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Spectral Modeling of Rotating Turbulent Flows  [PDF]
J. Baerenzung,P. D. Mininni,A. Pouquet,H. Politano,Y. Ponty
Physics , 2008,
Abstract: We test a subgrid-scale spectral model of rotating turbulent flows against direct numerical simulations. The particular case of Taylor-Green forcing at large scale is considered, a configuration that mimics the flow between two counter rotating disks as often used in the laboratory. We perform computations in the presence of moderate rotation down to Rossby numbers of 0.03, as can be encountered in the Earth atmosphere and oceans. We provide several classical measures of the degree of anisotropy of the small scales of the flows under study and conclude that an isotropic model may suffice at moderate Rossby numbers. The model, developed previously (Baerenzung et al., Phys. Rev. E 77, 046303 (2008)), incorporates eddy viscosity that depends dynamically on the inertial index of the energy spectrum, as well as eddy noise. We show that the model reproduces satisfactorily all large-scale properties of the direct numerical simulations up to Reynolds numbers of the order of 10000 and for long times after the onset of the inverse cascade of energy at low Rossby number.
Spectral Modeling of Magnetohydrodynamic Turbulent Flows  [PDF]
J. Baerenzung,H. Politano,Y. Ponty,A. Pouquet
Physics , 2008, DOI: 10.1103/PhysRevE.78.026310
Abstract: We present a dynamical spectral model for Large Eddy Simulation of the incompressible magnetohydrodynamic (MHD) equations based on the Eddy Damped Quasi Normal Markovian approximation. This model extends classical spectral Large Eddy Simulations for the Navier-Stokes equations to incorporate general (non Kolmogorovian) spectra as well as eddy noise. We derive the model for MHD and show that introducing a new eddy-damping time for the dynamics of spectral tensors in the absence of equipartition between the velocity and magnetic fields leads to better agreement with direct numerical simulations, an important point for dynamo computations.
Spectral Modeling of Turbulent Flows and the Role of Helicity  [PDF]
Julien Baerenzung,Helene Politano,Yannick Ponty,Annick Pouquet
Physics , 2007, DOI: 10.1103/PhysRevE.77.046303
Abstract: We present a new version of a dynamical spectral model for Large Eddy Simulation based on the Eddy Damped Quasi Normal Markovian approximation \cite{sao,chollet_lesieur}. Three distinct modifications are implemented and tested. On the one hand, whereas in current approaches, a Kolmogorov-like energy spectrum is usually assumed in order to evaluate the nonlocal transfer, in our method the energy spectrum of the subgrid scales adapts itself dynamically to the large-scale resolved spectrum; this first modification allows in particular for a better treatment of transient phases and instabilities, as shown on one specific example. Moreover, the model takes into account the phase relationships of the small-scales, embodied for example in strong localized structures such as vortex filaments. To that effect, phase information is implemented in the treatment of the so-called eddy noise in the closure model. Finally, we also consider the role that helical small scales may play in the evaluation of the transfer of energy and helicity, the two invariants of the primitive equations in the inviscid case; this leads as well to intrinsic variations in the development of helicity spectra. Therefore, our model allows for simulations of flows for a variety of circumstances and a priori at any given Reynolds number. Comparisons with Direct Numerical Simulations of the three-dimensional Navier-Stokes equation are performed on fluids driven by an ABC (Beltrami) flow which is a prototype of fully helical flows. Good agreements are obtained for physical and spectral behavior of the large scales.
Particle drift in turbulent flows: the influence of local structure and inhomogeneity  [PDF]
Michael W. Reeks
Physics , 2012,
Abstract: The way particles interact with turbulent structures, particularly in regions of high vorticity and strain rate, has been investigated in simulations of homogeneous turbulence and in simple flows which have a periodic or persistent structure e.g. separating flows and mixing layers. The influence on both settling under gravity and diffusion has been reported and the divergence (compressibility) of the underlying particle velocity field along a particle trajectory has been recognized as an important quantity in quantifying these features. This paper shows how these features can be incorporated in a formal way into a two-fluid model of the dispersed particle phase. In particular the PDF equation for the particle velocity and position is formerly derived on the basis of a stochastic process that involves the statistics of both the particle velocity and local compressibility along particle trajectories. The PDF equation gives rise to contributions to both the drift and particle diffusion coefficient that depend upon the correlation of these quantities with the local carrier flow velocity. Key Words: turbulent structures, particle dispersion, drift, PDF approach
Spectral decomposition approach to macroscopic parameters of Fokker-Planck flows: Part 1  [PDF]
Igor A. Tanski
Physics , 2007,
Abstract: In this paper we proceed with investigation of connections between Fokker - Planck equation and continuum mechanics. In spectral decomposition of Fokker - Planck equation solution we preserve only terms with the smallest degree of damping. We find, that macroscopic parameters of Fokker-Planck flows, obtained in this way, have following properties: velocities field possess potential, its potential is proportional to density logarithm and satisfy diffusion equation. We proved, that such a pair of density and velocities field satisfy the set of classic hydrodynamics equations for isothermal compressible fluid with friction mass force, proportional to velocity. We proved also, that the potential velocities field alone, with potential, which satisfy diffusion equation, satisfy Burgers equation without mass forces.
