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Open accessJournal ArticleDOI: 10.1093/MNRAS/STAB053

Radiative mixing layers: insights from turbulent combustion

02 Mar 2021-Monthly Notices of the Royal Astronomical Society (Oxford Academic)-Vol. 502, Iss: 3, pp 3179-3199
Abstract: Radiative mixing layers arise wherever multiphase gas, shear, and radiative cooling are present. Simulations show that in steady state, thermal advection from the hot phase balances radiative cooling. However, many features are puzzling. For instance, hot gas entrainment appears to be numerically converged despite the scale-free, fractal structure of such fronts being unresolved. Additionally, the hot gas heat flux has a characteristic velocity $v_{\rm in} \approx c_{\rm s,cold} (t_{\rm cool}/t_{\rm sc,cold})^{-1/4}$ whose strength and scaling are not intuitive. We revisit these issues in 1D and 3D hydrodynamic simulations. We find that over-cooling only happens if numerical diffusion dominates thermal transport; convergence is still possible even when the Field length is unresolved. A deeper physical understanding of radiative fronts can be obtained by exploiting parallels between mixing layers and turbulent combustion, which has well-developed theory and abundant experimental data. A key parameter is the Damk\"ohler number ${\rm Da} = \tau_{\rm turb}/t_{\rm cool}$, the ratio of the outer eddy turnover time to the cooling time. Once ${\rm Da} > 1$, the front fragments into a multiphase medium. Just as for scalar mixing, the eddy turnover time sets the mixing rate, independent of small scale diffusion. For this reason, thermal conduction often has limited impact. We show that $v_{\rm in}$ and the effective emissivity can be understood in detail by adapting combustion theory scalings. Mean density and temperature profiles can also be reproduced remarkably well by mixing length theory. These results have implications for the structure and survival of cold gas in many settings, and resolution requirements for large scale galaxy simulations.

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Topics: Characteristic velocity (55%), Radiative cooling (53%), Radiative transfer (52%) ... read more
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14 results found


Journal ArticleDOI: 10.1111/J.1753-4887.1975.TB07431.X
27 Apr 2009-Nutrition Reviews
Abstract: Follow up what we will offer in this article about philosophical transactions of the royal society of london series b biological sciences no 600 vol 233 studies of the post glacial history of british vegetation x correlation between climate forest composition prehistoric agriculture and peat st. You know really that this book is coming as the best seller book today. So, when you are really a good reader or you're fans of the author, it does will be funny if you don't have this book. It means that you have to get this book. For you who are starting to learn about something new and feel curious about this book, it's easy then. Just get this book and feel how this book will give you more exciting lessons.

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480 Citations


Open access
Kyujin Kwak1, Robin L. Shelton1Institutions (1)
01 Jan 2010-
Abstract: Highly ionized species, such as C IV, N V, and O VI, are commonly observed in diffuse gas in various places in the universe, such as in our Galaxy's disk and halo, high velocity clouds (HVCs), external galaxies, and the intergalactic medium. These ions are often used to trace hot gas whose temperature is a few times 105 K. One possible mechanism for producing high ions is turbulent mixing of cool gas (such as that in a high or intermediate velocity cloud) with hotter (a few times 106 K) gas in locations where these gases slide past each other. By using hydrodynamic simulations with radiative cooling and non-equilibrium ionization (NEI) calculations, we investigate the physical properties of turbulent mixing layers and the production of high ions (C IV, N V, and O VI). We find that most of the mixing occurs on the hot side of the hot/cool interface, where denser cool gas is entrained and mixed into the hotter, more diffuse gas. Our simulations reveal that the mixed region separates into a tepid zone containing radiatively cooled, C IV-rich gas and a hotter zone which is rich in C IV, N V, and O VI. The hotter zone contains a mixture of low and intermediate ions contributed by the cool gas and intermediate and high-stage ions contributed by the hot gas. Mixing occurs faster than ionization or recombination, making the mixed gas a better source of C IV, N V, and O VI in our NEI simulations than in our collisional ionization equilibrium (CIE) simulations. In addition, the gas radiatively cools faster than the ions recombine, which also allows large numbers of C IV, N V, and O VI ions to linger in the NEI simulations. For these reasons, our NEI calculations predict more C IV, N V, and O VI than our CIE calculations predict. We also simulate various initial configurations and find that more C IV is produced when the shear speed is smaller or the hot gas has a higher temperature. We find no significant differences between simulations having different perturbation amplitudes in the initial boundary between the hot and cool gas. We discuss the results of our simulations, compare them with observations of the Galactic halo and highly ionized HVCs, and compare them with other models, including other turbulent mixing calculations. The ratios of C IV to N V and N V to O VI are in reasonable agreement with the averages calculated from observations of the halo. There is a great deal of variation from sightline to sightline and with time in our simulations. Such spatial and temporal variation may explain some of the variation seen among observations.

