scholarly journals How do velocity structure functions trace gas dynamics in simulated molecular clouds?

2019 ◽  
Vol 630 ◽  
pp. A97 ◽  
Author(s):  
R.-A. Chira ◽  
J. C. Ibáñez-Mejía ◽  
M.-M. Mac Low ◽  
Th. Henning
Keyword(s):  
Gravitational Collapse ◽  
Molecular Clouds ◽  
Velocity Structure ◽  
Structure Functions ◽  
Radiative Heating ◽  
Three Dimensions ◽  
Small Scale ◽  
Velocity Relationship ◽  
Crossing Time ◽  
Density Weighting

Context. Supersonic disordered flows accompany the formation and evolution of molecular clouds (MCs). It has been argued that this is turbulence that can support against gravitational collapse and form hierarchical sub-structures. Aims. We examine the time evolution of simulated MCs to investigate: What physical process dominates the driving of turbulent flows? How can these flows be characterised? Are they consistent with uniform turbulence or gravitational collapse? Do the simulated flows agree with observations? Methods. We analysed three MCs that have formed self-consistently within kiloparsec-scale numerical simulations of the interstellar medium (ISM). The simulated ISM evolves under the influence of physical processes including self-gravity, stratification, magnetic fields, supernova-driven turbulence, and radiative heating and cooling. We characterise the flows using velocity structure functions (VSFs) with and without density weighting or a density cutoff, and computed in one or three dimensions. However, we do not include optical depth effects that can hide motions in the densest gas, limiting comparison of our results with observations. Results. In regions with sufficient resolution, the density-weighted VSFs initially appear to follow the expectations for uniform turbulence, with a first-order power-law exponent consistent with Larson’s size-velocity relationship. Supernova blast wave impacts on MCs produce short-lived coherent motions at large scales, increasing the scaling exponents for a crossing time. Gravitational contraction drives small-scale motions, producing scaling coefficients that drop or even turn negative as small scales become dominant. Removing the density weighting eliminates this effect as it emphasises the diffuse ISM. Conclusions. We conclude that two different effects coincidentally reproduce Larson’s size velocity relationship. Initially, uniform turbulence dominates, so the energy cascade produces VSFs that are consistent with Larson’s relationship. Later, contraction dominates and the density-weighted VSFs become much shallower or even inverted, but the relationship of the global average velocity dispersion of the MCs to their radius follows Larson’s relationship, reflecting virial equilibrium or free-fall collapse. The injection of energy by shocks is visible in the VSFs, but decays within a crossing time.

scholarly journals Small-scale physical and chemical structure of diffuse and translucent molecular clouds along the line of sight to Sgr B2

2019 ◽  
Vol 623 ◽  
pp. A68 ◽  
Author(s):  
V. Thiel ◽  
A. Belloche ◽  
K. M. Menten ◽  
A. Giannetti ◽  
H. Wiesemeyer ◽  
...  
Keyword(s):  
Molecular Clouds ◽  
Velocity Structure ◽  
Angular Resolution ◽  
Principal Component ◽  
High Sensitivity ◽  
Field Of View ◽  
Continuum Emission ◽  
Line Of Sight ◽  
Small Scale ◽  
Galactic Centre

Context. The diffuse and translucent molecular clouds traced in absorption along the line of sight to strong background sources have so far been investigated mainly in the spectral domain because of limited angular resolution or small sizes of the background sources. Aims. We aim to resolve and investigate the spatial structure of molecular clouds traced by several molecules detected in absorption along the line of sight to Sgr B2(N). Methods. We have used spectral line data from the EMoCA survey performed with the Atacama Large Millimeter/submillimeter Array (ALMA), taking advantage of its high sensitivity and angular resolution. The velocity structure across the field of view is investigated by automatically fitting synthetic spectra to the detected absorption features, which allows us to decompose them into individual clouds located in the Galactic centre (GC) region and in spiral arms along the line of sight. We compute opacity maps for all detected molecules. We investigated the spatial and kinematical structure of the individual clouds with statistical methods and perform a principal component analysis to search for correlations between the detected molecules. To investigate the nature of the molecular clouds along the line of sight to Sgr B2, we also used archival Mopra data. Results. We identify, on the basis of c-C3H2, 15 main velocity components along the line of sight to Sgr B2(N) and several components associated with the envelope of Sgr B2 itself. The c-C3H2 column densities reveal two categories of clouds. Clouds in Category I (3 kpc arm, 4 kpc arm, and some GC clouds) have smaller c-C3H2 column densities, smaller linewidths, and smaller widths of their column density PDFs than clouds in Category II (Scutum arm, Sgr arm, and other GC clouds). We derive opacity maps for the following molecules: c-C3H2, H13CO+, 13CO, HNC and its isotopologue HN13C, HC15N, CS and its isotopologues C34S and 13CS, SiO, SO, and CH3OH. These maps reveal that most molecules trace relatively homogeneous structures that are more extended than the field of view defined by the background continuum emission (about 15′′, that is 0.08–0.6 pc depending on the distance). SO and SiO show more complex structures with smaller clumps of size ~5–8′′. Our analysis suggests that the driving of the turbulence is mainly solenoidal in the investigated clouds. Conclusions. On the basis of HCO+, we conclude that most line-of-sight clouds towards Sgr B2 are translucent, including all clouds where complex organic molecules were recently detected. We also conclude that CCH and CH are good probes of H2 in both diffuse and translucent clouds, while HCO+ and c-C3H2 in translucent clouds depart from the correlations with H2 found in diffuse clouds.