Large Eddy Simulation of Turbulent Barotropic Flows in Spectral Space on the Sphere  [PDF]
Leila N. Azadani,Anne E. Staples
Physics , 2014,
Abstract: Numerical simulations of atmospheric circulation models are limited by their finite spatial resolution, and so large eddy simulation (LES) is the preferred approach to study these models. In LES a low-pass filter is applied to the flow field to separate the large and small scale motions. In implicitly filtered LES the computational mesh and discretization schemes are considered to be the low-pass filter while in the explicitly filtered LES approach the filtering procedure is separated from the grid and discretization operators and allows for better control of the numerical errors. The aim of this paper is to study and compare implicitly filtered and explicitly filtered LES of atmospheric circulation models in spectral space. To achieve this goal we present the results of implicitly filtered and explicitly filtered LES of a barotropic atmosphere circulation model on the sphere in spectral space and compare them with the results obtained from direct numerical simulation (DNS). Our study shows that although in the computation of some integral quantities like total kinetic energy and total enstrophy the results obtained from implicitly filtered LES and explicitly filtered LES show the same good agreement with the DNS results, explicit filtering produces energy spectra that show better agreement with the DNS results. More importantly, explicit filtering captures the location of coherent structures over time while implicit filtering does not.
Spectral decomposition approach to macroscopic parameters of Fokker-Planck flows: Part 2  [PDF]
Igor A. Tanski
Physics , 2007,
Abstract: In this paper we proceed with investigation of connections between Fokker - Planck equation and continuum mechanics. We base upon expressions from our work [2], based upon the spectral decomposition of Fokker - Planck equation solution. In this decomposition we preserve only terms with the smallest degrees of damping. We find, that macroscopic parameters of Fokker-Planck flows, obtained in this way, satisfy the set of conservation laws of classic hydrodynamics. The expression for stresses (30) contains additional term - this term is negligible in big times limit. We proved also, that the velocities field alone satisfy Burgers equation without mass forces - but with some additional term. This term is also negligible in big times limit. For the zero degree theory, considered in [1], there are no additional terms. But this theory is valid only for the potential velocities field, fully deductible from density - the potential is proportional to density logarithm. In this theory we can not specify initial conditions for velocities independently from density. Taking in account of the next degree terms could partly solve this problem, but result in some loss of exactness.
The 3D structure of the Lagrangian acceleration in turbulent flows  [PDF]
Nicolas Mordant,Alice M. Crawford,Eberhard Bodenschatz
Physics , 2004, DOI: 10.1103/PhysRevLett.93.214501
Abstract: We report experimental results on the three dimensional Lagrangian acceleration in highly turbulent flows. Tracer particles are tracked optically using four silicon strip detectors from high energy physics that provide high temporal and spatial resolution. The components of the acceleration are shown to be statistically dependent. The probability density function (PDF) of the acceleration magnitude is comparable to a log-normal distribution. Assuming isotropy, a log-normal distribution of the magnitude can account for the observed dependency of the components. The time dynamics of the acceleration components is found to be typical of the dissipation scales whereas the magnitude evolves over longer times, possibly close to the integral time scale.
Dispersed Phase of Non-Isothermal Particles in Rotating Turbulent Flows  [PDF]
R. V. R. Pandya,P. Stansell
Physics , 2015,
Abstract: We suggest certain effects, caused by interaction between rotation and gravitation with turbulence structure, for the cooling/heating of dispersed phase of non-isothermal particles in rotating turbulent fluid flows. These effects are obtained through the derivation of kinetic or probability density function based macroscopic equations for the particles. In doing so, for one-way temperature coupling, we also show that homogeneous, isotropic non-isothermal fluid turbulence does not influence the mean temperature (though it influences mean velocity) of the dispersed phase of particles settling due to gravitational force in the isotropic turbulence.
Influence of Cooling-Induced Compressibility on the Structure of Turbulent Flows and Gravitational Collapse  [PDF]
E. Vazquez-Semadeni,T. Passot,A. Pouquet
Physics , 1996, DOI: 10.1086/178200
Abstract: We investigate the properties of highly compressible turbulence, the compressibility arising from a small effective polytropic exponent $\gamma_e$ due to cooling. In the limit of small $\gamma_e$, the density jump at shocks is shown to be of the order of $e^{M^2}$. Without self-gravity, the density structures arising in the moderately compressible case consist mostly of patches separated by shocks and behaving like waves, while in the highly compressible case clearly defined long-lived object-like clouds emerge. When the forcing in the momentum equation is purely compressible, the rotational energy decays monotonically in time, indicating that the vortex-stretching term is not efficient in transferring energy to rotational modes. This property may be at the origin of the low amount of rotation found in interstellar clouds. Vorticity production is found to rely heavily on the presence of additional terms in the equations. In the presence of self-gravity, we suggest that turbulence can produce bound structures for $\gamma_e < 2(1-1/n)$, where $n$ is the typical dimensionality of the turbulent compressions. We support this result by means of numerical simulations in which, for sufficiently small $\gamma_e$, small-scale turbulent density fluctuations eventually collapse even though the medium is globally stable. This result is preserved in the presence of a magnetic field for supercritical mass-to-flux ratios. At larger polytropic exponents, turbulence alone is not capable of producing bound structures, and collapse can only occur when the medium is globally unstable. This mechanism is a plausible candidate for the differentiation between primordial and present-day stellar-cluster formation and for the low efficiency of star formation.
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