Shear Instability

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Peter A Davies - One of the best experts on this subject based on the ideXlab platform.

  • convectively induced Shear Instability in large amplitude internal solitary waves
    Physics of Fluids, 2008
    Co-Authors: Magda Carr, Dorian Fructus, John Grue, Atle Jensen, Peter A Davies
    Abstract:

    Laboratory study has been carried out to investigate the Instability of an internal solitary wave of depression in a shallow stratified fluid system. The experimental campaign has been supported by theoretical computations and has focused on a two layered stratification consisting of a homogeneous dense layer below a linearly stratified top layer. The initial background stratification has been varied and it is found that the onset and intensity of breaking are affected dramatically by changes in the background stratification. Manifestations of a combination of Shear and convective Instability are seen on the leading face of the wave. It is shown that there is an interplay between the two Instability types and convective Instability induces Shear by enhancing isopycnal compression. Variation in the upper boundary condition is also found to have an effect on stability. In particular, the implications for convective Instability are shown to be profound and a dramatic increase in wave amplitude is seen for a ...

  • convectively induced Shear Instability in large amplitude internal solitary waves
    Physics of Fluids, 2008
    Co-Authors: Magda Carr, Dorian Fructus, John Grue, Atle Jensen, Peter A Davies
    Abstract:

    Laboratory study has been carried out to investigate the Instability of an internal solitary wave of depression in a shallow stratified fluid system. The experimental campaign has been supported by theoretical computations and has focused on a two layered stratification consisting of a homogeneous dense layer below a linearly stratified top layer. The initial background stratification has been varied and it is found that the onset and intensity of breaking are affected dramatically by changes in the background stratification. Manifestations of a combination of Shear and convective Instability are seen on the leading face of the wave. It is shown that there is an interplay between the two Instability types and convective Instability induces Shear by enhancing isopycnal compression. Variation in the upper boundary condition is also found to have an effect on stability. In particular, the implications for convective Instability are shown to be profound and a dramatic increase in wave amplitude is seen for a fixed (as opposed to free) upper boundary condition.

Hubert Klahr - One of the best experts on this subject based on the ideXlab platform.

  • high resolution parameter study of the vertical Shear Instability ii dependence on temperature gradient and cooling time
    Monthly Notices of the Royal Astronomical Society, 2021
    Co-Authors: Natascha Manger, Thomas Pfeil, Hubert Klahr
    Abstract:

    A certain appeal to the alpha model for turbulence and related viscosity in accretion disks was that one scales the Reynolds stresses simply on the thermal pressure, assuming that turbulence driven by a certain mechanism will attain a characteristic Mach number in its velocity fluctuations. Besides the notion that there are different mechanism driving turbulence and angular momentum transport in a disk, we also find that within a single Instability mechanism, here the Vertical Shear Instability, stresses do not linearly scale with thermal pressure. Here we demonstrate in numerical simulations the effect of the gas temperature gradient and the thermal relaxation time on the average stresses generated in the non-linear stage of the Instability. We find that the stresses scale with the square of the exponent of the radial temperature profile at least for a range of $d \log T /d \log R = [-0.5, -1]$, beyond which the pressure scale height varies too much over the simulation domain, to provide clear results. Stresses are also dependent on thermal relaxation times, provided they are longer than $10^{-3}$ orbital periods. The strong dependence of viscous transport of angular momentum on the local conditions in the disk (especially temperature, temperature gradient, and surface density/optical depth) challenges the ideas of viscosity leading to smooth density distributions, opening a route for structure (ring) formation and time variable mass accretion.

