TY - JOUR

T1 - Viscous inertial modes on a differentially rotating sphere

T2 - Comparison with solar observations

AU - Fournier, Damien

AU - Gizon, Laurent

AU - Hyest, Laura

N1 - Funding Information:
Acknowledgements. This work is supported by the ERC Synergy Grant WHOLE SUN #810218 and by the DFG Collaborative Research Center SFB 1456 (project C04). LG acknowledges NYUAD Institute Grant G1502. LH acknowledges an internship agreement between SUPAERO and the MPS as part of her Bachelor thesis. The source code is available at https://doi.org/10.17617/3.OM51HE.
Publisher Copyright:
© 2022 EDP Sciences. All rights reserved.

PY - 2022/8/1

Y1 - 2022/8/1

N2 - Context. In a previous paper, we studied the effect of latitudinal rotation on solar equatorial Rossby modes in the β-plane approximation. Since then, a rich spectrum of inertial modes has been observed on the Sun, which is not limited to the equatorial Rossby modes and includes high-latitude modes. Aims. Here we extend the computation of toroidal modes in 2D to spherical geometry using realistic solar differential rotation and including viscous damping. The aim is to compare the computed mode spectra with the observations and to study mode stability. Methods. At a fixed radius, we solved the eigenvalue problem numerically using a spherical harmonics decomposition of the velocity stream function. Results. Due to the presence of viscous critical layers, the spectrum consists of four different families: Rossby modes, high-latitude modes, critical-latitude modes, and strongly damped modes. For each longitudinal wavenumber m ≤ 3, up to three Rossby-like modes are present on the sphere, in contrast to the equatorial β plane where only the equatorial Rossby mode is present. The least damped modes in the model have eigenfrequencies and eigenfunctions that resemble the observed modes; the comparison improves when the radius is taken in the lower half of the convection zone. For radii above 0:75 R⊙ and Ekman numbers E < 10-4, at least one mode is unstable. For either m = 1 or m = 2, up to two Rossby modes (one symmetric and one antisymmetric) are unstable when the radial dependence of the Ekman number follows a quenched diffusivity model (E ≈ 2 x 10-5 at the base of the convection zone). For m = 3, up to two Rossby modes can be unstable, including the equatorial Rossby mode. Conclusions. Although the 2D model discussed here is highly simplified, the spectrum of toroidal modes appears to include many of the observed solar inertial modes. The self-excited modes in the model have frequencies close to those of the observed modes with the largest amplitudes.

AB - Context. In a previous paper, we studied the effect of latitudinal rotation on solar equatorial Rossby modes in the β-plane approximation. Since then, a rich spectrum of inertial modes has been observed on the Sun, which is not limited to the equatorial Rossby modes and includes high-latitude modes. Aims. Here we extend the computation of toroidal modes in 2D to spherical geometry using realistic solar differential rotation and including viscous damping. The aim is to compare the computed mode spectra with the observations and to study mode stability. Methods. At a fixed radius, we solved the eigenvalue problem numerically using a spherical harmonics decomposition of the velocity stream function. Results. Due to the presence of viscous critical layers, the spectrum consists of four different families: Rossby modes, high-latitude modes, critical-latitude modes, and strongly damped modes. For each longitudinal wavenumber m ≤ 3, up to three Rossby-like modes are present on the sphere, in contrast to the equatorial β plane where only the equatorial Rossby mode is present. The least damped modes in the model have eigenfrequencies and eigenfunctions that resemble the observed modes; the comparison improves when the radius is taken in the lower half of the convection zone. For radii above 0:75 R⊙ and Ekman numbers E < 10-4, at least one mode is unstable. For either m = 1 or m = 2, up to two Rossby modes (one symmetric and one antisymmetric) are unstable when the radial dependence of the Ekman number follows a quenched diffusivity model (E ≈ 2 x 10-5 at the base of the convection zone). For m = 3, up to two Rossby modes can be unstable, including the equatorial Rossby mode. Conclusions. Although the 2D model discussed here is highly simplified, the spectrum of toroidal modes appears to include many of the observed solar inertial modes. The self-excited modes in the model have frequencies close to those of the observed modes with the largest amplitudes.

KW - Hydrodynamics

KW - Instabilities

KW - Methods: numerical

KW - Sun: interior

KW - Sun: rotation

KW - Waves

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U2 - 10.1051/0004-6361/202243473

DO - 10.1051/0004-6361/202243473

M3 - Article

AN - SCOPUS:85132270975

SN - 0004-6361

VL - 664

JO - Astronomy and Astrophysics

JF - Astronomy and Astrophysics

M1 - A6

ER -