Large-eddy simulation of magnetohydrodynamic turbulence in compressible fluid
TL;DR: In this article, a large eddy simulation (LES) technique for the study of compressible magnetohydrodynamic turbulence is developed, where the filtered equations of magnetodynamic dynamics of a compressible fluid are obtained with the use of a mass-weighted filtering procedure (Favre filtering).
Abstract: In the present article, the large eddy simulation (LES) technique for the study of compressible magnetohydrodynamic turbulence is developed. The filtered equations of magnetohydrodynamics of compressible fluid are obtained with the use of a mass-weighted filtering procedure (Favre filtering). Favre-filtered equations for large-scale components of turbulence include subgrid-scale terms describing subgrid phenomena. Different models for closure of subgrid terms are suggested. In this work numerical simulation of filtered magnetohydrodynamic equations and an analysis of the received characteristics of turbulent flow is carried out. The obtained results of numerical computations for different LES models are compared with the results of direct numerical simulation.
Citations
More filters
TL;DR: In this article, scale-dependent spatial filtering on the Vlasov equation is used to extract information at prescribed scales and introduce several energy transfer functions, such as − (P · ∇ ) · u, which can trigger a channel of the energy conversion between fluid flow and random motions.
Abstract: Kinetic plasma turbulence cascade spans multiple scales ranging from macroscopic fluid flow to sub-electron scales. Mechanisms that dissipate large scale energy, terminate the inertial range cascade, and convert kinetic energy into heat are hotly debated. Here, we revisit these puzzles using fully kinetic simulation. By performing scale-dependent spatial filtering on the Vlasov equation, we extract information at prescribed scales and introduce several energy transfer functions. This approach allows highly inhomogeneous energy cascade to be quantified as it proceeds down to kinetic scales. The pressure work, − ( P · ∇ ) · u , can trigger a channel of the energy conversion between fluid flow and random motions, which contains a collision-free generalization of the viscous dissipation in collisional fluid. Both the energy transfer and the pressure work are strongly correlated with velocity gradients.
131 citations
TL;DR: In this article, an axisymmetric steady-state solar wind model that describes properties of the large-scale solar wind, interplanetary magnetic field, and turbulence throughout the heliosphere from 0.3 AU to 100 AU was developed.
Abstract: We have developed an axisymmetric steady-state solar wind model that describes properties of the large-scale solar wind, interplanetary magnetic field, and turbulence throughout the heliosphere from 0.3 AU to 100 AU. The model is based on numerical solutions of large-scale Reynolds-averaged magnetohydrodynamic equations coupled with a set of small-scale transport equations for the turbulence energy, normalized cross helicity, and correlation scale. The combined set of time-dependent equations is solved in the frame of reference corotating with the Sun using a time-relaxation method. We use the model to study the self-consistent interaction between the large-scale solar wind and smaller-scale turbulence and the role of the turbulence in the large-scale structure and temperature distribution in the solar wind. To illuminate the roles of the turbulent cascade and the pickup protons in heating the solar wind depending on the heliocentric distance, we compare the model results with and without turbulence/pickup protons. The variations of plasma temperature in the outer heliosphere are compared with Ulysses and Voyager 2 observations.
120 citations
Additional excerpts
...…Alazraki & Couturier 1971), non-WKB two-scale decomposition (Marsch & Tu 1989; Zhou & Matthaeus 1990), large eddy simulation (LES; Shimomura 1991; Chernyshov et al. 2006, 2007), or Reynolds decomposition and averaging to follow large scales together with evolution/transport equations that…...
[...]
TL;DR: The large eddy simulation method was developed as an alternative to direct modeling and which filters the initial magnetohydrodynamic equations and uses the subgrid-scale modeling of universal small-scale turbulence.
Abstract: A state-of-the-art review is given of research by computing physics methods on compressible magnetohydrodynamic turbulence in space plasmas. The presence of magnetic fields and compressibility in this case makes space plasma turbulence much less amenable to direct numerical simulations than a neutral incompressible fluid. The large eddy simulation method is discussed, which was developed as an alternative to direct modeling and which filters the initial magnetohydrodynamic equations and uses the subgrid-scale modeling of universal small-scale turbulence. A detailed analysis is made of both the method itself and different subgrid-scale parametrizations for compressible magnetohydrodynamic turbulent flows in polytropic and heat-conducting plasmas. The application of subgrid-scale modeling to study turbulence in the local interstellar medium and the scale-invariant spectra of magnetohydrodynamic turbulence are discussed.
118 citations
National Center for Atmospheric Research1, University of Delaware2, Stockholm University3, Russian Academy of Sciences4, Moscow Institute of Physics and Technology5, University of Colorado Boulder6, École centrale de Lyon7, University of California, Los Angeles8, Princeton University9, University of Leeds10
TL;DR: The nature of MHD turbulence and the small-scale processes that give rise to energy dissipation, plasma heating, and magnetic reconnection are discussed, and how these processes may best be captured within an LES/SGS framework is considered.
