SignificanceThe large-scale circulation (LSC) is the key dynamical feature of turbulent thermal convection. It is the underlying structure that shapes the appearance of geo- and astrophysical systems, such as the solar granulation or cloud streets, and the cornerstone of theoretical models. Our laboratory-numerical experiments reveal that the LSC can perform a fully 3D motion resembling a twirling jump rope. The discovery of this LSC mode implies that the currently accepted paradigm of a quasi-planar oscillating LSC needs to be augmented. Moreover, it provides an important link between studies in confined geometries used in experiments and simulations and the effectively unconfined fluid layers in natural settings where an agglomeration of LSCs forms larger patterns.
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.
We present laboratory experimental results demonstrating that librational forcing of an ellipsoidal container of water can produce intense motions through the mechanism of a libration driven elliptical instability (LDEI). These libration studies are conducted using an ellipsoidal acrylic container filled with water. A particle image velocimetry method is used to measure the 2D velocity field in the equatorial plane over hundreds libration cycles for a fixed Ekman number, E = 2 × 10 −5 . In doing so, we recover the libration induced base flow and a time averaged zonal flow. Further, we show that LDEI in non-axisymmetric container geometries is capable of driving both intermittent and saturated turbulent motions in the bulk fluid. Additionally, we measure the growth rate and amplitude of the LDEI induced excited flow in a fully ellipsoidal container at more extreme parameters than previously studied [Noir
Earth’s magnetic field is generated by convective motions in its liquid metal core. In this fluid, the heat diffuses significantly more than momentum, and thus the Prandtl number$Pr$is well below unity. The thermally driven convective flow dynamics of liquid metals are very different from moderate-$Pr$fluids, such as water and those used in current dynamo simulations. In order to characterise rapidly rotating thermal convection in low-$Pr$number fluids, we have performed laboratory experiments in a cylinder of aspect ratio$\unicode[STIX]{x1D6E4}=1.94$using liquid gallium ($Pr\simeq 0.025$) as the working fluid. The Ekman number varies from$E\simeq 5\times 10^{-6}$to$5\times 10^{-5}$and the Rayleigh number varies from$Ra\simeq 2\times 10^{5}$to$1.5\times 10^{7}$. Using spectral analysis stemming from point-wise temperature measurements within the fluid and measurements of the Nusselt number$Nu$, we characterise the different styles of low-$Pr$rotating convective flow. The convection threshold is first overcome in the form of container-scale inertial oscillatory modes. At stronger forcing, sidewall-attached modes are identified for the first time in liquid metal laboratory experiments. These wall modes coexist with the bulk oscillatory modes. At$Ra$well below the values where steady rotating columnar convection occurs, the bulk flow becomes turbulent. Our results imply that rotating convective flows in liquid metals do not develop in the form of quasisteady columns, as in moderate-$Pr$fluids, but in the form of oscillatory convective motions. Thus, thermally driven flows in low-$Pr$geophysical and astrophysical fluids can differ substantively from those occurring in$Pr\simeq 1$models. Furthermore, our experimental results show that relatively low-frequency wall modes are an essential dynamical component of rapidly rotating convection in liquid metals.
The turbulence generated in the liquid metal cores and subsurface oceans of planetary bodies may be due to the role of mechanical forcing through precession/nutation, libration, tidal forcing and collisions. Here, we model the response of an enclosed constant density fluid to tidal forcing by combining laboratory equatorial velocity measurements with selected highresolution numerical simulations to show, for the first time, the generation of bulk filling turbulence. The transition to saturated turbulence is characterized by an elliptical instability that first excites primary inertial modes of the system, then secondary inertial modes forced by the primary inertial modes, and then bulk filling turbulence. The amplitude of this saturated turbulence scales with the body's elliptical distortion, U ∼ β, while a time-and radially averaged azimuthal zonal flow scales with β 2. The results of the current tidal experiments are compared with recent studies of the libration-driven turbulent flows studied by Grannan et al. and Favier et al. Tides and libration correspond to two end-member types of geophysical mechanical forcings. For satellites dominated by tidal forcing, the ellipsoidal boundary enclosing the internal fluid layers is elastically deformed while, for librational forcing, the core-mantle boundary possesses an inherently rigid, frozen-in ellipsoidal shape. We find striking similarities between tidally and librationally driven flow transitions to bulk turbulence and zonal flows. This suggests a generic fluid response independent of the style of mechanical forcing. Since β 10 −4 in planetary bodies, it is often argued that mechanically driven zonal velocities will be small. In contrast, our linear scaling for mechanically driven bulk turbulence, U ∼ β, suggests geophysically significant velocities that can play a significant role in planetary processes including tidal dissipation and magnetic field generation.
Planets and satellites can undergo physical librations, which consist of forced periodic variations in their rotation rate induced by gravitational interactions with nearby bodies. This mechanical forcing may drive turbulence in interior fluid layers such as subsurface oceans and metallic liquid cores through a libration‐driven elliptical instability (LDEI) that refers to the resonance of two inertial modes with the libration‐induced base flow. LDEI has been studied in the case of a full ellipsoid. Here we address for the first time the question of the persistence of LDEI in the more geophysically relevant ellipsoidal shell geometries. In the experimental setup, an ellipsoidal container with spherical inner cores of different sizes is filled with water. Direct side view flow visualizations are made in the librating frame using Kalliroscope particles. A Fourier analysis of the light intensity fluctuations extracted from recorded movies shows that the presence of an inner core leads to spatial heterogeneities but does not prevent LDEI. Particle image velocimetry and direct numerical simulations are performed on selected cases to confirm our results. Additionally, our survey at a fixed forcing frequency and variable rotation period (i.e., variable Ekman number, E) shows that the libration amplitude at the instability threshold varies as ∼E0.65. This scaling is explained by a competition between surface and bulk dissipation. When extrapolating to planetary interior conditions, this leads to the E1/2 scaling commonly considered. We argue that Enceladus' subsurface ocean and the core of the exoplanet 55 CnC e should both be unstable to LDEI.
The interplay between convective, rotational and magnetic forces defines the dynamics within the electrically conducting regions of planets and stars. Yet their triadic effects are separated from one another in most studies, arguably due to the richness of each subset. In a single laboratory experiment, we apply a fixed heat flux, two different magnetic field strengths and one rotation rate, allowing us to chart a continuous path through Rayleigh–Bénard convection (RBC), two regimes of magnetoconvection, rotating convection and two regimes of rotating magnetoconvection, before finishing back at RBC. Dynamically rapid transitions are determined to exist between jump rope vortex states, thermoelectrically driven magnetoprecessional modes, mixed wall- and oscillatory-mode rotating convection and a novel magnetostrophic wall mode. Thus, our laboratory ‘pub crawl’ provides a coherent intercomparison of the broadly varying responses arising as a function of the magnetorotational forces imposed on a liquid-metal convection system.
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