Numerical and experimental investigation of shear-driven inertial oscillations in an Earth-like geometry

Matsui, H.; Adams, Matthew; Kelley, Douglas H.; Triana, S. A.; Zimmerman, Daniel S.; Buffett, B. A.

doi:10.1016/j.pepi.2011.07.012

Cited by 10 publications

(20 citation statements)

References 23 publications

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“…The dominant mode is illustrated in figure 24(c) which should be compared with figure 19(d) to reveal the similarity with the spherical Couette simulation. Both inertial modes have been found in the spherical Couette experiments (Kelley et al 2007;Rieutord et al 2012) and previous numerical simulations (Matsui et al 2011;Rieutord et al 2012). The full-sphere inertial mode with (m = 2, N = 0, n = 1) has a frequency of σ = 0.333 while the dominant m = 2 contribution in the simulation has σ SC = 0.36 at Ω = 10 4 and Ω = −2 × 10 4 .…”

Section: Inertial Modessupporting

confidence: 60%

“…Inertial modes have previously been found in spherical Couette experiments (Kelley et al 2007;Rieutord et al 2012) and related numerical simulations (Matsui et al 2011;Rieutord et al 2012). They are a solution of the inviscid linearized Navier-Stokes equation (3.11) and are thus expected to be excited for large Ω (small Ekman number).…”

Section: Inertial Modesmentioning

confidence: 81%

“…Experiments and numerical simulations at more supercritical parameters suggest that inertial modes can also play an important role in the spherical Couette system (Kelley et al 2007;Matsui et al 2011;Rieutord et al 2012). They form a class of natural solutions in fast rotating spheres and can thus be expected for larger Ω values (Greenspan 1968;Rieutord & Valdettaro 1997).…”

Section: Introductionmentioning

confidence: 99%

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Flow instabilities in the wide-gap spherical Couette system

Wicht

2013

J. Fluid Mech.

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The spherical Couette system is a spherical shell filled with a viscous fluid. Flows are driven by the differential rotation between the inner and the outer boundary that rotate with Ω and Ω + Ω about a common axis. This setup has been proposed for second-generation dynamo experiments. We numerically explore the different instabilities emerging for rotation rates up to Ω = (1/3) × 10 7 , venturing also into the nonlinear regime where oscillatory and chaotic solutions are found. The results provide a comprehensive overview of the possible flow regimes. For low values of Ω viscosity dominates and an equatorial jet in meridional circulation and zonal flow develops that becomes unstable as the differential rotation is increased beyond a critical value. For intermediate Ω and an inner boundary rotating slower than the outer one, new double-roll and helical instabilities are found. For large Ω values Coriolis effects enforce a nearly two-dimensional fundamental flow where a Stewartson shear layer develops at the tangent cylinder. This shear layer is the source of nearly geostrophic non-axisymmetric instabilities that resemble columnar Rossby modes. At first, the instabilities differ significantly depending on whether the inner boundary rotates faster ( Ω > 0) or slower ( Ω < 0) than the outer one. For very large outer boundary rotation rates, however, both instabilities once more become comparable. Fast inertial waves similar to those observed in recent spherical Couette experiments prevail for larger Ω values and Ω < 0 in when Ω and Ω are of comparable magnitude. For larger differential rotations Ω Ω, however, the equatorial jet instability always takes over.

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Section: Inertial Modessupporting

confidence: 60%

Section: Inertial Modesmentioning

confidence: 81%

Section: Introductionmentioning

confidence: 99%

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Flow instabilities in the wide-gap spherical Couette system

Wicht

2013

J. Fluid Mech.

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“…Inertial modes are the oscillatory linear response of a fluid to a time-dependent perturbation where the Coriolis force is the restoring force. Several hypotheses have been put forward to explain the excitation of inertial modes in these experiments: overcritical reflection off the inner Stewartson layer (Kelley et al 2010), and turbulence from the tangent cylinder on the inner sphere (Matsui et al 2011). Most recently, Rieutord et al (2012) presented data recorded in the 3m-diameter spherical Couette experiment of Dan Lathrop's group at the University of Maryland, and proposed a new interpretation.…”

Section: Introductionmentioning

confidence: 99%

Modes and instabilities in magnetized spherical Couette flow

et al. 2013

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Several teams have reported peculiar frequency spectra for flows in a spherical shell. To address their origin, we perform numerical simulations of the spherical Couette flow in a dipolar magnetic field, in the configuration of the DT S experiment. The frequency spectra computed from time-series of the induced magnetic field display similar bumpy spectra, where each bump corresponds to a given azimuthal mode number m. The bumps show up at moderate Reynolds number (≃ 2 600) if the time-series are long enough (> 300 rotations of the inner sphere). We present a new method that permits to retrieve the dominant frequencies for individual mode numbers m, and to extract the modal structure of the full non-linear flow. The maps of the energy of the fluctuations and the spatio-temporal evolution of the velocity field suggest that fluctuations originate in the outer boundary layer. The threshold of instability if found at Re c = 1 860. The fluctuations result from two coupled instabilities: high latitude Bödewadt-type boundary layer instability, and secondary non-axisymmetric instability of a centripetal jet forming at the equator of the outer sphere. We explore the variation of the magnetic and kinetic energies with the input parameters, and show that a modified Elsasser number controls their evolution. We can thus compare with experimental determinations of these energies and find a good agreement. Because of the dipolar nature of the imposed magnetic field, the energy of magnetic fluctuations is much larger near the inner sphere, but their origin lies in velocity fluctuations that initiate in the outer boundary layer.

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“…The meridional maps of kinetic energy favor the first hypothesis. In recent numerical 3D simulations of the magnetized spherical Couette flow, it has been found that bumps naturally appear in spectra of long time-series of the surface magnetic field (also see Matsui et al [27]). These bumps share the properties of the modes observed in DTS and can be linked to instabilities of the external shear layer.…”

Section: Discussionmentioning

confidence: 95%

Magneto–Coriolis waves in a spherical Couette flow experiment

Schmitt¹,

Cardin²,

Rizza³

et al. 2013

European Journal of Mechanics - B/Fluids

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The dynamics of fluctuations in a fast rotating spherical Couette flow experiment in the presence of a strong dipolar magnetic field is investigated in detail, through a thorough analysis of the experimental data as well as a numerical study. Fluctuations within the conducting fluid (liquid sodium) are characterized by the presence of several oscillation modes, identified as magneto-Coriolis (MC) modes, with definite symmetry and azimuthal number. A numerical simulation provides eigensolutions which exhibit oscillation frequencies and magnetic signature comparable to the observation. The main characteristics of these hydromagnetic modes is that the magnetic contribution has a fundamental influence on the dynamical properties through the Lorentz forces, although its importance remains weak in an energetical point of view. Another specificity is that the Lorentz forces are confined near the inner sphere where the dipolar magnetic field is the strongest, while the Coriolis forces are concentrated in the outer fluid volume close to the outer sphere.

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Numerical and experimental investigation of shear-driven inertial oscillations in an Earth-like geometry

Cited by 10 publications

References 23 publications

Flow instabilities in the wide-gap spherical Couette system

Flow instabilities in the wide-gap spherical Couette system

Modes and instabilities in magnetized spherical Couette flow

Magneto–Coriolis waves in a spherical Couette flow experiment

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