The Experts below are selected from a list of 28230 Experts worldwide ranked by ideXlab platform
Gregory L Eyink - One of the best experts on this subject based on the ideXlab platform.
-
physical mechanism of the inverse energy cascade of two dimensional turbulence a numerical investigation
Journal of Fluid Mechanics, 2009Co-Authors: Zuoli Xiao, Shiyi Chen, Gregory L EyinkAbstract:We report an investigation of inverse energy cascade in steady-state two-dimensional turbulence by direct numerical simulation (DNS) of the two-dimensional Navier–Stokes equation, with small-scale forcing and large-scale damping. We employed several types of damping and dissipation mechanisms in simulations up to 2048 2 resolution. For all these simulations we obtained a wavenumber range for which the mean spectral energy flux is a negative constant and the energy spectrum scales as k −5/3 , consistent with the predictions of Kraichnan ( Phys. Fluids , vol. 439, 1967, p. 1417). To gain further insight, we investigated the energy cascade in physical space, employing a local energy flux defined by smooth filtering. We found that the inverse energy cascade is scale local, but that the strongly local contribution vanishes identically, as argued by Kraichnan ( J. Fluid Mech ., vol. 47, 1971, p. 525). The mean flux across a length scale l was shown to be due mainly to interactions with modes two to eight times smaller. A major part of our investigation was devoted to identifying the physical mechanism of the two-dimensional inverse energy cascade. One popular idea is that inverse energy cascade proceeds via merger of like-sign vortices. We made a quantitative study employing a precise topological criterion of merger events. Our statistical analysis showed that vortex mergers play a negligible direct role in producing mean inverse energy flux in our simulations. Instead, we obtained with the help of other works considerable evidence in favour of a ‘vortex thinning’ mechanism, according to which the large-scale strains do negative work against Turbulent Stress as they stretch out the isolines of small-scale vorticity. In particular, we studied a multi-scale gradient (MSG) expansion developed by Eyink ( J. Fluid Mech ., vol. 549, 2006 a , p. 159) for the Turbulent Stress, whose contributions to inverse cascade can all be explained by ‘thinning’. The MSG expansion up to second order in space gradients was found to predict well the magnitude, spatial structure and scale distribution of the local energy flux. The majority of mean flux was found to be due to the relative rotation of strain matrices at different length scales, a first-order effect of ‘thinning’. The remainder arose from two second-order effects, differential strain rotation and vorticity gradient stretching. Our findings give strong support to vortex thinning as the fundamental mechanism of two-dimensional inverse energy cascade.
-
physical mechanism of the two dimensional inverse energy cascade
Physical Review Letters, 2006Co-Authors: Shiyi Chen, Gregory L Eyink, Robert E Ecke, Michael Rivera, Zuoli XiaoAbstract:: We study the physical mechanisms of the two-dimensional inverse energy cascade using theory, numerics, and experiment. Kraichnan's prediction of a -5/3 spectrum with constant, negative energy flux is verified in our simulations of 2D Navier-Stokes equations. We observe a similar but shorter range of inverse cascade in laboratory experiments. Our theory predicts, and the data confirm, that inverse cascade results mainly from Turbulent Stress proportional to small-scale strain rotated by 45 degrees. This "skew-Newtonian" Stress is explained by the elongation and thinning of small-scale vortices by large-scale strain which weakens their velocity and transfers their energy upscale.
