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Instabilities of Steady Flow in a Rotating Spherical Cavity Excited by Inner Core Oscillation

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Abstract

We experimentally investigated a stability of steady flow caused by inner core oscillation in a rotating spherical cavity with fluid. The inner core oscillation relative to the cavity is caused by steady external field, directed transversally to the rotation axis; thus, the oscillation frequency is equal to the rotation frequency of the system. Differential rotation of the core is deactivated, for that one of the core poles is connected with the nearest cavity pole by a torsionally elastic fish-line. It is found that the quasi-two-dimensional steady azimuthal flow is excited by the core oscillation; the flow intensity is proportional to the core oscillation amplitude squared. With increase of amplitude, the axially symmetrical flow loose stability; the instability mode is similar to the one found before in the case of free core oscillation, which was executing the mean differential rotation (Kozlov et al.: Eur. J. Mech. B-Fluid. 63(3), 39–46, 2017). The comparative analysis shows that the differential rotation of inner core is not an essential condition for the appearance of instabilities. The mechanism for the appearance of instabilities is related with inflection points in azimuthal velocity profile of the fluid flow caused by the core oscillation relative to the cavity.

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References

  • Aleksandrov, V., Kopysov, S., Tonkov, L.: Vortex flows in the liquid layer and droplets on a vibrating flexible plate. Microgravity Sci. Technol. 30, 85–93 (2018)

    Article  Google Scholar 

  • Brungs, S., Hauslage, J., Hemmersbach, R.: Validation of random positioning versus clinorotation using a macrophage model system. Microgravity Sci. Technol. 31, 223–230 (2019)

    Article  Google Scholar 

  • Calkins, M.A., Noir, J., Eldredge, J.D., Aurnou, J.M.: Axisymmetric simulations of libration-driven fluid dynamics in a spherical shell geometry. Phys. Fluids. 22, 086602 (2010)

    Article  Google Scholar 

  • Favier, B., Barker, A., Baruteau, C., Ogilvie, G.: Nonlinear evolution of tidally forced inertial waves in rotating fluid bodies. Mon. Not. R. Astron. Soc. 439, 845–860 (2014)

    Article  Google Scholar 

  • Fernandez, J., Sánchez, P.S., Tinao, I., Porter, J., Ezquerro, J.M.: The CFVib experiment: control of fluids in microgravity with vibrations. Microgravity Sci. Technol. 29, 351–364 (2017)

    Article  Google Scholar 

  • Greenspan, H.P.: The Theory of Rotating Fluids. University Press, Cambridge (1968)

    MATH  Google Scholar 

  • Hollerbach, R., Futterer, B., More, T., Egbers, C.: Instabilities of the Stewartson layer. Part 2. Supercritical mode transitions. Theor. Comp. Fluid Dyn. 18, 197–204 (2004)

    Article  Google Scholar 

  • Karpunin, I.E., Kozlova, A.N., Kozlov, N.V.: Behavior of a light solid in a rotating horizontal cylinder with liquid under vibration. Microgravity Sci. Technol. 30, 399–409 (2018)

    Article  Google Scholar 

  • Kim, S.M., Kim, H., Yang, D., Park, J., Park, R., Namkoong, S., Lee, J.I., Choi, I., Kim, H.S., Kim, H., Park, J.: An experimental and theoretical approach to optimize a three-dimensional clinostat for life science experiments. Microgravity Sci. Technol. 29, 97–106 (2017)

    Article  Google Scholar 

  • Kozlov, V.G., Kozlov, N.V.: Vibrational hydrodynamic gyroscope. Dokl. Phys. 52(8), 458–461 (2007)

    Article  Google Scholar 

  • Kozlov, V.G., Subbotin, S.V.: Steady flows generated by a core oscillating in a rotating spherical cavity. J. Appl. Mech. Tech. Phys. 59(1), 22–31 (2018)

    Article  Google Scholar 

  • Kozlov, V.G., Kozlov, N.V., Subbotin, S.V.: Motion of fluid and a solid core in a spherical cavity rotating in an external force field. Dokl. Phys. 59(1), 40–44 (2014)

    Article  Google Scholar 

  • Kozlov, V.G., Kozlov, N.V., Subbotin, S.V.: Steady flows excited by circular oscillations of free inner core in rotating spherical cavity. Eur. J. Mech. B-Fluid. 58(4), 85–94 (2016)

    Article  Google Scholar 

  • Kozlov, V.G., Kozlov, N.V., Subbotin, S.V.: Instabilities and pattern formation in rotating spherical cavity with oscillating inner core. Eur. J. Mech. B-Fluid. 63(3), 39–46 (2017)

