TY - JOUR

T1 - Mixing of a passive scalar by the instability of a differentially rotating axial pinch

AU - Paredes, A.

AU - Gellert, M.

AU - Rüdiger, G.

N1 - Publisher Copyright:
© ESO 2016.

PY - 2016/4/1

Y1 - 2016/4/1

N2 - The mean-field diffusion of passive scalars such as lithium, beryllium or temperature dispersals due to the magnetic Tayler instability of a rotating axial pinch is considered. Our study is carried out within a Taylor-Couette setup for two rotation laws: solid-body quasi-Kepler rotation. The minimum magnetic Prandtl number used is 0.05, and the molecular Schmidt number Sc of the fluid varies between 0.1 and 2. An effective diffusivity coefficient for the mixing is numerically measured by the decay of a prescribed concentration peak located between both cylinder walls. We find that only models with Sc exceeding 0.1 basically provide finite instability-induced diffusivity values. We also find that for quasi-Kepler rotation at a magnetic Mach number Mm ? 2, the flow transits from the slow-rotation regime to the fast-rotation regime that is dominated by the Taylor-Proudman theorem. For fixed Reynolds number, the relation between the normalized turbulent diffusivity and the Schmidt number of the fluid is always linear so that also a linear relation between the instability-induced diffusivity and the molecular viscosity results, just in the sense proposed by Schatzman (1977, A&A, 573, 80). The numerical value of the coefficient in this relation reaches a maximum at Mm ∼ 2 and decreases for larger Mm, implying that only toroidal magnetic fields on the order of 1 kG can exist in the solar tachocline.

AB - The mean-field diffusion of passive scalars such as lithium, beryllium or temperature dispersals due to the magnetic Tayler instability of a rotating axial pinch is considered. Our study is carried out within a Taylor-Couette setup for two rotation laws: solid-body quasi-Kepler rotation. The minimum magnetic Prandtl number used is 0.05, and the molecular Schmidt number Sc of the fluid varies between 0.1 and 2. An effective diffusivity coefficient for the mixing is numerically measured by the decay of a prescribed concentration peak located between both cylinder walls. We find that only models with Sc exceeding 0.1 basically provide finite instability-induced diffusivity values. We also find that for quasi-Kepler rotation at a magnetic Mach number Mm ? 2, the flow transits from the slow-rotation regime to the fast-rotation regime that is dominated by the Taylor-Proudman theorem. For fixed Reynolds number, the relation between the normalized turbulent diffusivity and the Schmidt number of the fluid is always linear so that also a linear relation between the instability-induced diffusivity and the molecular viscosity results, just in the sense proposed by Schatzman (1977, A&A, 573, 80). The numerical value of the coefficient in this relation reaches a maximum at Mm ∼ 2 and decreases for larger Mm, implying that only toroidal magnetic fields on the order of 1 kG can exist in the solar tachocline.

KW - Diffusion

KW - Instabilities

KW - Magnetic fields

KW - Magnetohydrodynamics (MHD)

KW - Turbulence

UR - http://www.scopus.com/inward/record.url?scp=84964330643&partnerID=8YFLogxK

U2 - 10.1051/0004-6361/201527960

DO - 10.1051/0004-6361/201527960

M3 - Artículo

AN - SCOPUS:84964330643

VL - 588

JO - Astronomy and Astrophysics

JF - Astronomy and Astrophysics

SN - 0004-6361

M1 - A147

ER -