-
multi scale gradient expansion of the Turbulent Stress tensor
Journal of Fluid Mechanics, 2006Co-Authors: Gregory L EyinkAbstract:Turbulent Stress is the fundamental quantity in the filtered equation for large-scale velocity that reflects its interactions with small-scale velocity modes. We develop an expansion of the Turbulent Stress tensor into a double series of contributions from different scales of motion and different orders of space derivatives of velocity, a multi-scale gradient (MSG) expansion. We compare our method with a somewhat similar expansion that is based instead on defiltering. Our MSG expansion is proved to converge to the exact Stress, as a consequence of the locality of cascade both in scale and in space. Simple estimates show, however, that the convergence rate may be slow for the expansion in spatial gradients of very small scales. Therefore, we develop an approximate expansion, based upon an assumption that similar or ‘coherent’ contributions to Turbulent Stress are obtained from disjoint subgrid regions. This coherent-subregions approximation (CSA) yields an MSG expansion that can be proved to converge rapidly at all scales and is hopefully still reasonably accurate. As an important first application of our methods, we consider the cascades of energy and helicity in three-dimensional turbulence. To first order in velocity gradients, the Stress has three contributions: a tensile Stress along principal directions of strain, a contractile Stress along vortex lines, and a shear Stress proportional to ‘skew-strain’. While vortex stretching plays the major role in energy cascade, there is a second, less scale-local contribution from ‘skew-strain’. For helicity cascade the situation is reversed, and it arises scale-locally from ‘skew-strain’ while the Stress along vortex lines gives a secondary, less scale-local contribution. These conclusions are illustrated with simple exact solutions of three-dimensional Euler equations. In the first, energy cascade occurs by Taylor's mechanism of stretching and spin-up of small-scale vortices owing to large-scale strain. In the second, helicity cascade occurs by ‘twisting’ of small-scale vortex filaments owing to a large-scale screw.
-
a Turbulent constitutive law for the two dimensional inverse energy cascade
Journal of Fluid Mechanics, 2006Co-Authors: Gregory L EyinkAbstract:The inverse energy cascade of two-dimensional turbulence is often represented phenomenologically by a Newtonian Stress-strain relation with a 'negative eddy viscosity'. Here we develop a fundamental approach to a Turbulent constitutive law for the two-dimensional inverse cascade, based upon a convergent multi-scale gradient (MSG) expansion. To first order in gradients, we find that the Turbulent Stress generated by small-scale eddies is proportional not to strain but instead to 'skew-strain,' i.e. the strain tensor rotated by 45°. The skew-strain from a given scale of motion makes no contribution to energy flux across eddies at that scale, so that the inverse cascade cannot be strongly scale-local. We show that this conclusion extends a result of Kraichnan for spectral transfer and is due to absence of vortex stretching in two dimensions. This 'weakly local' mechanism of inverse cascade requires a relative rotation between the principal directions of strain at different scales and we argue for this using both the dynamical equations of motion and also a heuristic model of 'thinning' of small-scale vortices by an imposed large-scale strain. Carrying out our expansion to second order in gradients, we find two additional terms in the Stress that can contribute to the energy cascade. The first is a Newtonian Stress with an 'eddy-viscosity' due to differential strain rotation, and the second is a tensile Stress exerted along vorticity contour lines. The latter was anticipated by Kraichnan for a very special model situation of small-scale vortex wave-packets in a uniform strain field. We prove a proportionality in two dimensions between the mean rates of differential strain rotation and of vorticity-gradient stretching, analogous to a similar relation of Betchov for three dimensions. According to this result, the second-order Stresses will also contribute to inverse cascade when, as is plausible, vorticity contour lines lengthen, on average, by Turbulent advection.
-
multi scale gradient expansion of the Turbulent Stress tensor
arXiv: Chaotic Dynamics, 2005Co-Authors: Gregory L EyinkAbstract:We develop an expansion of the Turbulent Stress tensor into a double series of contributions from different scales of motion and different orders of space-derivatives of velocity, a Multi-Scale Gradient (MSG) expansion. The expansion is proved to converge to the exact Stress, as a consequence of the locality of cascade both in scale and in space. Simple estimates show, however, that the convergence rate may be slow for the expansion in spatial gradients of very small scales. Therefore, we develop an approximate expansion, based upon an assumption that similar or `coherent' contributions to Turbulent Stress are obtained from disjoint subgrid regions. This Coherent-Subregions Approximation (CSA) yields an MSG expansion that can be proved to converge rapidly at all scales and is hopefully still reasonably accurate. As an application, we consider the cascades of energy and helicity in three-dimensional turbulence. To first order in velocity-gradients, the Stress has three contributions: a tensile Stress along principal directions of strain, a contractile Stress along vortex lines, and a shear Stress proportional to `skew-strain.' While vortex-stretching plays the major role in energy cascade, there is a second, less scale-local contribution from `skew-strain'. For helicity cascade the situation is reversed, and it arises scale-locally from `skew-strain' while the Stress along vortex-lines gives a secondary, less scale-local contribution. These conclusions are illustrated with simple exact solutions of 3D Euler equations. In the first, energy cascade occurs by Taylor's mechanism of stretching and spin-up of small-scale vortices due to large-scale strain. In the second, helicity cascade occurs by `twisting' of small-scale vortex filaments due to a large-scale screw.
