Simulations of a precession driven flow in a cylindrical cavity

Simulations of a precession driven flow in a cylindrical cavity

Giesecke, A.; Vogt, T.; Gundrum, T.; Stefani, F.; Herault, J.

The project DRESDYN (DREsden Sodium facility for DYNamo and thermohydraulic studies) conducted at Helmholtz-Zentrum Dresden-Rossendorf (HZDR) provides a new platform for a variety of liquid sodium experiments devoted to problems of geo- and astrophysical magnetohydrodynamics [1]. The most ambitious experiment will be a dynamo experiment which consists of a large precessing cylindrical cavity filled with liquid sodium. The experiment is motivated by the idea of a precession-driven flow as a complementary energy source for the geodynamo [2] or the ancient lunar dynamo [3].

Our presentation addresses corresponding hydrodynamic simulations that provide characteristic properties of the precession-driven flow such as amplitudes or helicity and their implications for the dynamo effect. Our results show that the primary response of the fluid to the precession is an azimuthally rotating inertial wave, called Kelvin mode [4]. Increasing the precession ratio the fundamental Kelvin mode becomes unstable which goes along with the emergence of two free inertial waves due to a parametric resonance caused by the periodic perturbation of the primary flow [5]. The free inertial waves only exist within a narrow range of rather small precession ratios because increasing non-linear interactions give rise to the formation of an azimuthal circulation flow which alters the resonance condition (detuning effect) [6].

For large precession ratios, instead, we find a clear signature of Kelvin modes with the frequency of the forcing and higher azimuthal and/or axial wave numbers. In the turntable frame these Kelvin modes correspond to standing inertial waves that are caused by non-linear self-interaction of the fundamental forced mode. The contributions of these modes provide a breaking of the parity with respect to the equatorial plane which has proven to be beneficial for dynamo action [7].

Further considerations on the dynamo-ability of the precession driven flow require larger Reynolds numbers which are numerically no longer accessible. Therefore, they have to be based solely on data from the downscaled water experiment that currently is running at HZDR in preparation for the large liquid sodium facility (see contribution of T. Vogt). Comparisons of our simulations with experimental data from Ultrasonic Doppler Velocimetry (UDV) measurements at similar Reynolds number show a surprisingly good consistency thus providing a basis for the development of flow models at larger Reynolds numbers for future kinematic dynamo models.

[1] Stefani, F. et al., Magnetohydrodynamics, 48 (1), 103--114, 2012.
[2] Malkus, W. V. R., Science, 160, 259--264, 1968.
[3] Noir, J., and D. C{\'e}bron, J. Fluids Mech., 737, 412--439, 2013.
[4] Thomson W, Phil. Mag. J. Sci. 10 (61), 155--168, 1880.
[5] Kerswell, R. R., J. Fluids Mech., 382, 283--306, 1999.
[6] Herault, J. et al., Phys. Rev. Fluids, in preparation, 2017.
[7] Tilgner, A., Phys. Fluids, 17 (3), 034, 104, 2005.

Keywords: Dynamo; DRESDYN; precession

  • Lecture (Conference)
    Natural Dynamos, 26.-30.06.2017, Valtice, Tschechien

Publ.-Id: 25753