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

Abstract

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 endwalls of the cylinder. The corresponding frequencies can be grouped into frequency sets satisfying resonance conditions with the forced Kelvin mode.We show that one set forms a triad that is associated with a parametric resonance of Kelvin modes. We observe a significant frequency variation of the unstable modes with the precession ratio, which can be explained by 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.The second frequency set includes a very low frequency and does not exhibit the properties of a parametric resonance between Kelvin modes. Interestingly this frequency set always emerges before the occurence of the triadic resonances, i.e. at a lower precession ratio, which implies that it may correspond to a new type of instability. We discuss the relevance of an instability of a geostrophic mode described by Kerswell [J. Fluid Mech. 1999, 382, 283-306] although other mechanisms cannot be completely ruled out.

On the origins of steady streaming in precessing fluids

“…2011; Herault et al. 2019). Finally, streaming is a very efficient source of dynamo action (Giesecke et al.…”

“…The resulting large-amplitude forced response may then excite other inertial modes via triadic resonance. These topics have been addressed in many past studies (Manasseh 1992;Kobine 1996;Kerswell 1999;Lagrange et al 2011;Albrecht et al 2015;Marques & Lopez 2015;Herault et al 2015;Kong et al 2015;Lopez & Marques 2016;Albrecht et al 2018;Lopez & Marques 2018;Giesecke et al 2018;Herault et al 2019).…”

Kinematic dynamo action of a precession-driven flow based on the results of water experiments and hydrodynamic simulations.

“…In the intermediate range (approximately for 0.03 Po 0.06) we observe a weakly nonlinear behavior characterized by erratic fluctuations of the minimum pressure line (similar to the observations of Noir et al 2003, in a precessing sphere) and by a breaking of the equatorial symmetry (central panel in figure 4). In this regime measurements of pressure fluctuations show periodic signatures that indicate the presence of two free Kelvin modes with azimuthal wave numbers m = 5 and m = 6 which constitute a triadic resonance with the forced mode (Herault et al 2018). Triadic resonances have also been found in numerical simulations.…”

“…Nevertheless, it is precisely these interactions that are responsible for the major flow contributions beyond the directly forced mode and for the considerable modification of the azimuthal circulation (Kobine 1995) which is always oriented opposite to the (initial) solid body rotation, giving rise to a "braking" of the flow in the bulk of the cylinder. A direct consequence is the detuning of free inertial modes that appear in terms of triadic resonances , Lopez and Marques 2016, Herault et al 2018, Albrecht et al 2018 Let us briefly describe the setup of the precession water experiment and the measurement techniques that are used to determine the flow structure and amplitude. The setup in the downscaled water experiment consists of a cylindrical vessel having an inner length of H = 326 mm and an inner radius of R = 163 mm.…”

Magnetic field dynamos and magnetically triggered flow instabilities

“…The design of the experiment is finalized (see Figure 4a), the construction is ongoing, and first test-experiments with water are expected for 2019. The wealth of results (Herault et al 2015, Stefani et al 2017, Herault et al 2018), obtained at a 1:6 down-scaled water-dummy experiment (Figure 4f) working up to Re = 1.5 × 10 6 , and by numerical simulations up to Re = 10 4 , provides a sound basis for the large-scale liquid sodium experiment. Since the centrifugal pressure (up to 20 bar), in combination with the precession-driven pressure swing (up to 10 bar) (Stefani et al 2017), make the safe construction of the cylindrical shell a great challenge, the first water experiments will serve for confirming the ultimately allowable rotation and precession rates which by now are supposed to be 10 Hz and 1 Hz, respectively.…”