Zuoli Xiao - One of the best experts on this subject based on the ideXlab platform.
-
physical mechanism of the inverse energy cascade of two dimensional turbulence a numerical investigation
Journal of Fluid Mechanics, 2009Co-Authors: Zuoli Xiao, Shiyi Chen, Gregory L EyinkAbstract:We report an investigation of inverse energy cascade in steady-state two-dimensional turbulence by direct numerical simulation (DNS) of the two-dimensional Navier–Stokes equation, with small-scale forcing and large-scale damping. We employed several types of damping and dissipation mechanisms in simulations up to 2048 2 resolution. For all these simulations we obtained a wavenumber range for which the mean spectral energy flux is a negative constant and the energy spectrum scales as k −5/3 , consistent with the predictions of Kraichnan ( Phys. Fluids , vol. 439, 1967, p. 1417). To gain further insight, we investigated the energy cascade in physical space, employing a local energy flux defined by smooth filtering. We found that the inverse energy cascade is scale local, but that the strongly local contribution vanishes identically, as argued by Kraichnan ( J. Fluid Mech ., vol. 47, 1971, p. 525). The mean flux across a length scale l was shown to be due mainly to interactions with modes two to eight times smaller. A major part of our investigation was devoted to identifying the physical mechanism of the two-dimensional inverse energy cascade. One popular idea is that inverse energy cascade proceeds via merger of like-sign vortices. We made a quantitative study employing a precise topological criterion of merger events. Our statistical analysis showed that vortex mergers play a negligible direct role in producing mean inverse energy flux in our simulations. Instead, we obtained with the help of other works considerable evidence in favour of a ‘vortex thinning’ mechanism, according to which the large-scale strains do negative work against Turbulent Stress as they stretch out the isolines of small-scale vorticity. In particular, we studied a multi-scale gradient (MSG) expansion developed by Eyink ( J. Fluid Mech ., vol. 549, 2006 a , p. 159) for the Turbulent Stress, whose contributions to inverse cascade can all be explained by ‘thinning’. The MSG expansion up to second order in space gradients was found to predict well the magnitude, spatial structure and scale distribution of the local energy flux. The majority of mean flux was found to be due to the relative rotation of strain matrices at different length scales, a first-order effect of ‘thinning’. The remainder arose from two second-order effects, differential strain rotation and vorticity gradient stretching. Our findings give strong support to vortex thinning as the fundamental mechanism of two-dimensional inverse energy cascade.
-
physical mechanism of the two dimensional inverse energy cascade
Physical Review Letters, 2006Co-Authors: Shiyi Chen, Gregory L Eyink, Robert E Ecke, Michael Rivera, Zuoli XiaoAbstract:: We study the physical mechanisms of the two-dimensional inverse energy cascade using theory, numerics, and experiment. Kraichnan's prediction of a -5/3 spectrum with constant, negative energy flux is verified in our simulations of 2D Navier-Stokes equations. We observe a similar but shorter range of inverse cascade in laboratory experiments. Our theory predicts, and the data confirm, that inverse cascade results mainly from Turbulent Stress proportional to small-scale strain rotated by 45 degrees. This "skew-Newtonian" Stress is explained by the elongation and thinning of small-scale vortices by large-scale strain which weakens their velocity and transfers their energy upscale.
