Examining the growth and evolution of magnetic fields in clusters of galaxies: a numerical perspective

Magnetic fields are ubiquitous in galaxy cluster atmospheres and have a variety of astrophysical and cosmological consequences. Magnetic fields can contribute to the pressure support of clusters, affect thermal conduction, and modify the evolution of bubbles driven by active galactic nuclei. However, we currently do not fully understand the origin and evolution of these fields throughout cosmic time. Furthermore, we do not have a general understanding of the relationship between magnetic field strength and topology and other cluster properties, such as mass and X-ray luminosity. We can now begin to answer some of these questions using large-scale cosmological magnetohydrodynamic (MHD) simulations of the formation of galaxy clusters including the seeding and growth of magnetic fields. Using large-scale cosmological simulations with the FLASH code combined with a simplified model of the acceleration of cosmic rays responsible for the generation of radio halos, we find that the galaxy cluster frequency distribution and expected number counts of radio halos from upcoming low-frequency sur- veys are strongly dependent on the strength of magnetic fields. Thus, a more complete understanding of the origin and evolution of magnetic fields is necessary to understand and constrain models of diffuse synchrotron emission from clusters. One favored model for generating magnetic fields is through the amplification of weak seed fields in active galactic nuclei (AGN) accretion disks and their subsequent injection into cluster atmospheres via AGN-driven jets and bubbles. However, current large-scale cosmological simulations cannot directly include the physical processes associated with the accretion and feedback processes of AGN or the seeding and merging of the associated SMBHs. Thus, we must include these effects as subgrid models. In order to carefully study the growth of magnetic fields in clusters via AGN-driven outflows, we present a systematic study of SMBH and AGN subgrid models. Using dark-matter only cosmological simulations, we find that many important quantities, such as the relationship between SMBH mass and galactic bulge velocity dispersion and the merger rate of black holes, are highly sensitive to the subgrid model assumptions of SMBHs. In addition, using MHD calculations of an isolated cluster, we find that magnetic field strengths, extent, topology, and relationship to other gas quantities such as temperature and density are also highly dependent on the chosen model of accretion and feedback. We use these systematic studies of SMBHs and AGN inform and constrain our choice of subgrid models, and we use those results to outline a fully cosmological MHD simulation to study the injection and growth of magnetic fields in clusters of galaxies. This simulation will be the first to study the birth and evolution of magnetic fields using a fully closed accretion-feedback cycle, with as few assumptions as possible and a clearer understanding of the effects of the various parameter choices.

A theoretical framework for energy and momentum consistency in subgrid-scale parameterization for climate models

A theoretical framework for the joint conservation of energy and momentum in the parameterization of subgrid-scale processes in climate models is presented. The framework couples a hydrostatic resolved (planetary scale) flow to a nonhydrostatic subgrid-scale (mesoscale) flow. The temporal and horizontal spatial scale separation between the planetary scale and mesoscale is imposed using multiple-scale asymptotics. Energy and momentum are exchanged through subgrid-scale flux convergences of heat, pressure, and momentum. The generation and dissipation of subgrid-scale energy and momentum is understood using wave-activity conservation laws that are derived by exploiting the (mesoscale) temporal and horizontal spatial homogeneities in the planetary-scale flow. The relations between these conservation laws and the planetary-scale dynamics represent generalized nonacceleration theorems. A derived relationship between the wave-activity fluxes-which represents a generalization of the second Eliassen-Palm theorem-is key to ensuring consistency between energy and momentum conservation. The framework includes a consistent formulation of heating and entropy production due to kinetic energy dissipation.

Testing of subgrid scale (SGS) models for large-eddy simulation (LES) of turbulent channel flow

Sub-grid scale (SGS) models are required in order to model the influence of the unresolved small scales on the resolved scales in large-eddy simulations (LES), the flow at the smallest scales of turbulence. In the following work two SGS models are presented and deeply analyzed in terms of accuracy through several LESs with different spatial resolutions, i.e. grid spacings. The first part of this thesis focuses on the basic theory of turbulence, the governing equations of fluid dynamics and their adaptation to LES. Furthermore, two important SGS models are presented: one is the Dynamic eddy-viscosity model (DEVM), developed by \cite{germano1991dynamic}, while the other is the Explicit Algebraic SGS model (EASSM), by \cite{marstorp2009explicit}. In addition, some details about the implementation of the EASSM in a Pseudo-Spectral Navier-Stokes code \cite{chevalier2007simson} are presented. The performance of the two aforementioned models will be investigated in the following chapters, by means of LES of a channel flow, with friction Reynolds numbers $Re_\tau=590$ up to $Re_\tau=5200$, with relatively coarse resolutions. Data from each simulation will be compared to baseline DNS data. Results have shown that, in contrast to the DEVM, the EASSM has promising potentials for flow predictions at high friction Reynolds numbers: the higher the friction Reynolds number is the better the EASSM will behave and the worse the performances of the DEVM will be. The better performance of the EASSM is contributed to the ability to capture flow anisotropy at the small scales through a correct formulation for the SGS stresses. Moreover, a considerable reduction in the required computational resources can be achieved using the EASSM compared to DEVM. Therefore, the EASSM combines accuracy and computational efficiency, implying that it has a clear potential for industrial CFD usage.

