The Taylor-Proudman Balance and the Solar Rotational Data

Details The Taylor-Proudman Balance and the Solar Rotational Data The Taylor-Proudman Balance and the Solar Rotational Data

Feb 1999

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1999apj...511..945d&link_type=abstract

The Astrophysical Journal, Volume 511, Issue 2, pp. 945-957.

Astronomy and Astrophysics

Astronomy

25

Magnetohydrodynamics: Mhd, Sun: Magnetic Fields, Sun: Rotation

Scientific paper

For the Sun (and because of the presence of buoyancy), the implications of the Taylor-Proudman balance (TPB, a balance between the pressure, Coriolis, and buoyancy forces in the radial and latitudinal momentum equations) differ fundamentally from those of an incompressible fluid. The TPB now only determines the latitudinal variations of the solar entropy in terms of the rotation law and known functions of r. As a consequence of the TPB, the energy equation is in fact an equation for the angular velocity, Omega(r, theta)=Omega_0(omega_0(r)+omega_2(r)P_2(costheta)), where P_2(costheta) is the second-order Legendre polynomial. In agreement with data from the Solar Oscillations Investigations project (SOI) Michelson Doppler Imager (MDI) on board SOHO, we assume that omega_0(r) is constant with r, and solve the equation for omega_2(r) with a simple, heuristic expression for the convective flux [if omega_0(r) is constant, then ∂Omega/∂r vanishes for theta_c=54.7d, P_2(costheta_c)=0, in remarkable agreement with Kosovichev's results inferred from isocontours for Omega(r, theta)]. For values of the meridional motions that are not too large, solutions for omega_2(r) exist that agree with these isocontours. These solutions are such that the latitudinal variation of the convective flux, arising from the latitudinal variations of the entropy, required by the TPB, are significantly reduced.

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