  • high resolution parameter study of the vertical Shear Instability
    Monthly Notices of the Royal Astronomical Society, 2020
    Co-Authors: Hubert Klahr, Natascha Manger, W Kley, Mario Flock
    Abstract:

    Theoretical models of protoplanetary disks have shown the Vertical Shear Instability (VSI) to be a prime candidate to explain turbulence in the dead zone of the disk. However, simulations of the VSI have yet to show consistent levels of key disk turbulence parameters like the stress-to-pressure ratio $\alpha$. We aim to reconcile these different values by performing a parameter study on the VSI with focus on the disk density gradient $p$ and aspect ratio $h := H/R$. We use full 2$\pi$ 3D simulations of the disk for chosen set of both parameters. All simulations are evolved for 1000 reference orbits, at a resolution of 18 cells per h. We find that the saturated stress-to-pressure ratio in our simulations is dependent on the disk aspect ratio with a \review{strong} scaling of $\alpha\propto h^{2.6}$, in contrast to the traditional $\alpha$ model, where viscosity scales as $\nu \propto \alpha h^2$ with a constant $\alpha$. We also observe consistent formation of large scale vortices across all investigated parameters. The vortices show uniformly aspect ratios of $\chi \approx 10$ and radial widths of approximately 1.5 $H$. With our findings we can reconcile the different values reported for the stress-to-pressure ratio from both isothermal and radiation hydrodynamics models, and show long-term evolution effects of the VSI that could aide in the formation of planetesimals.

  • the sandwich mode for vertical Shear Instability in protoplanetary disks
    arXiv: Earth and Planetary Astrophysics, 2020
    Co-Authors: Thomas Pfeil, Hubert Klahr
    Abstract:

    Turbulence has a profound impact on the evolution of gas and dust in protoplanetary disks (PPDs), from driving the collisions and the diffusion of dust grains, to the concentration of pebbles in giant vortices, thus, facilitating planetesimal formation. The Vertical Shear Instability (VSI) is a hydrodynamic mechanism, operating in PPDs if the local rate of thermal relaxation is high enough. Previous studies of the VSI have, however, relied on the assumption of constant cooling rates, or neglected the finite coupling time between the gas particles and the dust grains. Here, we present the results of hydrodynamic simulations of PPDs with the PLUTO code that include a more realistic thermal relaxation prescription, which enables us to study the VSI in the optically thick and optically thin parts of the disk under consideration of the thermal dust-gas coupling. We show the VSI to cause turbulence even in the optically thick inner regions of PPDs in our two- and three-dimensional simulations. The collisional decoupling of dust and gas particles in the upper atmosphere and the correspondingly inefficient thermal relaxation rates lead to the damping of the VSI turbulence. Long-lived anticyclonic vortices form in our three-dimensional simulation. These structures emerge from the turbulence in the VSI active layer, persist over hundreds of orbits and extend vertically over several pressure scale heights. We conclude that the VSI leads to turbulence and the formation of long-lived dust traps in PPDs, even under non-ideal conditions and under consideration of a more realistic thermal relaxation model.

  • efficiency of thermal relaxation by radiative processes in protoplanetary discs constraints on hydrodynamic turbulence
    Astronomy and Astrophysics, 2017
    Co-Authors: M G Malygin, Hubert Klahr, D Semenov, Th Henning, C P Dullemond
    Abstract:

    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, 2017
    Co-Authors: M G Malygin, Hubert Klahr, D Semenov, Th Henning, C P Dullemond
    Abstract:

    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.

Yu Zou - One of the best experts on this subject based on the ideXlab platform.

Magda Carr - One of the best experts on this subject based on the ideXlab platform.

  • convectively induced Shear Instability in large amplitude internal solitary waves
    Physics of Fluids, 2008
    Co-Authors: Magda Carr, Dorian Fructus, John Grue, Atle Jensen, Peter A Davies
    Abstract:

    Laboratory study has been carried out to investigate the Instability of an internal solitary wave of depression in a shallow stratified fluid system. The experimental campaign has been supported by theoretical computations and has focused on a two layered stratification consisting of a homogeneous dense layer below a linearly stratified top layer. The initial background stratification has been varied and it is found that the onset and intensity of breaking are affected dramatically by changes in the background stratification. Manifestations of a combination of Shear and convective Instability are seen on the leading face of the wave. It is shown that there is an interplay between the two Instability types and convective Instability induces Shear by enhancing isopycnal compression. Variation in the upper boundary condition is also found to have an effect on stability. In particular, the implications for convective Instability are shown to be profound and a dramatic increase in wave amplitude is seen for a ...

