Astrophysical magnetic fields and nonlinear dynamo theory

Thermophysical Properties Research Literature Retrieval Guide Edited by Y. S. Touloukian, J. K. Gerritsen and N. Y. Moore Second edition, revised and expanded. Book 1: Pp. xxi + 819. Book 2: Pp.621. Book 3: Pp. ix + 1315. (New York: Plenum Press, 1967.) n.p.

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Heat and Mass Transfer

▪ Abstract Turbulence affects the structure and motions of nearly all temperature and density regimes in the interstellar gas. This two-part review summarizes the observations, theory, and simulations of interstellar turbulence and their implications for many fields of astrophysics. The first part begins with diagnostics for turbulence that have been applied to the cool interstellar medium and highlights their main results. The energy sources for interstellar turbulence are then summarized along with numerical estimates for their power input. Supernovae and superbubbles dominate the total power, but many other sources spanning a large range of scales, from swing-amplified gravitational instabilities to cosmic ray streaming, all contribute in some way. Turbulence theory is considered in detail, including the basic fluid equations, solenoidal and compressible modes, global inviscid quadratic invariants, scaling arguments for the power spectrum, phenomenological models for the scaling of higher-order structu...

http://www.ifa.hawaii.edu/%7Ereipurth/reviews/elmegreen1_araa.pdf

Interstellar Turbulence I: Observations and Processes

Coherent structures in wall turbulence transport momentum and provide a means of producing turbulent kinetic energy. Above the viscous wall layer, the hairpin vortex paradigm of Theodorsen coupled with the quasistreamwise vortex paradigm have gained considerable support from multidimensional visualization using particle image velocimetry and direct numerical simulation experiments. Hairpins can autogenerate to form packets that populate a significant fraction of the boundary layer, even at very high Reynolds numbers. The dynamics of packet formation and the ramifications of organization of coherent structures (hairpins or packets) into larger-scale structures are discussed. Evidence for a large-scale mechanism in the outer layer suggests that further organization of packets may occur on scales equal to and larger than the boundary layer thickness.

Hairpin vortex organization in wall turbulencea)

In this paper they conclude that turbulent fragmentation is unavoidable in super-sonically turbulent molecular clouds, and given the success of the present model to predict the observed shape of the Stellar IMF, they conclude that turbulent fragmentation is essential to the origin of the stellar IMF.

https://iopscience.iop.org/article/10.1086/341790/pdf

The Stellar Initial Mass Function from Turbulent Fragmentation

We review studies of the statistics of isotropic turbulence in an incompressible fluid at high Reynolds numbers using direct numerical simulation (DNS) from the viewpoint of fundamental physics. The Reynolds number achieved by the largest DNS, with 4096 3 grid points, is comparable with the largest Reynolds number in laboratory experiments. The high-quality DNS data in the inertial subrange and the dissipative range enable the examination of detailed statistics at small scales, such as the normalized energy-dissipation rate, energy and energy-flux spectra, the intermittency of the velocity gradients and increments, scaling exponents, and flow-field structure. We emphasize basic questions of turbulence, universality in the sense of Kolmogorov’s theory, and the dependence of the statistics on the Reynolds number and scale.

http://www.o3d.org/abracco/annual_rev_3dnumerical.pdf

Study of High-Reynolds Number Isotropic Turbulence by Direct Numerical Simulation

Velocity field statistics in the inertial to dissipation range of three-dimensional homogeneous steady turbulent flow are studied using a high-resolution DNS with up to N=10243 grid points. The range of the Taylor microscale Reynolds number is between 38 and 460. Isotropy at the small scales of motion is well satisfied from half the integral scale (L) down to the Kolmogorov scale (η). The Kolmogorov constant is 1.64±0.04, which is close to experimentally determined values. The third order moment of the longitudinal velocity difference scales as the separation distance r, and its coefficient is close to 4/5. A clear inertial range is observed for moments of the velocity difference up to the tenth order, between 2λ≈100η and L/2≈300η, where λ is the Taylor microscale. The scaling exponents are measured directly from the structure functions; the transverse scaling exponents are smaller than the longitudinal exponents when the order is greater than four. The crossover length of the longitudinal velocity struct...

