On the energy spectrum of rapidly rotating forced turbulence

Sharma, Manohar K.; Verma, Mahendra K.; Chakraborty, Sagar

doi:10.1063/1.5051444

Cited by 56 publications

(9 citation statements)

References 83 publications

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“…This was expected, as the VSI produces weak turbulence that is always and at all scales dominated by the disk rotation. This means, if the injection scale has a Rossby-number Ro (defined as the ratio of inertial to coriolis forces) of smaller than unity, then the turbulence will always be in the Ro < 1 regime at all scales and will not develop isotropic 3D turbulence at any scale (Sharma et al, 2018). Instead, the results show that the spectrum is proportional to m −5 with a turn-over into a shallower power law at low m, which is consistent with an upward cascade transporting energy to larger scales combined with an downward cascade transporting enstrophy, a quantity related to the square of vorticity, to smaller scales (Lyra & Umurhan, 2019).…”

Section: Specific Kinetic Energy Spectrummentioning

confidence: 99%

High Resolution Parameter Study of the Vertical Shear Instability

Manger,

Klahr,

Kley

et al. 2020

Preprint

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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 α. 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 2π 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 strong scaling of α ∝ h 2.6 , in contrast to the traditional α model, where viscosity scales as ν ∝ αh 2 with a constant α. We also observe consistent formation of large scale vortices across all investigated parameters. The vortices show uniformly aspect ratios of χ ≈ 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 full radiation hydrodynamics models, and show long-term evolution effects of the VSI that could aide in the formation of planetesimals.

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Section: Specific Kinetic Energy Spectrummentioning

confidence: 99%

High Resolution Parameter Study of the Vertical Shear Instability

Manger,

Klahr,

Kley

et al. 2020

Preprint

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“…The dip and the subsequent peak in the FSLE plot are signatures of the slow and the fast dynamics in the inertial range, respectively [44]. We speculate that the enhancement of predictability can be attributed to the coherent dynamics in the columnar structures formed in real rotating turbulence as predicted in theory (Taylor-Proudman theorem) and observed in direct numerical simulations [10,45,46].…”

Section: Discussionmentioning

confidence: 57%

Predictability in Rotating Turbulence: Insights from a Shell Model Study

Rathor¹

2022

Preprint

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We investigate the predictability aspects of rotating turbulent flows through extensive numerical simulations of a shell model of rotating turbulence. In particular, we measure the large-scale predictability time and find that it increases with rotation rate to satisfy a power law in Rossby number with a scaling exponent of −2/3. Intriguingly, we find that before entering the algebraic growth stage, the error dynamics freezes for a time period determined by the finite Rossby number. We further analyse the scale dependence of the predictability time and observe that it tends to become scale independent in the Zeman range as the Rossby number decreases. Finally, we compute the finite size Lyapunov exponent and validate the dimensional prediction of its scaling ∼ δ −1 for large δ of the order of velocities in the Zeman range for small Rossby numbers.

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“…Indeed, according to the corresponding theories, it is well known that inverse or direct cascades of energy/enstrophy in 2D or 3D turbulence or the presence of a Bolgiano-Obukhov regime in Rayleigh-Bénard convection can be detected using energy/enstrophy/temperature spectra and fluxes [24]. Very recently, Sharma et al [35,36] published new results on rapidly rotating forced and decaying turbulence. Their studies are based on numerical simulations in a cube of size (2π) 3 with periodic boundary conditions on all the sides.…”

Section: Spectra and Fluxesmentioning

confidence: 99%

Numerical Study of Rotating Thermal Convection on a Hemisphere

Fischer

Bruneau

Kellay

2020

Fluids

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Numerical simulations of rotating two-dimensional turbulent thermal convection on a hemisphere are presented in this paper. Previous experiments on a half soap bubble located on a heated plate have been used for studying thermal convection as well as the effects of rotation on a curved surface. Here, two different methods have been used to produce the rotation of the hemisphere: the classical rotation term added to the velocity equation, and a non-zero azimuthal velocity boundary condition. This latter method is more adapted to the soap bubble experiments. These two methods of forcing the rotation of the hemisphere induce different fluid dynamics. While the first method is classically used for describing rotating Rayleigh–Bénard convection experiments, the second method seems to be more adapted for describing rotating flows where a shear layer may be dominant. This is particularly the case where the fluid is not contained in a closed container and the rotation is imposed on only one side of it. Four different diagnostics have been used to compare the two methods: the Nusselt number, the effective computation of the convective heat flux, the velocity and temperature fluctuations root mean square (RMS) generation of vertically aligned vortex tubes (to evaluate the boundary layers) and the energy/enstrophy/temperature spectra/fluxes. We observe that the dynamics of the convective heat flux is strongly inhibited by high rotations for the two different forcing methods. Also, and contrary to classical three-dimensional rotating Rayleigh–Bénard convection experiments, almost no significant improvement of the convective heat flux has been observed when adding a rotation term in the velocity equation. However, moderate rotations induced by non-zero velocity boundary conditions induce a significant enhancement of the convective heat flux. This enhancement is closely related to the presence of a shear layer and to the thermal boundary layer just above the equator.

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On the energy spectrum of rapidly rotating forced turbulence

Cited by 56 publications

References 83 publications

High Resolution Parameter Study of the Vertical Shear Instability

High Resolution Parameter Study of the Vertical Shear Instability

Predictability in Rotating Turbulence: Insights from a Shell Model Study

Numerical Study of Rotating Thermal Convection on a Hemisphere

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