Shiyi Chen - One of the best experts on this subject based on the ideXlab platform.
-
physical mechanism of the inverse energy cascade of two dimensional turbulence a numerical investigation
Journal of Fluid Mechanics, 2009Co-Authors: Zuoli Xiao, Shiyi Chen, Gregory L EyinkAbstract:We report an investigation of inverse energy cascade in steady-state two-dimensional turbulence by direct numerical simulation (DNS) of the two-dimensional Navier–Stokes equation, with small-scale forcing and large-scale damping. We employed several types of damping and dissipation mechanisms in simulations up to 2048 2 resolution. For all these simulations we obtained a wavenumber range for which the mean spectral energy flux is a negative constant and the energy spectrum scales as k −5/3 , consistent with the predictions of Kraichnan ( Phys. Fluids , vol. 439, 1967, p. 1417). To gain further insight, we investigated the energy cascade in physical space, employing a local energy flux defined by smooth filtering. We found that the inverse energy cascade is scale local, but that the strongly local contribution vanishes identically, as argued by Kraichnan ( J. Fluid Mech ., vol. 47, 1971, p. 525). The mean flux across a length scale l was shown to be due mainly to interactions with modes two to eight times smaller. A major part of our investigation was devoted to identifying the physical mechanism of the two-dimensional inverse energy cascade. One popular idea is that inverse energy cascade proceeds via merger of like-sign vortices. We made a quantitative study employing a precise topological criterion of merger events. Our statistical analysis showed that vortex mergers play a negligible direct role in producing mean inverse energy flux in our simulations. Instead, we obtained with the help of other works considerable evidence in favour of a ‘vortex thinning’ mechanism, according to which the large-scale strains do negative work against Turbulent Stress as they stretch out the isolines of small-scale vorticity. In particular, we studied a multi-scale gradient (MSG) expansion developed by Eyink ( J. Fluid Mech ., vol. 549, 2006 a , p. 159) for the Turbulent Stress, whose contributions to inverse cascade can all be explained by ‘thinning’. The MSG expansion up to second order in space gradients was found to predict well the magnitude, spatial structure and scale distribution of the local energy flux. The majority of mean flux was found to be due to the relative rotation of strain matrices at different length scales, a first-order effect of ‘thinning’. The remainder arose from two second-order effects, differential strain rotation and vorticity gradient stretching. Our findings give strong support to vortex thinning as the fundamental mechanism of two-dimensional inverse energy cascade.
-
physical mechanism of the two dimensional inverse energy cascade
Physical Review Letters, 2006Co-Authors: Shiyi Chen, Gregory L Eyink, Robert E Ecke, Michael Rivera, Zuoli XiaoAbstract:: We study the physical mechanisms of the two-dimensional inverse energy cascade using theory, numerics, and experiment. Kraichnan's prediction of a -5/3 spectrum with constant, negative energy flux is verified in our simulations of 2D Navier-Stokes equations. We observe a similar but shorter range of inverse cascade in laboratory experiments. Our theory predicts, and the data confirm, that inverse cascade results mainly from Turbulent Stress proportional to small-scale strain rotated by 45 degrees. This "skew-Newtonian" Stress is explained by the elongation and thinning of small-scale vortices by large-scale strain which weakens their velocity and transfers their energy upscale.
R V E Lovelace - One of the best experts on this subject based on the ideXlab platform.
-
advection of magnetic fields in accretion disks not so difficult after all
The Astrophysical Journal, 2008Co-Authors: David M Rothstein, R V E LovelaceAbstract:We show that a large-scale, weak magnetic field threading a Turbulent accretion disk tends to be advected inward, contrary to previous suggestions that it will be stopped by outward diffusion. The efficient inward transport is a consequence of the diffuse, magnetically dominated surface layers of the disk, where the turbulence is suppressed and the conductivity is very high. This structure arises naturally in three-dimensional simulations of magnetorotationally unstable disks, and we demonstrate here that it can easily support inward advection and compression of a weak field. The advected field is anchored in the surface layer but penetrates the main body of the disk, where it can generate strong turbulence and produce values of α (i.e., the Turbulent Stress) that are large enough to match observational constraints; typical values of the vertical magnetic field merely need to reach a few percent of equipartition for this to occur. Overall, these results have important implications for models of jet formation that require strong, large-scale magnetic fields to exist over a region of the inner accretion disk.