Velocity field statistics in homogeneous steady turbulence obtained using a high-resolution direct numerical simulation

Statistics of a passive scalar with Sc=1 transported by steady homogeneous turbulence at Rλ=427 and Pλ=427 is studied by using high-resolution direct numerical simulation. The Obukhov–Corrsin constant of the three-dimensional scalar spectrum in the inertial-convective range is found to be 0.68±0.04. It is proved that the -law for the scalar-velocity triple correlation holds in both inertial-convective and viscous-convective ranges when Sc>1, and found that the -law is approached with increase in Peclet number. Structure functions of the passive scalar increment and their local scaling exponents are computed as functions of the separation distance, and it is found that there exist two scaling ranges: the inertial-convective range and a narrow precursory range to the viscous-convective range. The scaling exponents in the inertial-convective range are found to be smaller than those of the velocity field and do not saturate, whereas they saturate at about 1.5 in the short precursory range to the viscous-convective range. It is also found that, contrary to the scalar case, the mixed scalar velocity structure function has a well-developed single scaling range. The scalar and scalar dissipation fields are visualized and compared with the kinetic energy dissipation field. The scalar field has a particular shape with a large-scale plateau, sharp cliff and deep valley, a mesa-canyon structure.

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Statistics of a passive scalar in homogeneous turbulence

The pressure spectrum in homogeneous steady turbulence is studied using direct numerical simulation with resolution up to 1024(3) and the Reynolds number R(lambda) between 38 and 478. The energy spectrum is found to have a finite inertial range with the Kolmogorov constant K = 1.65+/-0.05 followed by a bump at large wave numbers. The pressure spectrum in the inertial range is found to be approximately P(k) = B(p)epsilon;(4/3)k(-7/3) with B(p) = 8.0+/-0.5, and followed by a bump of nearly k(-5/3) at higher wave numbers. Universality and a new scaling of the pressure spectrum are discussed.

Pressure Spectrum in Homogeneous Turbulence

We examine the effects of the variation in dissipation-range resolution on the accuracy of inertial-range statistics and intermittency in terms of the direct numerical simulations of homogeneous turbulence and passive-scalar turbulence by changing the spatial resolution up to 20483 grid points while maintaining a constant Reynolds number at Rλ ≃ 180 or ≃ 420 and Schmidt number at Sc = 1. Although large fluctuations of the derivative fields depended strongly on Kmaxη and were underestimated when Kmaxη≃1, where Kmax is the maximum wavenumber in the computations and η is the mean Kolmogorov length, the behaviour of the spectra and the scaling exponents of the structure functions up to the eighth order in the range of scales greater than 10η was insensitive to variations in Kmaxη, even when Kmaxη≃1. The relationship between the spatial resolution and asymptotic tail of the probability density functions of the energy dissipation fields was studied using the multifractal model for dissipation, and the results were confirmed by comparison to the simulation data. Degradation of the statistics arises from modifications to the flow dynamics due to the finite wavenumber cutoff and the use of a coarser filter width for the data, which is obtained using a reasonable accuracy criterion for the flow dynamics. The effect of the former was less than that of the latter for the low-to-moderate-order statistics when Kmaxη≥1. We also discuss the universality of the inertial-range statistics with respect to variations in the dissipation-range characteristics.

Toshiyuki Gotoh

Papers

Study of High-Reynolds Number Isotropic Turbulence by Direct Numerical Simulation

Velocity field statistics in homogeneous steady turbulence obtained using a high-resolution direct numerical simulation

Statistics of a passive scalar in homogeneous turbulence

Pressure Spectrum in Homogeneous Turbulence

Inertial-range intermittency and accuracy of direct numerical simulation for turbulence and passive scalar turbulence