Onset of Convection in Rotating Spherical Shells: Variations With Radius Ratio. Issue 1 (29th December 2022)

• Record Type: Journal Article
• Authors: Barik, A.; Triana, S. A.; Calkins, M.; Stanley, S.; Aurnou, J.
• Is Part Of: Earth and space science. Volume 10:Issue 1(2023)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2022-12-29
• Subjects: planetary interiors -- rotating convection -- spherical shells -- eigenvalue -- numerical methods -- dynamo theory; Space sciences -- Periodicals; Geophysics -- Periodicals; 500.5
• DOI: 10.1029/2022EA002606
• Languages: English
• ISSNs: 2333-5084

Abstract

Abstract: Convection in rotating spherical layers of fluid is ubiquitous in spherical astrophysical objects like planets and stars. A complete understanding of the magnetohydrodynamics requires understanding of the linear problem—when convection onsets in these systems. This is a fluid dynamics problem that has been studied since the early 1900s. Theoretical scaling laws exist for the variation of critical quantities—the Rayleigh number Ra c, the azimuthal wavenumber m c, and the angular drift frequency ω c —with respect to the Ekman number E . However, their variation with the radius ratio χ of the spherical shell is still poorly studied. To address this, we use an open source eigenvalue code Kore to compute these critical quantities over an extensive range of parameters spanning four decades in Ekman number and a dense grid of radius ratio from very thick to very thin shells, focusing on no‐slip and fixed temperature boundary conditions. We find that these variations are explained well by the theoretical scaling laws, especially at low E, but variations in radius ratio also exist. We obtain scaling laws of boundary layer thicknesses and spatial extent of onset modes with respect to the Ekman number which differ only slightly from theoretical scalings. We show that our data set can be used to obtain good estimates of critical quantities in the moderate E range, where the vast majority of current geophysical and astrophysical fluid dynamics simulations are performed, yet where asymptotic theory is only moderately accurate. We further verify asymptotic predictions and determine best‐fit asymptotic model coefficients. Plain Language Summary: Thermal buoyancy drives motions in the fluid layers of rotating planets and stars throughout the universe. In this study, we use a large ensemble of numerical solutions to determine the minimal strength of the thermal forcing needed to start such fluid motions, called convection. Further, we predict the spatial structure of these rotating convective flows and their rate of azimuthal drift, all as a function of spherical shell geometry and compare our results to previous studies. Our database of solutions is made easily accessible to the broader scientific community via an online repository as well as Supporting Information S1 Python notebook and data set. Key Points: Critical parameters for onset of convection in rotating spherical shells are computed over a large range of radius ratios and rotation rates We obtain scaling laws for critical Rayleigh number, wavenumber, angular drift frequency, boundary layers, and spatial extent of modes Our data set and Jupyter Notebook (Supporting Information S1 ) can be used to obtain accurate estimates of critical quantities