Instability of precession driven Kelvin modes: Evidence of a detuning effect

We report an experimental study of the instability of a nearly-resonant Kelvin mode forced by precession in a cylindrical vessel. The instability is detected above a critical precession ratio via the appearance of peaks in the temporal power spectrum of pressure fluctuations measured at the end-walls of the cylinder. The corresponding frequencies can be grouped into frequency sets satisfying resonance conditions with the forced Kelvin mode. We show that one triad is associated with a parametric resonance of Kelvin modes. For the first time, we observe a significant frequency variation of the unstable modes with the precession ratio. We explain this frequency modification by considering a detuning mechanism due to the slowdown of the background flow. By introducing a semi-analytical model, we show that the departure of the flow from the solid body rotation leads to a modification of the dispersion relation of Kelvin modes and to a detuning of the resonance condition. Our calculations reproduce the features of experimental measurements. We also show that a second frequency set, including one very low frequency as observed in the experiment, does not exhibit the properties of a parametric resonance between Kelvin modes. Our observations suggest that it may correspond to the instability of a geostrophic mode.Comment: 26 pages, 17 figures, accepted by Phys. Rev. Fluid

Contactless inductive flow tomography

The three-dimensional velocity field of a propeller driven liquid metal flow is reconstructed by a contactless inductive flow tomography (CIFT). The underlying theory is presented within the framework of an integral equation system that governs the magnetic field distribution in a moving electrically conducting fluid. For small magnetic Reynolds numbers this integral equation system can be cast into a linear inverse problem for the determination of the velocity field from externally measured magnetic fields. A robust reconstruction of the large scale velocity field is already achieved by applying the external magnetic field alternately in two orthogonal directions and measuring the corresponding sets of induced magnetic fields. Kelvin's theorem is exploited to regularize the resulting velocity field by using the kinetic energy of the flow as a regularizing functional. The results of the new technique are shown to be in satisfactory agreement with ultrasonic measurements.Comment: 9 Figures; to appear in Phys. Rev

Rotating waves arising from the instability of magnetized spherical Couette flows

Rotating waves of various azimuthal wavenumbers appear in magnetized spherical Couette flows in time- dependent states. The criteria for the flow to enter a time-dependent state are determined by the values of Reynolds and Hartmann numbers for a given geometric configuration of the spherical Couette system. These time-dependent states of the flow have been referred to as the radial jet, the return flow and the shear layer instabilities. In the present work, rotating waves in the flow during radial jet and return flow instabilities are observed. The rotating waves both have an azimuthal wavenumber of 3, but vary in their spatial and temporal properties.Postprint (published version

Rotating waves arising from the instability of magnetized spherical Couette flows

Rotating waves of various azimuthal wavenumbers appear in magnetised spherical Couette flows in time-dependent states. The criteria for the flow to enter a time-dependent state are determined by the values of Reynolds and Hartmann numbers for a given geometric configuration of the spherical Couette system. These time-dependent states of the flow have been referred to as the radial jet, the return flow and the shear layer instabilities. In the present work, rotating waves in the flow during radial jet and return flow instabilities are observed. The rotating waves both have an azimuthal wavenumber of 3, but vary in their spatial and temporal properties.Postprint (published version