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**Effect of latitudinal differential rotation on solar Rossby waves: Critical layers, eigenfunctions, and momentum fluxes in the equatorial β plane**

Gizon, L., Fournier, D., & Albekioni, M. (2020). Effect of latitudinal differential
rotation on solar Rossby waves: Critical layers, eigenfunctions, and momentum fluxes in the equatorial β plane.*
Astronomy and Astrophysics,* *642*: A178. doi:10.1051/0004-6361/202038525.

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show hide**Item Permalink:**http://hdl.handle.net/21.11116/0000-0007-709C-B

**Version Permalink:**http://hdl.handle.net/21.11116/0000-0008-38DF-F

**Genre:**Journal Article

**Other :**Effect of latitudinal differential rotation on solar Rossby waves: Critical layers, eigenfunctions, and momentum fluxes in the equatorial beta plane

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**Free keywords:**hydrodynamics / waves / turbulence / Sun: rotation / Sun: interior / Sun: oscillations

**MPIS_PROJECTS:**SDO: German Data Center

**Abstract:**Context. Retrograde-propagating waves of vertical vorticity with longitudinal wavenumbers between 3 and 15 have been observed on the Sun with a dispersion relation close to that of classical sectoral Rossby waves. The observed vorticity eigenfunctions are symmetric in latitude, peak at the equator, switch sign near 20°–30°, and decrease at higher latitudes. Aims. We search for an explanation that takes solar latitudinal differential rotation into account. Methods. In the equatorial β plane, we studied the propagation of linear Rossby waves (phase speed c < 0) in a parabolic zonal shear flow, U = − U̅ ξ2 < 0, where U̅ = 244 m s−1, and ξ is the sine of latitude. Results. In the inviscid case, the eigenvalue spectrum is real and continuous, and the velocity stream functions are singular at the critical latitudes where U = c. We add eddy viscosity to the problem to account for wave attenuation. In the viscous case, the stream functions solve a fourth-order modified Orr-Sommerfeld equation. Eigenvalues are complex and discrete. For reasonable values of the eddy viscosity corresponding to supergranular scales and above (Reynolds number 100 ≤ Re ≤ 700), all modes are stable. At fixed longitudinal wavenumber, the least damped mode is a symmetric mode whose real frequency is close to that of the classical Rossby mode, which we call the R mode. For Re ≈ 300, the attenuation and the real part of the eigenfunction is in qualitative agreement with the observations (unlike the imaginary part of the eigenfunction, which has a larger amplitude in the model). Conclusions. Each longitudinal wavenumber is associated with a latitudinally symmetric R mode trapped at low latitudes by solar differential rotation. In the viscous model, R modes transport significant angular momentum from the dissipation layers toward the equator.

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Published Online: 2020

**Language(s):**eng - English

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**Publication Status:**Published online

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**Rev. Type:**Peer

**Identifiers:**DOI: 10.1051/0004-6361/202038525

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ISSN: 0004-6361

CoNE: https://pure.mpg.de/cone/journals/resource/954922828219_1

**Title:**Astronomy and Astrophysics

**Other :**Astron. Astrophys.

**Source Genre:**Journal

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**Publ. Info:**Les Ulis Cedex A France : EDP Sciences

**Pages:**-**Volume / Issue:**642**Sequence Number:**A178**Start / End Page:**-**Identifier:**ISSN: 1432-0746ISSN: 0004-6361

CoNE: https://pure.mpg.de/cone/journals/resource/954922828219_1