Effects of Subgrid-Scale Modeling on Time Correlations in Large Eddy Simulation

The effects of the unresolved subgrid-scale (SGS) motions on the energy balance of the resolved scales in large eddy simulation (LES) have been investigated actively because modeling the energy transfer between the resolved and unresolved scales is crucial to constructing accurate SGS models. But the subgrid scales not only modify the energy balance, they also contribute to temporal decorrelation of the resolved scales. The importance of this effect in applications including the predictability problem and the evaluation of sound radiation by turbulent flows motivates the present study of the effect of SGS modeling on turbulent time correlations. This paper compares the two-point, two-time Eulerian velocity correlation in isotropic homogeneous turbulence evaluated by direct numerical simulation (DNS) with the correlations evaluated by LES using a standard spectral eddy viscosity. It proves convenient to express the two-point correlations in terms of spatial Fourier decomposition of the velocity field. The LES fields are more coherent than the DNS fields: their time correlations decay more slowly at all resolved scales of motion and both their integral scales and microscales are larger than those of the DNS field. Filtering alone is not responsible for this effect: in the Fourier representation, the time correlations of the filtered DNS field are identical to those of the DNS field itself. The possibility of modeling the decorrelating effects of the unresolved scales of motion by including a random force in the model is briefly discussed. The results could have applications to the problem of computing sound sources in isotropic homogeneous turbulence by LES

Effects Of Subgrid-Scale Modeling On Lagrangian Statistics In Large-Eddy Simulation

The application of large-eddy simulation (LES) to turbulent transport processes requires accurate prediction of the Lagrangian statistics of flow fields. However, in most existing SGS models, no explicit consideration is given to Lagrangian statistics. In this paper, we focus on the effects of SGS modeling on Lagrangian statistics in LES ranging from statistics determining single-particle dispersion to those of pair dispersion and multiparticle dispersion. Lagrangian statistics in homogeneous isotropic turbulence are extracted from direct numerical simulation (DNS) and the LES with a spectral eddy-viscosity model. For the case of longtime single-particle dispersion, it is shown that, compared to DNS, LES overpredicts the time scale of the Lagrangian velocity correlation but underpredicts the Lagrangian velocity fluctuation. These two effects tend to cancel one another leading to an accurate prediction of the longtime turbulent dispersion coefficient. Unlike the single-particle dispersion, LES tends to underestimate significantly the rate of relative dispersion of particle pairs and multiple-particles, when initial separation distances are less than the minimum resolved scale due to the lack of subgrid fluctuations. The overprediction of LES on the time scale of the Lagrangian velocity correlation is further confirmed by a theoretical analysis using a turbulence closure theory.

A second-order dynamic subgrid-scale stress model

A second-order dynamic model based on the general relation between the subgrid-scale stress and the velocity gradient tensors was proposed. A priori test of the second-order model was made using moderate resolution direct numerical simulation date at high Reynolds number ( Taylor microscale Reynolds number R-lambda = 102 similar to 216) for homogeneous, isotropic forced flow, decaying flow, and homogeneous rotating flow. Numerical testing shows that the second-order dynamic model significantly improves the correlation coefficient when compared to the first-order dynamic models.

Subgrid-scale contributions to Lagrangian time correlations in isotropic turbulence

The application of large-eddy simulation (LES) to particle-laden turbulence raises such a fundamental question as whether the LES with a subgrid scale (SGS) model can correctly predict Lagrangian time correlations (LTCs). Most of the currently existing SGS models are constructed based on the energy budget equations. Therefore, they are able to correctly predict energy spectra, but they may not ensure the correct prediction on the LTCs. Previous researches investigated the effect of the SGS modeling on the Eulerian time correlations. This paper is devoted to study the LTCs in LES. A direct numerical simulation (DNS) and the LES with a spectral eddy viscosity model are performed for isotropic turbulence and the LTCs are calculated using the passive vector method. Both a priori and a posteriori tests are carried out. It is observed that the subgrid-scale contributions to the LTCs cannot be simply ignored and the LES overpredicts the LTCs than the DNS. It is concluded from the straining hypothesis that an accurate prediction of enstrophy spectra is most critical to the prediction of the LTCs.

RAMI4PILPS: An intercomparison of formulations for the partitioning of solar radiation in land surface models

[1] Remotely sensed, multiannual data sets of shortwave radiative surface fluxes are now available for assimilation into land surface schemes (LSSs) of climate and/or numerical weather prediction models. The RAMI4PILPS suite of virtual experiments assesses the accuracy and consistency of the radiative transfer formulations that provide the magnitudes of absorbed, reflected, and transmitted shortwave radiative fluxes in LSSs. RAMI4PILPS evaluates models under perfectly controlled experimental conditions in order to eliminate uncertainties arising from an incomplete or erroneous knowledge of the structural, spectral and illumination related canopy characteristics typical for model comparison with in situ observations. More specifically, the shortwave radiation is separated into a visible and near-infrared spectral region, and the quality of the simulated radiative fluxes is evaluated by direct comparison with a 3-D Monte Carlo reference model identified during the third phase of the Radiation transfer Model Intercomparison (RAMI) exercise. The RAMI4PILPS setup thus allows to focus in particular on the numerical accuracy of shortwave radiative transfer formulations and to pinpoint to areas where future model improvements should concentrate. The impact of increasing degrees of structural and spectral subgrid variability on the simulated fluxes is documented and the relevance of any thus emerging biases with respect to gross primary production estimates and shortwave radiative forcings due to snow and fire events are investigated.

