TY - JOUR

T1 - Effect of latitudinal differential rotation on solar Rossby waves

T2 - Critical layers, eigenfunctions, and momentum fluxes in the equatorial β plane

AU - Gizon, L.

AU - Fournier, D.

AU - Albekioni, M.

N1 - Funding Information:
Acknowledgements. We thank Aaron Birch, Leonie Frantzen, Shravan Hanasoge (CSS), and Bastian Proxauf for useful discussions. Author contributions: L. G. proposed and designed research. L. G. and M. A. solved the inviscid problem analytically. D. F. solved the viscous problem numerically (code available at https://edmond.mpdl.mpg.de/imeji/ collection/50wepJqIODg7Jg13). L. G. wrote the draft paper. All authors reviewed the final manuscript. Funding: L. G. acknowledges partial support from ERC Synergy Grant WHOLE SUN 810218 and NYUAD Institute Grant G1502. M. A. acknowledges funding from the Volkswagen Foundation and the Shota Rustaveli National Science Foundation of Georgia (SRNSFG Grant N04/46). The computational resources were provided by the German Data Center for SDO through grant 50OL1701 from the German Aerospace Center (DLR).

PY - 2020/10/1

Y1 - 2020/10/1

N2 - 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 ß plane, we studied the propagation of linear Rossby waves (phase speed c < 0) in a parabolic zonal shear flow, U = -U °2 < 0, where U = 244 m s-1, and ° 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.

AB - 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 ß plane, we studied the propagation of linear Rossby waves (phase speed c < 0) in a parabolic zonal shear flow, U = -U °2 < 0, where U = 244 m s-1, and ° 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.

KW - Hydrodynamics

KW - Sun: interior

KW - Sun: oscillations

KW - Sun: rotation

KW - Turbulence

KW - Waves

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U2 - 10.1051/0004-6361/202038525

DO - 10.1051/0004-6361/202038525

M3 - Article

AN - SCOPUS:85094891827

VL - 642

JO - Astronomy and Astrophysics

JF - Astronomy and Astrophysics

SN - 0004-6361

M1 - A178

ER -