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

Subbotin, S. V.; Shiryaeva, Mariya

doi:10.1007/s12217-022-10008-x

Cited by 5 publications

(3 citation statements)

References 32 publications

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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%

“…The global K spectra are dominated by the boundary spectra, where the largest oscillations reside, as is evident from Video S3. Notice, however, that for precession, the various peaks in the global K spectra are 3× the frequencies of those for the local spectra; this is due to the spatio-temporal symmetry (20). The onset of instability appears to be due to a symmetry-breaking Neimark-Sacker bifurcation, a secondary Hopf-like bifurcation from a limit cycle that introduces a new second frequency ω NS [24].…”

Section: Instabilities To Broadband Dynamicsmentioning

confidence: 96%

“…corresponding to the composition of R 0 with a time shift of a third of a period. The symmetry (20) of the Navier-Stokes system (11) results from the property of the rotation vector Ω p…”

Section: Symmetriesmentioning

confidence: 99%

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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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Section: Primary Viscous Nonlinear Responsesmentioning

confidence: 74%

Section: Instabilities To Broadband Dynamicsmentioning

confidence: 96%

See 1 more Smart Citation

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

Wu,

Welfert,

Lopez

2024

Fluids

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Inertial Wave Beam Path in a Non-uniformly Rotating Cylinder with Sloping Ends

Subbotin

Shiryaeva

2023

Microgravity Sci. Technol.

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Nonlinear regimes of inertial wave attractors generated by a precessing lid: Zonal flows and Rossby waves

et al. 2023

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Fluid flow excited by inertial waves in a rotating annulus with a trapezoidal cross section is experimentally investigated. The forcing is introduced by the precession of a flat annular lid bounding the cavity. Such a setup allows to investigate interactions between inertial waves and zonal flows in the presence of equivalent topographic beta-effect, and its dynamic behavior under weak and strong forcing is experimentally studied for the first time. Due to the specific dispersion relation of inertial waves, a cavity shape supports wave attractors that appear only for retrograde lid precession. At a relatively low wave intensity, a zonal flow is generated in the vicinity of a “virtual” axial cylinder, the radius of which coincides with the radius of the focusing reflection from the conical bottom. A succession of non-linear regimes is observed as forcing increases, starting with a clearly identifiable case of triadic resonance. Further, the frequency spectrum is progressively enriched by emergence of additional discrete components, gradually reaching the state of “overheated” wave turbulence with a significant continuous background of the frequency spectrum. Finally, a strong low-frequency component develops in the frequency spectrum, and the continuous background of the spectrum decreases dramatically. The low-frequency component corresponds to azimuthally periodic structures identified as Rossby waves. In the case of strong forcing, a long-term variability of zonal-flow velocity at the timescale of tens of forcing periods is observed, which is likely a consequence of the interaction of azimuthal structures corresponding to a rich wave number set.

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

Cited by 5 publications

References 32 publications

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

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

Inertial Wave Beam Path in a Non-uniformly Rotating Cylinder with Sloping Ends

Nonlinear regimes of inertial wave attractors generated by a precessing lid: Zonal flows and Rossby waves

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