Coupled atmosphere-biophysics-hydrology models for environmental modeling

The formulation and implementation of LEAF-2, the Land Ecosystem–Atmosphere Feedback model, which comprises the representation of land–surface processes in the Regional Atmospheric Modeling System (RAMS), is described. LEAF-2 is a prognostic model for the temperature and water content of soil, snow cover, vegetation, and canopy air, and includes turbulent and radiative exchanges between these components and with the atmosphere. Subdivision of a RAMS surface grid cell into multiple areas of distinct land-use types is allowed, with each subgrid area, or patch, containing its own LEAF-2 model, and each patch interacts with the overlying atmospheric column with a weight proportional to its fractional area in the grid cell. A description is also given of TOPMODEL, a land hydrology model that represents surface and subsurface downslope lateral transport of groundwater. Details of the incorporation of a modified form of TOPMODEL into LEAF-2 are presented. Sensitivity tests of the coupled system are presented that demonstrate the potential importance of the patch representation and of lateral water transport in idealized model simulations. Independent studies that have applied LEAF-2 and verified its performance against observational data are cited. Linkage of RAMS and TOPMODEL through LEAF-2 creates a modeling system that can be used to explore the coupled atmosphere–biophysical–hydrologic response to altered climate forcing at local watershed and regional basin scales.

Basic concepts for convection parameterization in weather forecast and climate models: COST Action ES0905 final report

The research network “Basic Concepts for Convection Parameterization in Weather Forecast and Climate Models” was organized with European funding (COST Action ES0905) for the period of 2010–2014. Its extensive brainstorming suggests how the subgrid-scale parameterization problem in atmospheric modeling, especially for convection, can be examined and developed from the point of view of a robust theoretical basis. Our main cautions are current emphasis on massive observational data analyses and process studies. The closure and the entrainment–detrainment problems are identified as the two highest priorities for convection parameterization under the mass–flux formulation. The need for a drastic change of the current European research culture as concerns policies and funding in order not to further deplete the visions of the European researchers focusing on those basic issues is emphasized.

The DYMECS project: a statistical approach for the evaluation of convective storms in high-resolution NWP models

A new frontier in weather forecasting is emerging by operational forecast models now being run at convection-permitting resolutions at many national weather services. However, this is not a panacea; significant systematic errors remain in the character of convective storms and rainfall distributions. The DYMECS project (Dynamical and Microphysical Evolution of Convective Storms) is taking a fundamentally new approach to evaluate and improve such models: rather than relying on a limited number of cases, which may not be representative, we have gathered a large database of 3D storm structures on 40 convective days using the Chilbolton radar in southern England. We have related these structures to storm life-cycles derived by tracking features in the rainfall from the UK radar network, and compared them statistically to storm structures in the Met Office model, which we ran at horizontal grid length between 1.5 km and 100 m, including simulations with different subgrid mixing length. We also evaluated the scale and intensity of convective updrafts using a new radar technique. We find that the horizontal size of simulated convective storms and the updrafts within them is much too large at 1.5-km resolution, such that the convective mass flux of individual updrafts can be too large by an order of magnitude. The scale of precipitation cores and updrafts decreases steadily with decreasing grid lengths, as does the typical storm lifetime. The 200-m grid-length simulation with standard mixing length performs best over all diagnostics, although a greater mixing length improves the representation of deep convective storms.

Reducing noise associated with the Monte Carlo Independent Column Approximation for weather forecasting models

The Monte Carlo Independent Column Approximation (McICA) is a flexible method for representing subgrid-scale cloud inhomogeneity in radiative transfer schemes. It does, however, introduce conditional random errors but these have been shown to have little effect on climate simulations, where spatial and temporal scales of interest are large enough for effects of noise to be averaged out. This article considers the effect of McICA noise on a numerical weather prediction (NWP) model, where the time and spatial scales of interest are much closer to those at which the errors manifest themselves; this, as we show, means that noise is more significant. We suggest methods for efficiently reducing the magnitude of McICA noise and test these methods in a global NWP version of the UK Met Office Unified Model (MetUM). The resultant errors are put into context by comparison with errors due to the widely used assumption of maximum-random-overlap of plane-parallel homogeneous cloud. For a simple implementation of the McICA scheme, forecasts of near-surface temperature are found to be worse than those obtained using the plane-parallel, maximum-random-overlap representation of clouds. However, by applying the methods suggested in this article, we can reduce noise enough to give forecasts of near-surface temperature that are an improvement on the plane-parallel maximum-random-overlap forecasts. We conclude that the McICA scheme can be used to improve the representation of clouds in NWP models, with the provision that the associated noise is sufficiently small.