The Energy Dissipation Rate of Supersonic, Magnetohydrodynamic Turbulence in Molecular Clouds
Open Access
- 10 October 1999
- journal article
- research article
- Published by American Astronomical Society in The Astrophysical Journal
- Vol. 524 (1) , 169-178
- https://doi.org/10.1086/307784
Abstract
Molecular clouds have broad line widths, which suggests turbulent supersonic motions in the clouds. These motions are usually invoked to explain why molecular clouds take much longer than a free-fall time to form stars. Classically, it was thought that supersonic hydrodynamical turbulence would dissipate its energy quickly but that the introduction of strong magnetic fields could maintain these motions. A previous paper has shown, however, that isothermal, compressible MHD and hydrodynamical turbulence decay at virtually the same rate, requiring that constant driving occur to maintain the observed turbulence. In this paper, direct numerical computations of uniform, randomly driven turbulence with the ZEUS astrophysical MHD code are used to derive the value of the energy-dissipation coefficient, which is found to be with ηv = 0.21/π, where vrms is the root-mean-square (rms) velocity in the region, Ekin is the total kinetic energy in the region, m is the mass of the region, and is the driving wavenumber. The ratio τ of the formal decay time Ekin/kin of turbulence to the free-fall time of the gas can then be shown to be where Mrms is the rms Mach number, and κ is the ratio of the driving wavelength to the Jeans wavelength. It is likely that κ < 1 is required for turbulence to support gas against gravitational collapse, so the decay time will probably always be far less than the free-fall time in molecular clouds, again showing that turbulence there must be constantly and strongly driven. Finally, the typical decay time constant of the turbulence can be shown to be where is the driving wavelength.Keywords
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This publication has 33 references indexed in Scilit:
- Clouds as Turbulent Density Fluctuations: Implications for Pressure Confinement and Spectral Line Data InterpretationThe Astrophysical Journal, 1999
- Dust Extinction and Molecular Cloud Structure: L977The Astrophysical Journal, 1998
- Instability, turbulence, and enhanced transport in accretion disksReviews of Modern Physics, 1998
- The Chemical Composition and Evolution of Giant Molecular Cloud Cores: A Comparison of Observation and TheoryThe Astrophysical Journal, 1997
- A Parsec‐Scale Herbig‐Haro Jet in Barnard 5The Astrophysical Journal, 1996
- Jeans collapse of turbulent gas clouds: tentative theoryJournal of Fluid Mechanics, 1992
- Simulation of magnetohydrodynamic flows - A constrained transport methodThe Astrophysical Journal, 1988
- On the generation and maintenance of turbulence in the interstellar mediumThe Astrophysical Journal, 1981
- The origin and lifetime of giant molecular cloud complexesThe Astrophysical Journal, 1980
- Hydromagnetic Waves in Molecular CloudsThe Astrophysical Journal, 1975