Generation and maintenance of bulk turbulence by libration-driven elliptical instability

Abstract

Longitudinal libration corresponds to the periodic oscillation of a body’s rotation rate and is, along with precessional and tidal forcings, a possible source of mechanically-driven turbulence in the fluid interior of satellites and planets. In this study, we present a combination of direct numerical simulations and laboratory experiments, modeling this geophysically relevant mechanical forcing. We investigate the fluid motions inside a longitudinally librating ellipsoidal container filled with an incompressible fluid. The elliptical instability, which is a triadic resonance between two inertial modes and the oscillating base flow with elliptical streamlines, is observed both numerically and experimentally. The large-scale inertial modes eventually lead to small-scale turbulence, provided that the Ekman number is small enough. We characterize this transition to turbulence as additional triadic resonances develop while also investigating the properties of the turbulent flow that displays both intermittent and sustained regimes. These turbulent flows may play an important role in the thermal and magnetic evolution of bodies subject to mechanical forcing, which is not considered in standard models of convectively driven magnetic field generation.

Inertial Wave Turbulence Driven by Elliptical Instability

“…As shown here, the fundamental quantity to be considered is, therefore, the ratio between geostrophic flows and 3D modes, which depends on the specifics of the considered system and has been mostly neglected when comparing different rotating turbulence configurations. In previous experiments and simulations in spherical or ellipsoidal geometries, the geostrophic modes resulting from the nonlinear interactions of inertial waves manifest themselves as zonal flows, i.e., mean steady axisymmetric flows pervading the fluid interior [16,17,[51][52][53] (see [54], however). Their amplitudes tend to be proportional to β 2 E −α , with α ranging from 0 to 2 [52,55,56], depending on the excitation frequency.…”

“…First, columnar vortices are typically not observed in global simulations. Instead, geostrophic modes emerge as steady axisymmetric flows, which do not necessarily inhibit the instability mechanism [17] (but see [20]). Moreover, the inverse cascade shown in Fig.…”

“…The presence or absence of geostrophic modes appears to be important, but the diversity remains to be explained in detail. Indeed, each inertial wave excited by elliptical instability of the base flow can be itself unstable to a triadic resonance with another pair of inertial waves [22]: these secondary instabilities have been observed both numerically [17,23] and experimentally [24]. Whether these multiple resonances asymptotically lead to a wave turbulence regime [25,26], similar to the recently observed regimes with flexural waves in plates [27], gravity-capillary waves [28], and internal waves [29], remains to be seen.…”

“…The saturation of the instability can lead to either sustained flows [15][16][17] or cyclic behaviors between laminar and turbulent states [12,[18][19][20], reminiscent of the "resonant collapse" of inertial waves observed by McEwan [21]. The presence or absence of geostrophic modes appears to be important, but the diversity remains to be explained in detail.…”

“…The spatial resolution is up to 512 grid points in each direction (see details in Supplemental Material [36]). Contrary to previous global DNS [17,37], we focus on values of β as small as possible as it is below 10 −3 in planetary interiors. The value of E is a compromise between our desire to make the flow fully turbulent but have the simulation well resolved.…”