The sidewall-localized mode in a resonant precessing cylinder

Abstract

We investigate, via direct numerical simulation using a finite-element method, the precessionally driven flow of a homogeneous fluid confined in a fluid-filled circular cylinder that rotates rapidly about its symmetry axis and precesses about a different axis that is fixed in space. Our numerical simulation, after validating with the asymptotic analytical solution for a weakly precessing cylinder and with the constructed exact solution for the strongly nonlinear problem, focuses on the strongly precessing flow at asymptotically small Ekman numbers. An unusual form of the resonant precessing flow is found when the precessing rate is sufficiently large and the corresponding nonlinearity is sufficiently strong. The nonlinear precessing flow is marked by a sidewall-localized non-axisymmetric traveling wave and a wall-localized axisymmetric shear together with an overwhelmingly dominant interior rigid-body rotation whose direction and magnitude substantially reduce the angular momentum of the rotating fluid system.

Triadic resonances in nonlinear simulations of a fluid flow in a precessing cylinder

“…Instead, we see free Kelvin modes solely with retrograde drift motion which on the one hand agrees with experimental observations of inertial waves in a spherical Couette experiment with liquid sodium (Kelley et al 2007). On the other hand, they seem to contradict with the results from Albrecht et al (2015a) who show that at Re = 2482 (close to the threshold of the instability) the growth rate is very small resulting in a very long time required for the triadic resonance to emerge (which explains why Kong et al (2014) did not find the triadic resonances at the same parameters). However, the reason for the disappearance of the triads at larger Reynolds number is probably an instability of the m = 1 mode, which occurs close to the fundamental resonance due to the increased efficiency of the forcing, while around Γ = 1.825 or Γ = 2.2 the m = 1 mode may saturate by viscosity before becoming unstable.…”

“…Kerswell (1999) showed that a geostrophic instability even if it is subdominant to the triadic instability should finally outweigh the triad if Re is large enough because it does not suffer from detuning effects. This may be important for the observation of large mean ciculations in experiments but cannot explain alone the abrupt transition to a chaotic flow which is determined by the precession ratio and hardly depends on Re (Kong et al 2014. This does not mean that the geostrophic mode does not matter for this phanomenon, but in order to be able to judge this more simulations are required at larger Γ.…”

On the transition from the laminar to disordered flow in a precessing spherical-like cylinder

“…A numerical experiment at Ek = 5 × 10 −5 in the spherical-like cylinder, which is reported in a recent Letter (Kong et al 2014), reveals the existence of strongly precessing flow in the form of a wall-localized mode when Po/ √ Ek = O(10), whose structure is profoundly different from that of weakly precessing flow. The experimental study by Mouhali et al (2012) also indicates the existence of the strongly nonlinear wall-localized mode.…”

Precession-driven dynamos in a full sphere and the role of large scale cyclonic vortices

“…We believe that the small scale fields are related with viscous boundary layer instabilities. 34,35 The magnetic fields are extended upward to outside of the fluid domain. Since the magnetic potential decays as (1/r) l+1 outside the fluid domain, the field outside is mostly dipolar or quadrupolar.…”