Longitudinal and transverse structure functions in a turbulent round jet: effect of initial conditions and Reynolds number

2001 ◽  
Vol 436 ◽  
pp. 231-248 ◽  
Author(s):  
G. P. ROMANO ◽  
R. A. ANTONIA
Keyword(s):  
Reynolds Number ◽  
Large Scale ◽  
Velocity Structure ◽  
Initial Conditions ◽  
Transverse Velocity ◽  
Structure Functions ◽  
Small Scale ◽  
Round Jet ◽  
Jet Nozzle ◽  
The Difference

The difference between scaling exponents of longitudinal and transverse velocity structure functions in the far-field of a round jet is found to depend on the anisotropy of the flow. The effect of the large-scale anisotropy is assessed by considering different initial conditions at the jet nozzle, and hence different ratios of the longitudinal to transverse rms velocities. The effect of the Taylor microscale Reynolds number on the small scale anisotropy is also considered. Both effects account, to a large extent, for the observed difference between longitudinal and transverse exponents and the disagreement between previously published results of different authors. This disagreement also depends on the method used to determine the inertial range. An empirical description of the overall behaviour of the structure functions provides reasonable estimates for the longitudinal and transverse exponents, accounting reasonably well for the anisotropy of both large- and small-scale motions.

scholarly journals Scaling and Similarity of the Anisotropic Coherent Eddies in Near-Surface Atmospheric Turbulence

2018 ◽  
Vol 75 (3) ◽  
pp. 943-964 ◽  
Author(s):  
Khaled Ghannam ◽  
Gabriel G. Katul ◽  
Elie Bou-Zeid ◽  
Tobias Gerken ◽  
Marcelo Chamecki
Keyword(s):  
Scaling Laws ◽  
Velocity Structure ◽  
Scaling Law ◽  
Longitudinal Velocity ◽  
Structure Functions ◽  
Length Scale ◽  
Near Surface ◽  
Vegetation Canopies ◽  
Velocity Spectra ◽  
Attached Eddies

Abstract The low-wavenumber regime of the spectrum of turbulence commensurate with Townsend’s “attached” eddies is investigated here for the near-neutral atmospheric surface layer (ASL) and the roughness sublayer (RSL) above vegetation canopies. The central thesis corroborates the significance of the imbalance between local production and dissipation of turbulence kinetic energy (TKE) and canopy shear in challenging the classical distance-from-the-wall scaling of canonical turbulent boundary layers. Using five experimental datasets (two vegetation canopy RSL flows, two ASL flows, and one open-channel experiment), this paper explores (i) the existence of a low-wavenumber k−1 scaling law in the (wind) velocity spectra or, equivalently, a logarithmic scaling ln(r) in the velocity structure functions; (ii) phenomenological aspects of these anisotropic scales as a departure from homogeneous and isotropic scales; and (iii) the collapse of experimental data when plotted with different similarity coordinates. The results show that the extent of the k−1 and/or ln(r) scaling for the longitudinal velocity is shorter in the RSL above canopies than in the ASL because of smaller scale separation in the former. Conversely, these scaling laws are absent in the vertical velocity spectra except at large distances from the wall. The analysis reveals that the statistics of the velocity differences Δu and Δw approach a Gaussian-like behavior at large scales and that these eddies are responsible for momentum/energy production corroborated by large positive (negative) excursions in Δu accompanied by negative (positive) ones in Δw. A length scale based on TKE dissipation collapses the velocity structure functions at different heights better than the inertial length scale.

