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ABSTRACT In star-forming clouds, high velocity flow gives rise to large fluctuations of density. In this work, we explore the correlation between velocity magnitude (speed) and density. We develop an analytic formula for the joint probability distribution function (PDF) of density and speed, and discuss its properties. In order to develop an accurate model for the joint PDF, we first develop improved models of the marginalized distributions of density and speed. We confront our results with a suite of 12 supersonic isothermal simulations with resolution of $1024^3$ cells in which the turbulence is driven by 3 different forcing modes (solenoidal, mixed, and compressive) and 4 rms Mach numbers (1, 2, 4, 8). We show, that for transsonic turbulence, density and speed are correlated to a considerable degree and the simple assumption of independence fails to accurately describe their statistics. In the supersonic regime, the correlations tend to weaken with growing Mach number. Our new model of the joint and marginalized PDFs are a factor of 3 better than uncorrelated, and provides insight into this important process.
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Statistics of Energy in Isothermal Supersonic Turbulence
Abstract Supersonic isothermal turbulence is a common process in astrophysical systems. In this work, we explore the energy in such systems. We show that the conserved energy is the sum of the kinetic energy (K) and Helmholtz free energy (F). We develop analytic predictions for the probability distributions,P(F) andP(K), as well as their nontrivial joint distribution,P(F,K). We verify these predictions with a suite of driven turbulence simulations, finding excellent agreement. The turbulence simulations were performed at Mach numbers ranging from 1 to 8, and three modes of driving: purely solenoidal, purely compressive, and mixed. We find thatP(F) is discontinuous atF= 0, with the discontinuity increasing with Mach number and compressive driving.P(K) resembles a lognormal with a negative skew. The joint distribution,P(F,K), shows a bimodal distribution, with gas either existing at highFand highKor at lowFand lowK.
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- Award ID(s):
- 2009870
- PAR ID:
- 10520684
- Publisher / Repository:
- DOI PREFIX: 10.3847
- Date Published:
- Journal Name:
- The Astrophysical Journal
- Volume:
- 969
- Issue:
- 2
- ISSN:
- 0004-637X
- Format(s):
- Medium: X Size: Article No. 94
- Size(s):
- Article No. 94
- Sponsoring Org:
- National Science Foundation
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