On the sun's differential rotation

Abstract

It is assumed that the meridional motions (U) and angular velocity (Ω) in the surface layers of the convection zone are given by simple expressions of the form: Ur= 2ψ(r) P2(cosθ)/ϱr2, U0 = −ψ′(r) sinθ cosθ/ϱr, and Ω = Ω0[(1 + ω0(r) + ω2(r) P2(cosθ)]. Here ψ(r) is the stream function, P2(cosθ) the second order Legendre polynomial, and θ the polar angle. Allowance is made for a possible difference in the rate of momentum exchange between the directions parallel and perpendicular to gravity by introducing an anisotropic turbulent viscosity coefficient, μ, which is assumed furthermore to be proportional to the density, ϱ;μ = ϱν, and νθθ= νφφ= sνrr. It is shown that if the sunspots give an indication of the Sun's angular velocity at a depth h(∽ 3 × 104 km) then the turbulent viscosity is necessarily anisotropic. The radial variation introduced by this anisotropy seems to explain well the sunspot data if we assume that the sunspots act as tracers of the Sun's angular velocity.