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Mathematical models based on probability density functions (PDF) have been extensively used in hydrology and subsurface flow problems, to describe the uncertainty in porous media properties (e.g., permeability modelled as random field).…
In our recent works we proposed a theory of turbulence in inertial gas flow via the mean field effect of an intermolecular potential. We found that, in inertial flow, turbulence indeed spontaneously develops from a laminar initial…
Turbulent thermal diffusion is a combined effect of the temperature stratified turbulence and inertia of small particles. It causes the appearance of a non-diffusive turbulent flux of particles in the direction of the turbulent heat flux.…
Aims: We derive the probability density functions (PDFs) of column density for a complete sample of prominent molecular cloud complexes closer than 200 pc. Methods: We derive near-infrared dust extinction maps for 23 molecular cloud…
We present results of large-scale three-dimensional simulations of weakly magnetized supersonic turbulence at grid resolutions up to 1024^3 cells. Our numerical experiments are carried out with the Piecewise Parabolic Method on a Local…
The role of supersonic turbulence in structuring the interstellar medium (ISM) remains an unsettled question. Here, this problem is investigated using a newexact law of compressible isothermal hydrodynamic turbulence, which involves…
Observations indicate that turbulence in the interstellar medium (ISM) is supersonic ($M_{\rm turb}\gg1$) and strongly magnetized ($\beta\sim0.01-1$), while in the intracluster medium (ICM) it is subsonic ($M_{\rm turb}\lesssim1$) and…
Density is the turbulence statistics that is most readily available from observations. Different regimes of turbulence correspond to different density spectra. For instance, the viscosity-damped regime of MHD turbulence relevant, for…
The piece-wise parabolic method (PPM) is applied to simulations of forced isotropic turbulence with Mach numbers $\sim 0.1... 1$. The equation of state is dominated by the Fermi pressure of an electron-degenerate fluid. The dissipation in…
Radio-wave scintillation observations reveal a nearly Kolmogorov spectrum of density fluctuations in the ionized interstellar medium. Although this density spectrum is suggestive of turbulence, no theory relevant to its interpretation…
We discuss magnetic pressure and density fluctuations in strongly turbulent isothermal MHD flows in "1+2/3" dimensions. We first consider "simple" nonlinear MHD waves, which allow us show that the slow and fast modes have different…
We derive an analytical theory of the PDF of density fluctuations in supersonic turbulence in the presence of gravity in star-forming clouds. The theory is based on a rigorous derivation of a combination of the Navier-Stokes continuity…
We quantitatively study the probability distribution function (PDF) of cosmological nonlinear density fluctuations from N-body simulations with Gaussian initial condition. In particular, we examine the validity and limitations of one-point…
The density variance - Mach number relation of the turbulent interstellar medium is relevant for theoretical models of the star formation rate, efficiency, and the initial mass function of stars. Here we use high-resolution hydrodynamical…
We investigate the influence of the turbulence forcing on the mass distributions of gravitationally unstable cores by postprocessing data from simulations of non-selfgravitating isothermal supersonic turbulence with varying resolution. In…
We unify two approaches that have been taken to explain the non-Gaussian probability distribution functions (PDFs) obtained in measurements of longitudinal velocity differences in turbulence, and we apply our approach to Couette-Taylor…
Recent observations of column densities in molecular clouds find lognormal distributions with power-law high-density tails. These results are often interpreted as indications that supersonic turbulence dominates the dynamics of the observed…
Supersonic turbulence results in strong density fluctuations in the interstellar medium (ISM), which have a profound effect on the chemical structure. Particularly useful probes of the diffuse ISM are the ArH$^+$, OH$^+$, H$_2$O$^+$…
Despite the simplicity of theoretical models of supersonically turbulent, isothermal media, their predictions successfully match the observed gas structure and star formation activity within low-pressure (P/k < 10^5 K cm^-3) molecular…
In probability density function (PDF) methods a transport equation is solved numerically to compute the time and space dependent probability distribution of several flow variables in a turbulent flow. The joint PDF of the velocity…