C P Dullemond - One of the best experts on this subject based on the ideXlab platform.
-
efficiency of thermal relaxation by radiative processes in protoplanetary discs constraints on hydrodynamic turbulence
Astronomy and Astrophysics, 2017Co-Authors: M G Malygin, Hubert Klahr, D Semenov, Th Henning, C P DullemondAbstract:Context. Hydrodynamic, non-magnetic instabilities can provide Turbulent Stress in the regions of protoplanetary discs, where the magneto-rotational instability can not develop. The induced motions influence the grain growth, from which formation of planetesimals begins. Thermal relaxation of the gas constrains origins of the identified hydrodynamic sources of turbulence in discs. Aims. We aim to estimate the radiative relaxation timescale of temperature perturbations in protoplanetary discs. We study the dependence of the thermal relaxation on the perturbation wavelength, the location within the disc, the disc mass, and the dust-to-gas mass ratio. We then apply thermal relaxation criteria to localise modes of the convective overstability, the vertical shear instability, and the zombie vortex instability. Methods. For a given temperature perturbation, we estimated two timescales: the radiative diffusion timescale t thick and the optically thin emission timescale t thin . The longest of these timescales governs the relaxation: t relax = max (t thick , t thin ). We additionally accounted for the collisional coupling to the emitting species. Our calculations employed the latest tabulated dust and gas mean opacities. Results. The relaxation criterion defines the bulk of a typical T Tauri disc as unstable to the development of linear hydrodynamic instabilities. The midplane is unstable to the convective overstability from at most 2au and up to 40au, as well as beyond 140au. The vertical shear instability can develop between 15au and 180au. The successive generation of (zombie) vortices from a seeded noise can work within the inner 0.8au. Conclusions. A map of relaxation timescale constrains the origins of the identified hydrodynamic turbulence-driving mechanisms in protoplanetary discs. Dynamic disc modelling with the evolution of dust and gas opacities is required to clearly localise the hydrodynamic turbulence, and especially its non-linear phase.
-
efficiency of thermal relaxation by radiative processes in protoplanetary discs constraints on hydrodynamic turbulence
arXiv: Earth and Planetary Astrophysics, 2017Co-Authors: M G Malygin, Hubert Klahr, D Semenov, Th Henning, C P DullemondAbstract:Hydrodynamic, non-magnetic instabilities can provide Turbulent Stress in the regions of protoplanetary discs, where the MRI can not develop. The induced motions influence the grain growth, from which formation of planetesimals begins. Thermal relaxation of the gas constrains origins of the identified hydrodynamic sources of turbulence in discs. We estimate the radiative relaxation timescale of temperature perturbations and study the dependence of this timescale on the perturbation wavelength, the location within the disc, the disc mass, and the dust-to-gas mass ratio. We then apply thermal relaxation criteria to localise modes of the convective overstability, the vertical shear instability, and the zombie vortex instability. Our calculations employed the latest tabulated dust and gas mean opacities and we account for the collisional coupling to the emitting species. The relaxation criterion defines the bulk of a typical T Tauri disc as unstable to the development of linear hydrodynamic instabilities. The midplane is unstable to the convective overstability from at most $2\mbox{ au}$ and up to $40\mbox{ au}$, as well as beyond $140\mbox{ au}$. The vertical shear instability can develop between $15\mbox{ au}$ and $180\mbox{ au}$. The successive generation of (zombie) vortices from a seeded noise can work within the inner $0{.}8\mbox{ au}$. Dynamic disc modelling with the evolution of dust and gas opacities is required to clearly localise the hydrodynamic turbulence, and especially its non-linear phase.
