On the linear and non-linear fluid response to the circular forcing in a rotating spherical shell

Subbotin, S. V.; Shiryaeva, Mariya

doi:10.1063/5.0050403

Cited by 8 publications

(3 citation statements)

References 60 publications

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“…As shown in Fig. 6, but also in Paper I, Tilgner (2007), Morize et al (2010), or Subbotin & Shiryaeva (2021), zonal flows produced by nonlinear self-interaction of non-axisymmetric inertial waves always take the form of nested and axisymmetric cylinders with different angular velocity profiles depending upon cylindrical radius inside the shell. The radial distribution, magnitude and direction of the flow at a given location (prograde or retrograde, i.e.…”

Section: Surface Versus Body Forcingmentioning

confidence: 70%

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The effects of non-linearities on tidal flows in the convective envelopes of rotating stars and planets in exoplanetary systems

Astoul

Barker

2022

Monthly Notices of the Royal Astronomical Society

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In close exoplanetary systems, tidal interactions drive orbital and spin evolution of planets and stars over long timescales. Tidally-forced inertial waves (restored by the Coriolis acceleration) in the convective envelopes of low-mass stars and giant gaseous planets contribute greatly to the tidal dissipation when they are excited and subsequently damped (e.g. through viscous friction), especially early in the life of a system. These waves are known to be subject to nonlinear effects, including triggering differential rotation in the form of zonal flows. In this study, we use a realistic tidal body forcing to excite inertial waves through the residual action of the equilibrium tide in the momentum equation for the waves. By performing 3D nonlinear hydrodynamical simulations in adiabatic and incompressible convective shells, we investigate how the addition of nonlinear terms affects the tidal flow properties, and the energy and angular momentum redistribution. In particular, we identify and justify the removal of terms responsible for unphysical angular momentum evolution observed in a previous numerical study. Within our new set-up, we observe the establishment of strong cylindrically-sheared zonal flows, which modify the tidal dissipation rates from prior linear theoretical predictions. We demonstrate that the effects of this differential rotation on the waves neatly explains the discrepancies between linear and nonlinear dissipation rates in many of our simulations. We also highlight the major role of both corotation resonances and parametric instabilities of inertial waves, which are observed for sufficiently high tidal forcing amplitudes or low viscosities, in affecting the tidal flow response.

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Section: Surface Versus Body Forcingmentioning

confidence: 70%

“…7. The key role of shear layers and critical latitudes in the establishment of these geostrophic flows have already been pointed out for example in the experimental study of Subbotin & Shiryaeva (2021).…”

Section: Surface Versus Body Forcingmentioning

confidence: 88%

The effects of non-linearities on tidal flows in the convective envelopes of rotating stars and planets in exoplanetary systems

Astoul

Barker

2022

Monthly Notices of the Royal Astronomical Society

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“…In a related flow with a cuboid rapidly rotating in an orientation with some walls oblique to the rotation axis and subjected to libration, Wu et al [9] showed that vortex stretching and tilting (inherently 3D nonlinear processes) were most active where the shear layers of the inertial attractor reflect on the wall, leading to the local enhancement of ω 2 well beyond that due to the geometric focusing. Recent experiments in librationally forced spherical shells and cylinders with sloping endwalls have observed similar nonlinear interactions at reflection sites leading to mean shear flows [18][19][20][21][22]. Here, for ω = 0.24, these reflections occur in the equatorial region, and since the mean shears are aligned parallel to the rotation axis, their presence is localized to this region and not readily distinguishable from the focusing shear layers.…”

Section: Primary Viscous Nonlinear Responsesmentioning

confidence: 74%

Comparison of Libration- and Precession-Driven Flows: From Linear Responses to Broadband Dynamics

Wu,

Welfert,

Lopez

2024

Fluids

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Libration and precession are different body forces that are ubiquitous in many rapidly rotating systems, particularly in geophysical and astrophysical flows. Libration is a modulation of the background rotation magnitude, whereas precession is a modulation of the background rotation direction. Assessing the consequences of these body forces in large-scale flows is challenging. The Ekman number, the ratio of the rotation time scale to the viscous time scale quantifying the rotation speed, is extremely small, leading to extremely thin and intense shear layers in the flows even when the amplitudes of the body forces are very small. We consider the consequences of libration and precession numerically in a geometrically simple container, a cube, which lends itself to very efficient, accurate, and robust numerical treatment, with the axis of rotation passing through opposite vertices, so that all walls of the cube are at oblique angles to the rotation axis. This results in the geometric focusing of inertial wavebeams reflecting off the walls, whereby the energy density of the wavebeams increases along with the magnitude of their wavevector. The nature of this focusing depends on the forcing frequency but not on the body force. In the inviscid setting, wavebeams form infinitesimally thin vortex sheets, and their energy density becomes unbounded upon focusing. We present linear inviscid ray tracing to set the scene for the focusing of wavebeams and then consider viscous problems at an Ekman number that is typical of current state-of-the-art laboratory experiments. We begin by considering the linear responses, which are comprised of focusing viscous shear layers, of which their details are mostly captured via ray tracing, and particular solutions accounting for the body forces. These have complicated spatio-temporal structures, which differ for libration and precession. Increasing the forcing amplitude from zero introduces nonlinear interactions, enhances the focusing effects via vortex tilting and stretching when the shear layers reflect at the walls, and also introduces temporal superharmonics and a mean flow. When the magnitude of the mean flow is within a few percent of the magnitude of the instantaneous flow, instabilities breaking the spatio-temporal symmetries set in. These are localized in the oscillatory boundary layers where the reflections are concentrated and introduce broadband dynamics in the boundary layers, with additional inertial wavebeams emitted into the interior. The details again depend on the specifics of the body forces.

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Steady Vortex Flow Induced by Inertial Wave Attractor in a Librating Cylinder with Sloping Ends

Subbotin

Shiryaeva

2022

Microgravity Sci. Technol.

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On the linear and non-linear fluid response to the circular forcing in a rotating spherical shell

Cited by 8 publications

References 60 publications

The effects of non-linearities on tidal flows in the convective envelopes of rotating stars and planets in exoplanetary systems

The effects of non-linearities on tidal flows in the convective envelopes of rotating stars and planets in exoplanetary systems

Comparison of Libration- and Precession-Driven Flows: From Linear Responses to Broadband Dynamics

Steady Vortex Flow Induced by Inertial Wave Attractor in a Librating Cylinder with Sloping Ends

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