A Large Eddy Simulation of Turbulent Compressible Convection: Differential Rotation in the Solar Convection Zone

We present results of two simulations of the convection zone, obtained by solving the full hydrodynamic equations in a section of a spherical shell. The first simulation has cylindrical rotation contours (parallel to the rotation axis) and a strong meridional circulation, which traverses the entire depth. The second simulation has isorotation contours about mid-way between cylinders and cones, and a weak meridional circulation, concentrated in the uppermost part of the shell. We show that the solar differential rotation is directly related to a latitudinal entropy gradient, which pervades into the deep layers of the convection zone. We also offer an explanation of the angular velocity shear found at low latitudes near the top. A non-zero correlation between radial and zonal velocity fluctuations produces a significant Reynolds stress in that region. This constitutes a net transport of angular momentum inwards, which causes a slight modification of the overall structure of the differential rotation near the top. In essence, the {\it thermodynamics controls the dynamics through the Taylor-Proudman momentum balance}. The Reynolds stresses only become significant in the surface layers, where they generate a weak meridional circulation and an angular velocity `bump'.Comment: 11 pages, 14 figures, the first figure was too large and is excluded. Accepted for publication in MNRA

Two-Fluid RANS-RSTM-PDF Model for Turbulent Particulate Flows

A novel three-dimensional (3D) model based on Reynolds turbulence stress model (RSTM) closure of equations of carrier and particulate phases was elaborated for channel turbulent flows. The essence of the model is the direct calculation of normal and shear components of the Reynolds stresses for the particulate phase similar to the carrier fluid. The model is based on the Eulerian approach, which is applied for the 3D RANS modeling of the carrier flow and the particulate phase and the statistical probability dense function (PDF) approach focusing on the mathematical description of the second moments of the particulate phase

Prayer to Ta pi hri tsa - A short exposition of the Base, the Path and the Fruit in Bon Dzogchen teachings

Revue d’Etudes Tibétaines Number 16, April 200

Discovering explicit Reynolds-averaged turbulence closures for turbulent separated flows through deep learning-based symbolic regression with non-linear corrections

This work introduces a novel data-driven framework to formulate explicit algebraic Reynolds-averaged Navier-Stokes (RANS) turbulence closures. Recent years have witnessed a blossom in applying machine learning (ML) methods to revolutionize the paradigm of turbulence modeling. However, due to the black-box essence of most ML methods, it is currently hard to extract interpretable information and knowledge from data-driven models. To address this critical limitation, this work leverages deep learning with symbolic regression methods to discover hidden governing equations of Reynolds stress models. Specifically, the Reynolds stress tensor is decomposed into linear and non-linear parts. While the linear part is taken as the regular linear eddy viscosity model, a long short-term memory neural network is employed to generate symbolic terms on which tractable mathematical expressions for the non-linear counterpart are built. A novel reinforcement learning algorithm is employed to train the neural network to produce best-fitted symbolic expressions. Within the proposed framework, the Reynolds stress closure is explicitly expressed in algebraic forms, thus allowing for direct functional inference. On the other hand, the Galilean and rotational invariance are craftily respected by constructing the training feature space with independent invariants and tensor basis functions. The performance of the present methodology is validated through numerical simulations of three different canonical flows that deviate in geometrical configurations. The results demonstrate promising accuracy improvements over traditional RANS models, showing the generalization ability of the proposed method. Moreover, with the given explicit model equations, it can be easier to interpret the influence of input features on generated models

On the role of vortex stretching in energy optimal growth of three dimensional perturbations on plane parallel shear flows

The three dimensional optimal energy growth mechanism, in plane parallel shear flows, is reexamined in terms of the role of vortex stretching and the interplay between the span-wise vorticity and the planar divergent components. For high Reynolds numbers the structure of the optimal perturbations in Couette, Poiseuille, and mixing layer shear profiles is robust and resembles localized plane-waves in regions where the background shear is large. The waves are tilted with the shear when the span-wise vorticity and the planar divergence fields are in (out of) phase when the background shear is positive (negative). A minimal model is derived to explain how this configuration enables simultaneous growth of the two fields, and how this mutual amplification reflects on the optimal energy growth. This perspective provides an understanding of the three dimensional growth solely from the two dimensional dynamics on the shear plane

Entropic Lattice Boltzmann Simulation of the Flow Past Square Cylinder

Minimal Boltzmann kinetic models, such as lattice Boltzmann, are often used as an alternative to the discretization of the Navier-Stokes equations for hydrodynamic simulations. Recently, it was argued that modeling sub-grid scale phenomena at the kinetic level might provide an efficient tool for large scale simulations. Indeed, a particular variant of this approach, known as the entropic lattice Boltzmann method (ELBM), has shown that an efficient coarse-grained simulation of decaying turbulence is possible using these approaches. The present work investigates the efficiency of the entropic lattice Boltzmann in describing flows of engineering interest. In order to do so, we have chosen the flow past a square cylinder, which is a simple model of such flows. We will show that ELBM can quantitatively capture the variation of vortex shedding frequency as a function of Reynolds number in the low as well as the high Reynolds number regime, without any need for explicit sub-grid scale modeling. This extends the previous studies for this set-up, where experimental behavior ranging from $Re\sim O(10)$ to $Re\leq 1000$ were predicted by a single simulation algorithm.Comment: 12 pages, 5 figures, to appear in Int. J. Mod. Phys.

On the lack of X-ray iron line reverberation in MCG-6-30-15: Implications for the black hole mass and accretion disk structure

We use the method of Press, Rybicki & Hewitt (1992) to search for time lags and time leads between different energy bands of the RXTE data for MCG-6-30-15. We tailor our search in order to probe any reverberation signatures of the fluorescent iron Kalpha line that is thought to arise from the inner regions of the black hole accretion disk. In essence, an optimal reconstruction algorithm is applied to the continuum band (2-4keV) light curve which smoothes out noise and interpolates across the data gaps. The reconstructed continuum band light curve can then be folded through trial transfer functions in an attempt to find lags or leads between the continuum band and the iron line band (5-7keV). We find reduced fractional variability in the line band. The spectral analysis of Lee et al. (1999) reveals this to be due to a combination of an apparently constant iron line flux (at least on timescales of few x 10^4s), and flux correlated changes in the photon index. We also find no evidence for iron line reverberation and exclude reverberation delays in the range 0.5-50ksec. This extends the conclusions of Lee et al. and suggests that the iron line flux remains constant on timescales as short as 0.5ksec. The large black hole mass (>10^8Msun) naively suggested by the constancy of the iron line flux is rejected on other grounds. We suggest that the black hole in MCG-6-30-15 has a mass of M_BH~10^6-10^7Msun and that changes in the ionization state of the disk may produce the puzzling spectral variability. Finally, it is found that the 8-15keV band lags the 2-4keV band by 50-100s. This result is used to place constraints on the size and geometry of the Comptonizing medium responsible for the hard X-ray power-law in this AGN.Comment: 11 pages, 13 postscript figures. Accepted for publication in Ap