Bulletin of the American Physical Society
76th Annual Meeting of the Division of Fluid Dynamics
Sunday–Tuesday, November 19–21, 2023; Washington, DC
Session X18: Minisymposium III: Low Prandtl Number Dynamics in Stellar and Planetary InteriorsInvited

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Chair: Pascale Garaud, University of California Santa Cruz; Jonathan Aurnou, University of California, Los Angeles Room: 146A 
Tuesday, November 21, 2023 8:00AM  8:26AM 
X18.00001: Doublediffusive instabilities of differential rotation in low Pr stellar and planetary interiors Invited Speaker: Adrian Barker Differentiallyrotating stars and planets transport angular momentum internally due to hydrodynamic (or hydromagnetic) turbulence, whose transport rates have long been a challenge to model. Stars and planets both contain low Prandtl number fluid in their interiors, with values of Pr as low as 10^{6} in the solar radiative interior. I will present results on the linear and nonlinear properties of hydrodynamical instabilities of differential rotation in stablystratified radiation zones of stars and planets. In particular, I will discuss the doublediffusive GoldreichSchubertFricke (GSF) instability (the low Pr version of the "McIntyre instability", described by the same dispersion relation), which is driven by a destabilising angular momentum gradient if buoyancy forces are eliminated by fast thermal (relative to viscous) diffusion. This instability can drive turbulence in low Pr stellar and planetary interiors, leading to momentum transport and thermal and chemical mixing. I will first review the properties of the axisymmetric linear instability obtained within a local Cartesian Boussinesq model describing a small portion of a star, highlighting some new results. I will then present numerical simulations of its nonlinear evolution, demonstrating that it can lead to zonal jets (angular momentum layering) and enhanced turbulent transport. In a certain limit, the GSF instability is nonlinearly and formally equivalent to the salt fingering instability, so this analogy will be highlighted to aid understanding. Finally, I will describe the influence of magnetic fields, as well as a new parameterfree theory to model its turbulent transport. 
Tuesday, November 21, 2023 8:26AM  8:52AM 
X18.00002: Observational constraints on solar convection at large and intermediate scales Invited Speaker: Aaron Birch Observational methods have provided a wealth of information about solar convection, which takes place in the low Prandtl number regime. Both correlation tracking and helioseismology have been used to measure convective flows at large and intermediate scales. Correlation tracking methods use time series of images to follow the motion of features at the solar surface and produce measurements of the horizontal flows at the surface of the Sun. Helioseismology, the study of solar acoustic and surfacegravity waves, is used to infer the convective flows in the nearsurface layers of the Sun. Measurements of largescale flows from both of these methods suggest that the largescale convection is weaker than predicted by simulations. At intermediate (supergranulation) scales, the nearsurface convection on the Sun evolves in a wavelike pattern in which, on average, sites of horizontal divergence are replaced by sites of horizontal convergence after roughly two days. There is not yet a generally accepted explanation for this pattern. 
Tuesday, November 21, 2023 8:52AM  9:18AM 
X18.00003: Multimodal rotating magnetoconvection in liquid metals Invited Speaker: Susanne Horn Turbulence and thermal convection, often strongly constrained by Lorentz and Coriolis forces, are ubiquitous in geophysical and astrophysical settings. 
Tuesday, November 21, 2023 9:18AM  9:44AM 
X18.00004: Geo and astrophysically motivated liquid metal experiments at Helmholtz Zentrum Dresden Rossendorf Invited Speaker: Tobias Vogt Thermal turbulence at low Prandtl numbers is important for understanding stars and planets. Experiments with the lowest Prandtl numbers can only be realized with liquid metals and represent a great challenge. In the department of magnetohydrodynamics at the Helmholtz Zentrum Dresden Rossendorf (HZDR) these liquid metal convection flows as well as their interaction with magnetic fields are investigated experimentally. With a targeted use of ultrasonic Doppler velocimetry (UDV) as well as noncontact CIFT measurement techniques, the complex velocity fields in the liquid metal can be reconstructed. The velocity measurements are complemented by high temporal resolution temperature measurements. This allows the global scaling for the heat transport (Nußelt number) as well as the flow intensity (Reynolds number) to be determined. In this talk I will give an overview of the different low Prandtl number experiments at HZDR. The focus will be on convection experiments. The experiments were performed with the alloy gallium indium tin, which is liquid at room temperature and has a Prandtl number of Pr ≈ 0.03. I will also give a short outlook on the upcoming dynamo experiments with liquid sodium and present ideas for future sodium convection experiments at a Prandtl number Pr = O(10^{3}). 
Tuesday, November 21, 2023 9:44AM  10:10AM 
X18.00005: Largescale turbulent structures in liquid metal Rayleigh Bénard convection experiment Invited Speaker: Sylvie Su

Tuesday, November 21, 2023 10:10AM  10:36AM 
X18.00006: Regimes of stratified stellar turbulence Invited Speaker: Kasturi Shah Quantifying transport by strongly stratified turbulence in stellar interiors is important for the development of accurate stellar evolution models. Stratified turbulence in stars and planets differs fundamentally from geophysical turbulence because the Prandtl number, Pr, is very small there. In geophysical flows, when Pr = O(1), turbulent flows (Re » 1) are only weakly thermally diffusive, as reflected by the largeness of the Péclet number (Pe = PrRe) which is O(Re) » 1 when Pr = O(1). With Pr « 1, by contrast, Pe « Re, so it is possible to have Pe « 1 « Re, i.e. regimes of thermally diffusive stratified turbulence, which are not possible in geophysical fluids. Motivated by numerical simulations showing the emergence of anisotropic structures and scaleseparated features, we perform a multiscale analysis of the governing equations, demonstrating the existence of several distinct regimes depending on the emergent buoyancy Péclet number Pe_{b} = Pr Re_{b}, where Re_{b} = α^{2} Re, α is the aspect ratio of the turbulence and Re is the input Reynolds number. Scaling relationships linking the aspect ratio to the strength of the stratification naturally emerge from our analysis. For Pe_{b} « 1 flows, our results recover scaling laws that have been empirically obtained from direct numerical simulations, namely α ∝ (Fr^{2 }/ Pe)^{1/3}, where Fr is the Froude number. For Pe_{b} > 1, the aspect ratio scales as Fr, consistent with published work on strongly stratified geophysical turbulence at Pr = O(1). Finally, we have identified a new regime at intermediate values of Pe_{b}, in which slow, largescales are thermally diffusive while fast, smallscales are not. Using these results, we construct regime diagrams that identify transitions between nondiffusive stratified turbulence, diffusive stratified turbulence, and viscouslycontrolled regimes at Pr « 1 and Pr = O(1). 
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