Astrophysical turbulence modeling

The role of turbulence in various astrophysical settings is reviewed. Among the differences to laboratory and atmospheric turbulence we highlight the ubiquitous presence of magnetic fields that are generally produced and maintained by dynamo action. The extreme temperature and density contrasts and stratifications are emphasized in connection with turbulence in the interstellar medium and in stars with outer convection zones, respectively. In many cases turbulence plays an essential role in facilitating enhanced transport of mass, momentum, energy, and magnetic fields in terms of the corresponding coarse-grained mean fields. Those transport properties are usually strongly modified by anisotropies and often completely new effects emerge in such a description that have no correspondence in terms of the original (non coarse-grained) fields.Comment: 88 pages, 26 figures, published in Reports on Progress in Physic

Growth of a Richtmyer-Meshkov turbulent layer after reshock

This paper presents a numerical study of a reshocked turbulent mixing layer using high-order accurate Implicit Large-Eddy-Simulations (ILES). Existing theoretical approaches are discussed, and the theory of Youngs (detailed in Ref. 1) is extended to predict the behaviour of a reshocked mixing layer formed initially from a shock interacting with a broadband instability. The theory of Mikaelian2 is also extended to account for molecular mixing in the single-shocked layer prior to reshock. Simulations are conducted for broadband and narrowband initial perturbations and results for the growth rate of the reshocked layer and the decay rate of turbulent kinetic energy show excellent agreement with the extended theoretical approach. Reshock causes a marginal decrease in mixing parameters for the narrowband layer, but a significant increase for the broadband initial perturbation. The layer properties are observed to be very similar post-reshock, however, the growth rate exponent for the mixing layer width is higher in the broadband case, indicating that the reshocked layer still has a dependence (although weakened) on the initial conditions. These results have important implications for Unsteady Reynolds Averaged Navier Stokes modelling of such instabilities

Physical aspects of computing the flow of a viscous fluid

One of the main themes in fluid dynamics at present and in the future is going to be computational fluid dynamics with the primary focus on the determination of drag, flow separation, vortex flows, and unsteady flows. A computation of the flow of a viscous fluid requires an understanding and consideration of the physical aspects of the flow. This is done by identifying the flow regimes and the scales of fluid motion, and the sources of vorticity. Discussions of flow regimes deal with conditions of incompressibility, transitional and turbulent flows, Navier-Stokes and non-Navier-Stokes regimes, shock waves, and strain fields. Discussions of the scales of fluid motion consider transitional and turbulent flows, thin- and slender-shear layers, triple- and four-deck regions, viscous-inviscid interactions, shock waves, strain rates, and temporal scales. In addition, the significance and generation of vorticity are discussed. These physical aspects mainly guide computations of the flow of a viscous fluid

On the Hydrodynamic Interaction of Shock Waves with Interstellar Clouds. II. The Effect of Smooth Cloud Boundaries on Cloud Destruction and Cloud Turbulence

The effect of smooth cloud boundaries on the interaction of steady planar shock waves with interstellar clouds is studied using a high-resolution local AMR technique with a second-order accurate axisymmetric Godunov hydrodynamic scheme. A 3D calculation is also done to confirm the results of the 2D ones. We consider an initially spherical cloud whose density distribution is flat near the cloud center and has a power-law profile in the cloud envelope. When an incident shock is transmitted into a smooth cloud, velocity gradients in the cloud envelope steepen the smooth density profile at the upstream side, resulting in a sharp density jump having an arc-like shape. Such a ``slip surface'' forms immediately when a shock strikes a cloud with a sharp boundary. For smoother boundaries, the formation of slip surface and therefore the onset of hydrodynamic instabilities are delayed. Since the slip surface is subject to the Kelvin-Helmholtz and Rayleigh-Taylor instabilities, the shocked cloud is eventually destroyed in $\sim 3-10$ cloud crushing times. After complete cloud destruction, small blobs formed by fragmentation due to hydrodynamic instabilities have significant velocity dispersions of the order of 0.1 $v_b$, where $v_b$ is the shock velocity in the ambient medium. This suggests that turbulent motions generated by shock-cloud interaction are directly associated with cloud destruction. The interaction of a shock with a cold HI cloud should lead to the production of a spray of small HI shreds, which could be related to the small cold clouds recently observed by Stanimirovic & Heiles (2005). The linewidth-size relation obtained from our 3D simulation is found to be time-dependent. A possibility for gravitational instability triggered by shock compression is also discussed.Comment: 62 pages, 16 figures, submitted to Ap

