Wefindanasymptoticexpressionforthecharacteristictimescalesofdecorrelationprocessesinweaklycompressibleandisothermalturbulence.ThisresultisusedintheEddy-DampedQuasi-NormalMarkovianequationtoderivethescalingsofcompressibleenergyspectra:(1)iftheacousticwavesaredominant,thecompressibleenergyspectraexhibit?7/3scaling;(2)iflocaleddystrainingisdominant,thecompressibleenergyspectraarescaledas?3.Meanwhile,theenergyspectraofincompressiblecomponentsdisplaythesamescalingof?5/3asthoseinincompressibleturbulence.Thedirectnumericalsimulationsofweaklycompressibleturbulenceareusedtoexaminethescaling.