scholarly journals Solar wind low-frequency magnetohydrodynamic turbulence: extended self-similarity and scaling laws

1996 ◽  
Vol 3 (4) ◽  
pp. 247-261 ◽  
Author(s):  
V. Carbone ◽  
P. Veltri ◽  
R. Bruno
Keyword(s):  
Solar Wind ◽  
Scaling Laws ◽  
Velocity Structure ◽  
Fluid Flows ◽  
Structure Functions ◽  
Point Of View ◽  
Self Similarity ◽  
Extended Self ◽  
Scaling Exponents ◽  
Magnetohydrodynamic Turbulence

Abstract. In this paper we review some of the work done in investigating the scaling properties of Magnetohydrodynamic turbulence, by using velocity fluctuations measurements performed in the interplanetary space plasma by the Helios spacecraft. The set of scaling exponents ξq for the q-th order velocity structure functions, have been determined by using the Extended Self-Similarity hypothesis. We have found that the q-th order velocity structure function, when plotted vs. the 4-th order structure function, displays a range of self-similarity which extends over all the lengths covered by measurements, thus allowing for a very good determination of ξq. Moreover the results seem to show that the scaling exponents are the same regardless the various observation periods considered. The obtained scaling exponents have been compared with the results of some intermittency models for Kraichnan's turbulence, derived in the framework of infinitely divisible fragmentation processes, showing the good agreement between these models and our observations. Finally, on the basis of the actually available data sets, we show that scaling laws in Solar Wind turbulence seem to be different from turbulent scaling laws in the ordinary fluid flows. This is true for high-order velocity structure functions, while low-order velocity structure functions show the same scaling laws. Since our measurements involve length scales which extend over many order of magnitude where dissipation is practically absent, our results show that Solar Wind turbulence can be regarded as a testing bench for the investigation of general scaling behaviour in turbulent flows. In particular our results strongly support the point of view which attributes a key role to the inertial range dynamics in determining the intermittency characteristics in fluid flows, in contrast with the point of view which attributes intermittency to a finite Reynolds number effect.

scholarly journals Ion Dynamics in the Meso-scale 3-D Kelvin–Helmholtz Instability: Perspectives From Test Particle Simulations

2021 ◽  
Vol 8 ◽  
Author(s):  
Xuanye Ma ◽  
Peter Delamere ◽  
Katariina Nykyri ◽  
Brandon Burkholder ◽  
Stefan Eriksson ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Magnetic Reconnection ◽  
Test Particle ◽  
Acoustic Waves ◽  
Particle Simulation ◽  
Three Dimensions ◽  
Small Scale ◽  
Physical Processes ◽  
Length Scales ◽  
Ion Species

Over three decades of in-situ observations illustrate that the Kelvin–Helmholtz (KH) instability driven by the sheared flow between the magnetosheath and magnetospheric plasma often occurs on the magnetopause of Earth and other planets under various interplanetary magnetic field (IMF) conditions. It has been well demonstrated that the KH instability plays an important role for energy, momentum, and mass transport during the solar-wind-magnetosphere coupling process. Particularly, the KH instability is an important mechanism to trigger secondary small scale (i.e., often kinetic-scale) physical processes, such as magnetic reconnection, kinetic Alfvén waves, ion-acoustic waves, and turbulence, providing the bridge for the coupling of cross scale physical processes. From the simulation perspective, to fully investigate the role of the KH instability on the cross-scale process requires a numerical modeling that can describe the physical scales from a few Earth radii to a few ion (even electron) inertial lengths in three dimensions, which is often computationally expensive. Thus, different simulation methods are required to explore physical processes on different length scales, and cross validate the physical processes which occur on the overlapping length scales. Test particle simulation provides such a bridge to connect the MHD scale to the kinetic scale. This study applies different test particle approaches and cross validates the different results against one another to investigate the behavior of different ion species (i.e., H+ and O+), which include particle distributions, mixing and heating. It shows that the ion transport rate is about 1025 particles/s, and mixing diffusion coefficient is about 1010 m2 s−1 regardless of the ion species. Magnetic field lines change their topology via the magnetic reconnection process driven by the three-dimensional KH instability, connecting two flux tubes with different temperature, which eventually causes anisotropic temperature in the newly reconnected flux.

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