Towards a solution of the closure problem for convective atmospheric boundary-layer turbulence

We consider the closure problem for turbulence in the dry convective atmospheric boundary layer (CBL). Transport in the CBL is carried by small scale eddies near the surface and large plumes in the well mixed middle part up to the inversion that separates the CBL from the stably stratified air above. An analytically tractable model based on a multivariate Delta-PDF approach is developed. It is an extension of the model of Gryanik and Hartmann [1] (GH02) that additionally includes a term for background turbulence. Thus an exact solution is derived and all higher order moments (HOMs) are explained by second order moments, correlation coefficients and the skewness. The solution provides a proof of the extended universality hypothesis of GH02 which is the refinement of the Millionshchikov hypothesis (quasi- normality of FOM). This refined hypothesis states that CBL turbulence can be considered as result of a linear interpolation between the Gaussian and the very skewed turbulence regimes. Although the extended universality hypothesis was confirmed by results of field measurements, LES and DNS simulations (see e.g. [2-4]), several questions remained unexplained. These are now answered by the new model including the reasons of the universality of the functional form of the HOMs, the significant scatter of the values of the coefficients and the source of the magic of the linear interpolation. Finally, the closures 61 predicted by the model are tested against measurements and LES data. Some of the other issues of CBL turbulence, e.g. familiar kurtosis-skewness relationships and relation of area coverage parameters of plumes (so called filling factors) with HOM will be discussed also

Angular Momentum Transport in Stellar Interiors

Stars lose a significant amount of angular momentum between birth and death, implying that efficient processes transporting it from the core to the surface are active. Space asteroseismology delivered the interior rotation rates of more than a thousand low- and intermediate-mass stars, revealing that: 1) single stars rotate nearly uniformly during the core hydrogen and core helium burning phases; 2) stellar cores spin up to a factor 10 faster than the envelope during the red giant phase; 3) the angular momentum of the helium-burning core of stars is in agreement with the angular momentum of white dwarfs. Observations reveal a strong decrease of core angular momentum when stars have a convective core. Current theory of angular momentum transport fails to explain this. We propose improving the theory with a data-driven approach, whereby angular momentum prescriptions derived from multi-dimensional (magneto)hydrodynamical simulations and theoretical considerations are continously tested against modern observations. The TESS and PLATO space missions have the potential to derive the interior rotation of large samples of stars, including high-mass and metal-poor stars in binaries and clusters. This will provide the powerful observational constraints needed to improve theory and simulations.Comment: Manuscript submitted to Annual Reviews of Astronomy and Astrophysics for Volume 57. This is the authors' submitted version. Revisions and the final version will only become available from https://www.annualreviews.org/journal/astr

Hydrodynamic capabilities of an SPH code incorporating an artificial conductivity term with a gravity-based signal velocity

This paper investigates the hydrodynamic performances of an SPH code incorporating an artificial heat conductivity term in which the adopted signal velocity is applicable when gravity is present. In accordance with previous findings it is shown that the performances of SPH to describe the development of Kelvin-Helmholtz instabilities depend strongly on the consistency of the initial condition set-up and on the leading error in the momentum equation due to incomplete kernel sampling. An error and stability analysis shows that the quartic B-spline kernel (M_5) possesses very good stability properties and we propose its use with a large neighbor number, between ~50 (2D) to ~ 100 (3D), to improve convergence in simulation results without being affected by the so-called clumping instability. SPH simulations of the blob test show that in the regime of strong supersonic flows an appropriate limiting condition, which depends on the Prandtl number, must be imposed on the artificial conductivity SPH coefficients in order to avoid an unphysical amount of heat diffusion. Results from hydrodynamic simulations that include self-gravity show profiles of hydrodynamic variables that are in much better agreement with those produced using mesh-based codes. In particular, the final levels of core entropies in cosmological simulations of galaxy clusters are consistent with those found using AMR codes. Finally, results of the Rayleigh-Taylor instability test demonstrate that in the regime of very subsonic flows the code has still several difficulties in the treatment of hydrodynamic instabilities. These problems being intrinsically due to the way in which in standard SPH gradients are calculated and not to the implementation of the artificial conductivity term.Comment: 26 pages, 15 figures, accepted for publication in A&