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Topics: Ionization (52%)

43 Citations


Open accessJournal ArticleDOI: 10.1093/MNRAS/STAA3610
Abstract: We revisit the problem of the growth of dense/cold gas in the cloud-crushing setup with radiative cooling. The relative motion between the dense cloud and the diffuse medium produces a turbulent boundary layer of mixed gas with a short cooling time. This mixed gas may explain the ubiquity of the range of absorption/emission lines observed in various sources such as the circumgalactic medium and galactic/stellar/AGN outflows. Recently Gronke & Oh showed that the efficient radiative cooling of the mixed gas can lead to the continuous growth of the dense cloud. They presented a threshold cloud size for the growth of dense gas which was contradicted by the more recent works of Li et al. & Sparre et al. These thresholds are qualitatively different as the former is based on the cooling time of the mixed gas whereas the latter is based on the cooling time of the hot gas. Our simulations agree with the threshold based on the cooling time of the mixed gas. We argue that the radiative cloud-crushing simulations should be run long enough to allow for the late-time growth of the dense gas due to cooling of the mixed gas but not so long that the background gas cools catastrophically. Moreover, the simulation domain should be large enough that the mixed gas is not lost through the boundaries. While the mixing layer is roughly isobaric, the emissivity of the gas at different temperatures is fundamentally different from an isobaric single-phase steady cooling flow.

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Topics: Radiative cooling (59%), Cooling flow (56%), Radiative transfer (53%)

12 Citations


Open accessJournal ArticleDOI: 10.3847/1538-4357/ABF8AB
Abstract: Winds from massive stars have velocities of 1000 km/s or more, and produce hot, high pressure gas when they shock. We develop a theory for the evolution of bubbles driven by the collective winds from star clusters early in their lifetimes, which involves interaction with the turbulent, dense interstellar medium of the surrounding natal molecular cloud. A key feature is the fractal nature of the hot bubble's surface. The large area of this interface with surrounding denser gas strongly enhances energy losses from the hot interior, enabled by turbulent mixing and subsequent cooling at temperatures T = 10^4-10^5 K where radiation is maximally efficient. Due to the extreme cooling, the bubble radius scales differently (R ~ t^1/2) from the classical Weaver77 solution, and has expansion velocity and momentum lower by factors of 10-10^2 at given R, with pressure lower by factors of 10^2 - 10^3. Our theory explains the weak X-ray emission and low shell expansion velocities of observed sources. We discuss further implications of our theory for observations of the hot bubbles and cooled expanding shells created by stellar winds, and for predictions of feedback-regulated star formation in a range of environments. In a companion paper, we validate our theory with a suite of hydrodynamic simulations.