Abstract: We live in an age in which high-performance computing is transforming the way we do science. Previously intractable problems are now becoming accessible by means of increasingly realistic numerical simulations. One of the most enduring and most challenging of these problems is turbulence. Yet, despite these advances, the extreme parameter regimes encountered in space physics and astrophysics (as in atmospheric and oceanic physics) still preclude direct numerical simulation. Numerical models must take a Large Eddy Simulation (LES) approach, explicitly computing only a fraction of the active dynamical scales. The success of such an approach hinges on how well the model can represent the subgrid-scales (SGS) that are not explicitly resolved. In addition to the parameter regime, heliophysical and astrophysical applications must also face an equally daunting challenge: magnetism. The presence of magnetic fields in a turbulent, electrically conducting fluid flow can dramatically alter the coupling between large and small scales, with potentially profound implications for LES/SGS modeling. In this review article, we summarize the state of the art in LES modeling of turbulent magnetohydrodynamic (MHD) flows. After discussing the nature of MHD turbulence and the small-scale processes that give rise to energy dissipation, plasma heating, and magnetic reconnection, we consider how these processes may best be captured within an LES/SGS framework. We then consider several specific applications in heliophysics and astrophysics, assessing triumphs, challenges, and future directions.
74 citations
TL;DR: In this paper, a review article is presented to critically analyze turbulence and its role in the solar atmosphere and solar wind, as well as to provide a tutorial overview of topics worth clarification.
Abstract: The objective of this review article is to critically analyze turbulence and its role in the solar atmosphere and solar wind, as well as to provide a tutorial overview of topics worth clarification. Although turbulence is a ubiquitous phenomenon in the sun and its heliosphere, many open questions exist concerning the physical mechanisms of turbulence generation in solar environment. Also, the spatial and temporal evolution of the turbulence in the solar atmosphere and solar wind are still poorly understood. We limit the scope of this paper (leaving out the solar interior and convection zone) to the magnetized plasma that reaches from the photosphere and chromosphere upwards to the corona and inner heliosphere, and place particular emphasis on the magnetic field structures and fluctuations and their role in the dynamics and radiation of the coronal plasma. To attract the attention of scientists from both the fluid-dynamics and space-science communities we give in the first two sections a phenomenological overview of turbulence-related processes, in the context of solar and heliospheric physics and with emphasis on the photosphere-corona connection and the coupling between the solar corona and solar wind. We also discuss the basic tools and standard concepts for the empirical analysis and theoretical description of turbulence. The last two sections of this paper give a concise review of selected aspects of oscillations and waves in the solar atmosphere and related fluctuations in the solar wind. We conclude with some recommendations and suggest topics for future research.
67 citations
References
More filters
TL;DR: In this article, an extended period numerical integration of a baroclinic primitive equation model has been made for the simulation and the study of the dynamics of the atmosphere's general circulation, and the solution corresponding to external gravitational propagation is filtered by requiring the vertically integrated divergence to vanish identically.
Abstract: An extended period numerical integration of a baroclinic primitive equation model has been made for the simulation and the study of the dynamics of the atmosphere's general circulation. The solution corresponding to external gravitational propagation is filtered by requiring the vertically integrated divergence to vanish identically. The vertical structure permits as dependent variables the horizontal wind at two internal levels and a single temperature, with the static stability entering as a parameter. The incoming radiation is a function of latitude only corresponding to the annual mean, and the outgoing radiation is taken to be a function of the local temperature. With the requirement for thermal equilibrium, the domain mean temperature is specified as a parameter. The role of condensation is taken into account only as it effectively reduces the static stability. All other external sources and sinks of heat are assumed to balance each other locally, and are thus omitted. The kinematics are th...
12,952 citations
TL;DR: In this article, a new eddy viscosity model is presented which alleviates many of the drawbacks of the existing subgrid-scale stress models, such as the inability to represent correctly with a single universal constant different turbulent fields in rotating or sheared flows, near solid walls, or in transitional regimes.
Abstract: One major drawback of the eddy viscosity subgrid‐scale stress models used in large‐eddy simulations is their inability to represent correctly with a single universal constant different turbulent fields in rotating or sheared flows, near solid walls, or in transitional regimes. In the present work a new eddy viscosity model is presented which alleviates many of these drawbacks. The model coefficient is computed dynamically as the calculation progresses rather than input a priori. The model is based on an algebraic identity between the subgrid‐scale stresses at two different filtered levels and the resolved turbulent stresses. The subgrid‐scale stresses obtained using the proposed model vanish in laminar flow and at a solid boundary, and have the correct asymptotic behavior in the near‐wall region of a turbulent boundary layer. The results of large‐eddy simulations of transitional and turbulent channel flow that use the proposed model are in good agreement with the direct simulation data.
6,747 citations
TL;DR: In this paper, the subgrid-scale closure method developed by Germano et al. is modified by use of a least squares technique to minimize the difference between the closure assumption and the resolved stresses.
Abstract: The subgrid‐scale closure method developed by Germano et al. is modified by use of a least squares technique to minimize the difference between the closure assumption and the resolved stresses. This modification removes a source of singularity and is believed to improve the method’s applicability.
3,730 citations
TL;DR: The current understanding of astrophysical magnetic fields is reviewed in this paper, focusing on their generation and maintenance by turbulence, where analytical and numerical results are discussed both for small scale dynamos, which are completely isotropic, and for large scale dynamo, where some form of parity breaking is crucial.
1,548 citations
TL;DR: In this article, a two-part review summarizes the observations, theory, and simulations of interstellar turbulence and their implications for many fields of astrophysics, including 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...
Abstract: ▪ 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...
1,195 citations