418 research outputs found
Density probability distribution in one-dimensional polytropic gas dynamics
We discuss the generation and statistics of the density fluctuations in
highly compressible polytropic turbulence, based on a simple model and
one-dimensional numerical simulations. Observing that density structures tend
to form in a hierarchical manner, we assume that density fluctuations follow a
random multiplicative process. When the polytropic exponent is equal
to unity, the local Mach number is independent of the density, and our
assumption leads us to expect that the probability density function (PDF) of
the density field is a lognormal. This isothermal case is found to be singular,
with a dispersion which scales like the square turbulent Mach
number , where and is the fluid density.
This leads to much higher fluctuations than those due to shock jump relations.
Extrapolating the model to the case , we find that, as the
Mach number becomes large, the density PDF is expected to asymptotically
approach a power-law regime, at high densities when , and at low
densities when . This effect can be traced back to the fact that the
pressure term in the momentum equation varies exponentially with , thus
opposing the growth of fluctuations on one side of the PDF, while being
negligible on the other side. This also causes the dispersion to
grow more slowly than when . In view of these
results, we suggest that Burgers flow is a singular case not approached by the
high- limit, with a PDF that develops power laws on both sides.Comment: 9 pages + 12 postscript figures. Submitted to Phys. Rev.
A method for reconstructing the variance of a 3D physical field from 2D observations: Application to turbulence in the ISM
We introduce and test an expression for calculating the variance of a
physical field in three dimensions using only information contained in the
two-dimensional projection of the field. The method is general but assumes
statistical isotropy. To test the method we apply it to numerical simulations
of hydrodynamic and magnetohydrodynamic turbulence in molecular clouds, and
demonstrate that it can recover the 3D normalised density variance with ~10%
accuracy if the assumption of isotropy is valid. We show that the assumption of
isotropy breaks down at low sonic Mach number if the turbulence is
sub-Alfvenic. Theoretical predictions suggest that the 3D density variance
should increase proportionally to the square of the Mach number of the
turbulence. Application of our method will allow this prediction to be tested
observationally and therefore constrain a large body of analytic models of star
formation that rely on it.Comment: 8 pages, 9 figures, accepted for publication in MNRA
The pressure distribution in thermally bistable turbulent flows
We present a systematic numerical study of the effect of turbulent velocity
fluctuations on the thermal pressure distribution in thermally bistable flows.
The simulations employ a random turbulent driving generated in Fourier space
rather than star-like heating. The turbulent fluctuations are characterized by
their rms Mach number M and the energy injection wavenumber, k_for. Our results
are consistent with the picture that as either of these parameters is
increased, the local ratio of turbulent crossing time to cooling time
decreases, causing transient structures in which the effective behavior is
intermediate between the thermal-equilibrium and adiabatic regimes. As a
result, the effective polytropic exponent gamma_ef ranges between ~0.2 to ~1.1.
The fraction of high-density zones with P>10^4 Kcm^-3 increases from roughly
0.1% at k_for=2 and M=0.5 to roughly 70% for k_for=16 and M=1.25. A preliminary
comparison with the pressure measurements of Jenkins (2004) favors our case
with M=0.5 and k_for=2. In all cases, the dynamic range of the pressure summed
over the entire density range, typically spans 3-4 orders of magnitude. The
total pressure histogram widens as the Mach number is increased, and develops
near-power-law tails at high (resp.low) pressures when gamma_ef<~ 0.5 (resp.
gamma_ef>~ 1), which occurs at k_for=2 (resp.k_for=16) in our simulations. The
opposite side of the pressure histogram decays rapidly, in an approx. lognormal
form. Our results show that turbulent advection alone can generate large
pressure scatters, with power-law high-P tails for large-scale driving, and
provide validation for approaches attempting to derive the shape of the
pressure histogram through a change of variable from the known form of the
density histogram, such as that performed by MacLow et al.(2004).Comment: to be published in Ap
A method for reconstructing the PDF of a 3D turbulent density field from 2D observations
We introduce a method for calculating the probability density function (PDF)
of a turbulent density field in three dimensions using only information
contained in the projected two-dimensional column density field. We test the
method by applying it to numerical simulations of hydrodynamic and
magnetohydrodynamic turbulence in molecular clouds. To a good approximation,
the PDF of log(normalised column density) is a compressed, shifted version of
the PDF of log(normalised density). The degree of compression can be determined
observationally from the column density power spectrum, under the assumption of
statistical isotropy of the turbulence.Comment: 5 pages, 2 figures, accepted for publication in MNRAS Letter
Cooling Flows of Self-Gravitating, Rotating, Viscous Systems
We obtain self-similar solutions that describe the dynamics of a
self-gravitating, rotating, viscous system. We use simplifying assumptions; but
explicitly include viscosity and the cooling due to the dissipation of energy.
By assuming that the turbulent dissipation of energy is as power law of the
density and the speed v_{rms} and for a power-law dependence of viscosity on
the density, pressure, and rotational velocity, we investigate turbulent
cooling flows. It has been shown that for the cylindrically and the spherically
cooling flows the similarity indices are the same, and they depend only on the
exponents of the dissipation rate and the viscosity model. Depending on the
values of the exponents, which the mechanisms of the dissipation and viscosity
determine them, we may have solutions with different general physical
properties. The conservation of the total mass and the angular momentum of the
system strongly depends on the mechanisms of energy dissipation and the
viscosity model.Comment: 19 pages, 5 figures, To appear in ApJ (scheduled for the v574, July
20, 2002
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