    Article  Google Scholar 

  • Le Bars, M., Cébron, D., Le Gal, P.: Flows driven by libration, precession, and tides. Annu. Rev. Fluid Mech. 47, 163–193 (2015)

    Article  MathSciNet  Google Scholar 

  • Lorenzani, S., Tilgner, A.: Fluid instabilities in precessing spheroidal cavities. J. Fluid Mech. 447, 111–128 (2001)

    Article  Google Scholar 

  • Lorenzani, S., Tilgner, A.: Inertial instabilities of fluid flow in precessing spheroidal shells. J. Fluid Mech. 492, 363–379 (2003)

    Article  Google Scholar 

  • Morize, C., Le Bars, M., Le Gal, P., Tilgner, A.: Experimental determination of zonal winds driven by tides. Phys. Rev. Lett. 104, 214501 (2010)

    Article  Google Scholar 

  • Noir, J., Jault, D., Cardin, P.: Numerical study of the motions within a slowly precessing sphere at low Ekman number. J. Fluid Mech. 437, 283–299 (2001)

    Article  Google Scholar 

  • Pimenova, A.V., Goldobin, D.S., Lyubimova, T.P.: Comparison of the effect of horizontal vibrations on interfacial waves in a two-layer system of inviscid liquids to effective gravity inversion. Microgravity Sci. Technol. 30, 1–10 (2018)

    Article  Google Scholar 

  • Sauret, A., Cebron, D., Morize, C., Le Bars, M.: Experimental and numerical study of mean zonal flows generated by librations of a rotating spherical cavity. J. Fluid Mech. 662, 260–268 (2010)

    Article  Google Scholar 

  • Sauret, A., Le Bars, M., Le Gal, P.: Tide-driven shear instability in planetary liquid cores. Geophys. Res. Lett. 41, 6078–6083 (2014)

    Article  Google Scholar 

  • Schaeffer, N., Cardin, P.: Quasi-geostrophic model of the instabilities of the Stewartson layer in flat and depth varying containers. Phys. Fluids. 17, 104111 (2005)

    Article  MathSciNet  Google Scholar 

  • Schipitsyn, V.D., Kozlov, V.G.: Oscillatory and steady dynamics of a cylindrical body near the border of vibrating cavity filled with liquid. Microgravity Sci. Technol. 30, 103–112 (2018)

    Article  Google Scholar 

  • Slichter, L.B.: The fundamental free mode of the Earth’s inner. core. Proc. Natl. Acad. Sci. U.S.A. 47(2), 186–190 (1961)

    Article  Google Scholar 

  • Smorodin, B.L., Ishutov, S.M., Myznikova, B.I.: On the convection of a binary mixture in a horizontal layer under high-frequency vibrations. Microgravity Sci. Technol. 30, 95–102 (2018)

    Article  Google Scholar 

  • Stewartson, K.: On almost rigid rotations. Part 2. J. Fluid Mech. 26, 131–144 (1966)

    Article  Google Scholar 

  • Thielicke, W., Stamhuis, E.J.: PIVlab – time-resolved digital particle image velocimetry tool for MATLAB (version: 1.41). J. Open Res. Software. 2(1), e30 (2014)

    Google Scholar 

  • Vanyo, J., Wilde, P., Cardin, P., Olson, P.: Experiments on precessing flows in the Earth’s liquid core. Geophys. J. Int. 121, 136–142 (1995)

    Article  Google Scholar 

Download references

Acknowledgments

The research was supported by the Russian Science Foundation (project No. 18-71-10053).

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Authors and Affiliations

  1. Laboratory of Vibrational Hydromechanics, Perm State Humanitarian Pedagogical University, 24, Sibirskaya Street, 614990, Perm, Russia

    Victor Kozlov, Stanislav Subbotin & Mariya Shiryaeva

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  1. Victor Kozlov
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  2. Stanislav Subbotin
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  3. Mariya Shiryaeva
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Correspondence to Victor Kozlov.

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This article belongs to the Topical Collection: Multiphase Fluid Dynamics in Microgravity

Guest Editors: Tatyana P. Lyubimova, Jian-Fu Zhao

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Kozlov, V., Subbotin, S. & Shiryaeva, M. Instabilities of Steady Flow in a Rotating Spherical Cavity Excited by Inner Core Oscillation. Microgravity Sci. Technol. 31, 775–782 (2019). https://doi.org/10.1007/s12217-019-09706-w

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  • DOI: https://doi.org/10.1007/s12217-019-09706-w

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