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 - Publisher Copyright:
© 2020 L. Gizon et al.

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

SN - 0004-6361

VL - 642

JO - Astronomy and Astrophysics

JF - Astronomy and Astrophysics

M1 - A178

ER -