Beyond Mixing-length Theory: a step toward 321D

We examine the physical basis for algorithms to replace mixing-length theory (MLT) in stellar evolutionary computations. Our 321D procedure is based on numerical solutions of the Navier-Stokes equations. These implicit large eddy simulations (ILES) are three-dimensional (3D), time-dependent, and turbulent, including the Kolmogorov cascade. We use the Reynolds-averaged Navier-Stokes (RANS) formulation to make concise the 3D simulation data, and use the 3D simulations to give closure for the RANS equations. We further analyze this data set with a simple analytical model, which is non-local and time-dependent, and which contains both MLT and the Lorenz convective roll as particular subsets of solutions. A characteristic length (the damping length) again emerges in the simulations; it is determined by an observed balance between (1) the large-scale driving, and (2) small-scale damping. The nature of mixing and convective boundaries is analyzed, including dynamic, thermal and compositional effects, and compared to a simple model. We find that (1) braking regions (boundary layers in which mixing occurs) automatically appear {\it beyond} the edges of convection as defined by the Schwarzschild criterion, (2) dynamic (non-local) terms imply a non-zero turbulent kinetic energy flux (unlike MLT), (3) the effects of composition gradients on flow can be comparable to thermal effects, and (4) convective boundaries in neutrino-cooled stages differ in nature from those in photon-cooled stages (different P\'eclet numbers). The algorithms are based upon ILES solutions to the Navier-Stokes equations, so that, unlike MLT, they do not require any calibration to astronomical systems in order to predict stellar properties. Implications for solar abundances, helioseismology, asteroseismology, nucleosynthesis yields, supernova progenitors and core collapse are indicated.Comment: 22 pages, 4 figures, 2 tables; significantly re-written, critique of Pasetto, et al. model added, accepted for publication by Ap

Two-Dimensional Hydrodynamics of Pre-Core Collapse: Oxygen Shell Burning

By direct hydrodynamic simulation, using the Piecewise Parabolic Method (PPM) code PROMETHEUS, we study the properties of a convective oxygen burning shell in a SN 1987A progenitor star prior to collapse. The convection is too heterogeneous and dynamic to be well approximated by one-dimensional diffusion-like algorithms which have previously been used for this epoch. Qualitatively new phenomena are seen. The simulations are two-dimensional, with good resolution in radius and angle, and use a large (90-degree) slice centered at the equator. The microphysics and the initial model were carefully treated. Many of the qualitative features of previous multi-dimensional simulations of convection are seen, including large kinetic and acoustic energy fluxes, which are not accounted for by mixing length theory. Small but significant amounts of carbon-12 are mixed non-uniformly into the oxygen burning convection zone, resulting in hot spots of nuclear energy production which are more than an order of magnitude more energetic than the oxygen flame itself. Density perturbations (up to 8%) occur at the `edges' of the convective zone and are the result of gravity waves generated by interaction of penetrating flows into the stable region. Perturbations of temperature and electron fraction at the base of the convective zone are of sufficient magnitude to create angular inhomogeneities in explosive nucleosynthesis products, and need to be included in quantitative estimates of yields. Combined with the plume-like velocity structure arising from convection, the perturbations will contribute to the mixing of nickel-56 throughout supernovae envelopes. Runs of different resolution, and angular extent, were performed to test the robustness of theseComment: For mpeg movies of these simulations, see http://www.astrophysics.arizona.edu/movies.html Submitted to the Astrophysical Journa

Turbulent mixing

The ability of turbulent flows to effectively mix entrained fluids to a molecular scale is a vital part of the dynamics of such flows, with wide-ranging consequences in nature and engineering. It is a considerable experimental, theoretical, modeling, and computational challenge to capture and represent turbulent mixing which, for high Reynolds number (Re) flows, occurs across a spectrum of scales of considerable span. This consideration alone places high-Re mixing phenomena beyond the reach of direct simulation, especially in high Schmidt number fluids, such as water, in which species diffusion scales are one and a half orders of magnitude smaller than the smallest flow scales. The discussion below attempts to provide an overview of turbulent mixing; the attendant experimental, theoretical, and computational challenges; and suggests possible future directions for progress in this important field