliableestimates based on the Delta-variance, or equivalently, on Fourier spectra.Using these methods, we obtain D~2.3 for compressive and D~2.6 for solenoidalforcing, which is within the range of fractal dimension estimates inferred fromobservations (D~2.0-2.7). The velocity dispersion to size relations for bothsolenoidal and compressive forcing obtained from velocity spectra follow apower law with exponents in the range 0.4-0.5, in good agreement with previousstudies.

The Fractal Density Structure in Supersonic Isothermal Turbulence: Solenoidal versus Compressive Energy Injection