  • convectively induced Shear Instability in large amplitude internal solitary waves
    Physics of Fluids, 2008
    Co-Authors: Magda Carr, Dorian Fructus, John Grue, Atle Jensen, Peter A Davies
    Abstract:

    Laboratory study has been carried out to investigate the Instability of an internal solitary wave of depression in a shallow stratified fluid system. The experimental campaign has been supported by theoretical computations and has focused on a two layered stratification consisting of a homogeneous dense layer below a linearly stratified top layer. The initial background stratification has been varied and it is found that the onset and intensity of breaking are affected dramatically by changes in the background stratification. Manifestations of a combination of Shear and convective Instability are seen on the leading face of the wave. It is shown that there is an interplay between the two Instability types and convective Instability induces Shear by enhancing isopycnal compression. Variation in the upper boundary condition is also found to have an effect on stability. In particular, the implications for convective Instability are shown to be profound and a dramatic increase in wave amplitude is seen for a fixed (as opposed to free) upper boundary condition.

Natascha Manger - One of the best experts on this subject based on the ideXlab platform.

  • high resolution parameter study of the vertical Shear Instability ii dependence on temperature gradient and cooling time
    Monthly Notices of the Royal Astronomical Society, 2021
    Co-Authors: Natascha Manger, Thomas Pfeil, Hubert Klahr
    Abstract:

    A certain appeal to the alpha model for turbulence and related viscosity in accretion disks was that one scales the Reynolds stresses simply on the thermal pressure, assuming that turbulence driven by a certain mechanism will attain a characteristic Mach number in its velocity fluctuations. Besides the notion that there are different mechanism driving turbulence and angular momentum transport in a disk, we also find that within a single Instability mechanism, here the Vertical Shear Instability, stresses do not linearly scale with thermal pressure. Here we demonstrate in numerical simulations the effect of the gas temperature gradient and the thermal relaxation time on the average stresses generated in the non-linear stage of the Instability. We find that the stresses scale with the square of the exponent of the radial temperature profile at least for a range of $d \log T /d \log R = [-0.5, -1]$, beyond which the pressure scale height varies too much over the simulation domain, to provide clear results. Stresses are also dependent on thermal relaxation times, provided they are longer than $10^{-3}$ orbital periods. The strong dependence of viscous transport of angular momentum on the local conditions in the disk (especially temperature, temperature gradient, and surface density/optical depth) challenges the ideas of viscosity leading to smooth density distributions, opening a route for structure (ring) formation and time variable mass accretion.

  • high resolution parameter study of the vertical Shear Instability
    Monthly Notices of the Royal Astronomical Society, 2020
    Co-Authors: Hubert Klahr, Natascha Manger, W Kley, Mario Flock
    Abstract:

    Theoretical models of protoplanetary disks have shown the Vertical Shear Instability (VSI) to be a prime candidate to explain turbulence in the dead zone of the disk. However, simulations of the VSI have yet to show consistent levels of key disk turbulence parameters like the stress-to-pressure ratio $\alpha$. We aim to reconcile these different values by performing a parameter study on the VSI with focus on the disk density gradient $p$ and aspect ratio $h := H/R$. We use full 2$\pi$ 3D simulations of the disk for chosen set of both parameters. All simulations are evolved for 1000 reference orbits, at a resolution of 18 cells per h. We find that the saturated stress-to-pressure ratio in our simulations is dependent on the disk aspect ratio with a \review{strong} scaling of $\alpha\propto h^{2.6}$, in contrast to the traditional $\alpha$ model, where viscosity scales as $\nu \propto \alpha h^2$ with a constant $\alpha$. We also observe consistent formation of large scale vortices across all investigated parameters. The vortices show uniformly aspect ratios of $\chi \approx 10$ and radial widths of approximately 1.5 $H$. With our findings we can reconcile the different values reported for the stress-to-pressure ratio from both isothermal and radiation hydrodynamics models, and show long-term evolution effects of the VSI that could aide in the formation of planetesimals.