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Topics: Interstellar medium (58%), Star formation (57%), Molecular cloud (53%) ... read more

11 Citations


Open accessJournal ArticleDOI: 10.3847/1538-4357/ABF8AC
Abstract: In a companion paper, we develop a theory for the evolution of stellar wind driven bubbles in dense, turbulent clouds. This theory proposes that turbulent mixing at a fractal bubble-shell interface leads to highly efficient cooling, in which the vast majority of the input wind energy is radiated away. This energy loss renders the majority of the bubble evolution momentum-driven rather than energy-driven, with expansion velocities and pressures orders of magnitude lower than in the classical Weaver77 solution. In this paper, we validate our theory with three-dimensional, hydrodynamic simulations. We show that extreme cooling is not only possible, but is generic to star formation in turbulent clouds over more than three orders of magnitude in density. We quantify the few free parameters in our theory, and show that the momentum exceeds the wind input rate by only a factor ~ 1.2-4. We verify that the bubble/cloud interface is a fractal with dimension ~ 2.5-2.7. The measured turbulent amplitude (v_t ~ 200-400 km/s) in the hot gas near the interface is shown to be consistent with theoretical requirements for turbulent diffusion to efficiently mix and radiate away most of the wind energy. The fraction of energy remaining after cooling is only 1-\Theta ~ 0.1-0.01, decreasing with time, explaining observations that indicate low hot-gas content and weak dynamical effects of stellar winds.

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Topics: Turbulent diffusion (59%), Star formation (51%), Orders of magnitude (time) (50%) ... read more

10 Citations


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102 results found


Journal ArticleDOI: 10.1109/MCSE.2007.55
Abstract: Matplotlib is a 2D graphics package used for Python for application development, interactive scripting,and publication-quality image generation across user interfaces and operating systems

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Topics: 2D computer graphics (56%), Computer graphics (55%), Python (programming language) (54%) ... read more

16,056 Citations


Open accessBook
01 Jan 1972-
Abstract: Keywords: turbulence ; transport ; contraintes ; transport ; couche : limite ; ecoulement ; tourbillon ; energie Reference Record created on 2005-11-18, modified on 2016-08-08

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Topics: K-epsilon turbulence model (66%), Turbulence (51%)

7,966 Citations


Open accessJournal ArticleDOI: 10.1109/MCSE.2011.37
Abstract: In the Python world, NumPy arrays are the standard representation for numerical data and enable efficient implementation of numerical computations in a high-level language. As this effort shows, NumPy performance can be improved through three techniques: vectorizing calculations, avoiding copying data in memory, and minimizing operation counts.

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Topics: NumPy (71%), Python (programming language) (53%)

7,607 Citations


Open accessJournal ArticleDOI: 10.1038/S41592-019-0686-2
Pauli Virtanen1, Ralf Gommers, Travis E. Oliphant, Matt Haberland2  +33 moreInstitutions (15)
03 Feb 2020-Nature Methods
Abstract: SciPy is an open-source scientific computing library for the Python programming language. Since its initial release in 2001, SciPy has become a de facto standard for leveraging scientific algorithms in Python, with over 600 unique code contributors, thousands of dependent packages, over 100,000 dependent repositories and millions of downloads per year. In this work, we provide an overview of the capabilities and development practices of SciPy 1.0 and highlight some recent technical developments.

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6,244 Citations


Open accessBook
Randall J. LeVeque1Institutions (1)
01 Jan 2002-
Abstract: Preface 1. Introduction 2. Conservation laws and differential equations 3. Characteristics and Riemann problems for linear hyperbolic equations 4. Finite-volume methods 5. Introduction to the CLAWPACK software 6. High resolution methods 7. Boundary conditions and ghost cells 8. Convergence, accuracy, and stability 9. Variable-coefficient linear equations 10. Other approaches to high resolution 11. Nonlinear scalar conservation laws 12. Finite-volume methods for nonlinear scalar conservation laws 13. Nonlinear systems of conservation laws 14. Gas dynamics and the Euler equations 15. Finite-volume methods for nonlinear systems 16. Some nonclassical hyperbolic problems 17. Source terms and balance laws 18. Multidimensional hyperbolic problems 19. Multidimensional numerical methods 20. Multidimensional scalar equations 21. Multidimensional systems 22. Elastic waves 23. Finite-volume methods on quadrilateral grids Bibliography Index.

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Topics: Hyperbolic partial differential equation (62%), Euler equations (62%), Conservation law (60%) ... read more

5,409 Citations


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No. of citations received by the Paper in previous years
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