Experimental and numerical study of mean zonal flows generated by librations of a rotating spherical cavity

Sauret, Alban; Cébron, David; Morize, Cyprien; Bars, Michaël Le

doi:10.1017/s0022112010004052

Cited by 56 publications

(68 citation statements)

References 14 publications

(28 reference statements)

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“…The recent experimental and numerical study of Noir et al (2009) focuses on the nonlinear property of the spherical librating flow when the Poincaré K. Zhang, K. H. Chan and X. Liao number Po is sufficiently large. Busse (2010) showed that longitudinal libration can drive a weak mean zonal flow in librating spheres, which is confirmed by a recent experimental and numerical study (Sauret et al 2010). In spherical geometry, coupling between the librating container and its interior fluid is purely viscous and the fluid motion driven by longitudinal libration is weak and has the typical amplitude O(Po).…”

Section: Introduction and Formulationmentioning

confidence: 60%

Asymptotic theory of resonant flow in a spheroidal cavity driven by latitudinal libration

2012

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We consider a homogeneous fluid of viscosity ν confined within an oblate spheroidal cavity, x 2 /a 2 + y 2 /a 2 + z 2 /(a 2 (1 − E 2 )) = 1, with eccentricity 0 < E < 1. The spheroidal container rotates rapidly with an angular velocity Ω 0 , which is fixed in an inertial frame and defines a small Ekman number E = ν/(a 2 |Ω 0 |), and undergoes weak latitudinal libration with frequencyω|Ω 0 | and amplitude Po|Ω 0 |, where Po is the Poincaré number quantifying the strength of Poincaré force resulting from latitudinal libration. We investigate, via both asymptotic and numerical analysis, fluid motion in the spheroidal cavity driven by latitudinal libration. When |ω − 2/(2 − E 2 )| O(E 1/2 ), an asymptotic solution for E 1 and Po 1 in oblate spheroidal coordinates satisfying the no-slip boundary condition is derived for a spheroidal cavity of arbitrary eccentricity without making any prior assumptions about the spatial-temporal structure of the librating flow. In this case, the librationally driven flow is nonaxisymmetric with amplitude O(Po), and the role of the viscous boundary layer is primarily passive such that the flow satisfies the no-slip boundary condition. When |ω − 2/(2 − E 2 )| O(E 1/2 ), the librationally driven flow is also non-axisymmetric but latitudinal libration resonates with a spheroidal inertial mode that is in the form of an azimuthally travelling wave in the retrograde direction. The amplitude of the flow becomes O(Po/E 1/2 ) at E 1 and the role of the viscous boundary layer becomes active in determining the key property of the flow. An asymptotic solution for E 1 describing the librationally resonant flow is also derived for an oblate spheroidal cavity of arbitrary eccentricity. Three-dimensional direct numerical simulation in an oblate spheroidal cavity is performed to demonstrate that, in both the non-resonant and resonant cases, a satisfactory agreement is achieved between the asymptotic solution and numerical simulation at E 1.

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Section: Introduction and Formulationmentioning

confidence: 60%

Asymptotic theory of resonant flow in a spheroidal cavity driven by latitudinal libration

2012

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“…The non-linear self-interaction of (6) leads to an axisymmetric stationary zonal flow in the boundary layer that, by continuity, generates a flow in the interior fluid, as confirmed in axisymmetric containers. 8,9,25,[34][35][36][37] This stationary flow scales as ϵ 2 with an azimuthal wavenumber m = 0 and is expected in the ellipsoidal container. Additional axisymmetric and non-axisymmetric stationary flows arise due to the ellipsoidal geometry and scale as ϵ 2 β and ϵ 2 β 2 with azimuthal wavenumbers m = 2 and m = 0, 4, respectively.…”

Section: B Zonal Flowmentioning

confidence: 69%

“…These movies are separated into their constituent frames and passed through an open source PIV software, DPIVSoft2010, 51 that has been successfully employed in previous studies. 9,52 The velocity field for an entire equatorial plane is resolved into a 23 x 40 grid with a typical spatial resolution of 8 mm. All velocity measurements presented below have been non-dimensionalized using the long axis length, a, and the steady rotational period Ω …”

Section: Methods a Experimental Approachmentioning

confidence: 99%

“…By substituting the solutions for (u (9) and analyzing the resulting equations, we seek to determine the conditions that are required on the coefficients a j such that they grow through time.…”

Section: Elliptical Instabilitymentioning

confidence: 99%

“…7,8 Additional theoretical, numerical, and experimental works have verified the stationary zonal flow caused by non-linear interactions in the Ekman boundary layers of cylinders, spheres, and spherical shells. [8][9][10]25,26 Recent studies have focused on simulating librational effects in more realistic geometries that reflect the non-axisymmetric shape of planetary interior fluid layers. Theoretical and numerical studies of flows in non-axisymmetric containers have shown that longitudinal librational forcing cannot, through a direct resonance, excite eigenmodes of the system.…”

Section: Introductionmentioning

confidence: 99%

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Experimental study of global-scale turbulence in a librating ellipsoid

et al. 2014

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We present laboratory experimental results demonstrating that librational forcing of an ellipsoidal container of water can produce intense motions through the mechanism of a libration driven elliptical instability (LDEI). These libration studies are conducted using an ellipsoidal acrylic container filled with water. A particle image velocimetry method is used to measure the 2D velocity field in the equatorial plane over hundreds libration cycles for a fixed Ekman number, E = 2 × 10 −5 . In doing so, we recover the libration induced base flow and a time averaged zonal flow. Further, we show that LDEI in non-axisymmetric container geometries is capable of driving both intermittent and saturated turbulent motions in the bulk fluid. Additionally, we measure the growth rate and amplitude of the LDEI induced excited flow in a fully ellipsoidal container at more extreme parameters than previously studied [Noir

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Tide‐driven shear instability in planetary liquid cores

Sauret

Bars

Gal

2014

Geophysical Research Letters

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We present an experimental study on the shear instability driven by tidal forcing in a model planetary liquid core. The experimental setup consists of a water-filled deformable sphere rotating around its axis and subjected to an elliptical forcing. At resonant forcing frequencies, the nonlinear self-interaction of the excited inertial mode drives an intense and localized axisymmetric jet. The jet becomes unstable at low Ekman number because of a shear instability. Using particle image velocimetry measurements, we derive a semiempirical scaling law that captures the instability threshold of the shear instability. This mechanism is fully relevant to planetary systems, where it constitutes a new route to generate turbulence in their liquid cores.

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Experimental and numerical study of mean zonal flows generated by librations of a rotating spherical cavity

Cited by 56 publications

References 14 publications

Asymptotic theory of resonant flow in a spheroidal cavity driven by latitudinal libration

Asymptotic theory of resonant flow in a spheroidal cavity driven by latitudinal libration

Experimental study of global-scale turbulence in a librating ellipsoid

Tide‐driven shear instability in planetary liquid cores

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