TY - JOUR

T1 - Magnetic Suppression of Zonal Flows on a Beta Plane

AU - Constantinou, Navid C.

AU - Parker, Jeffrey B.

N1 - Publisher Copyright:
© 2018. The American Astronomical Society. All rights reserved..

PY - 2018/8/10

Y1 - 2018/8/10

N2 - Zonal flows in rotating systems have been previously shown to be suppressed by the imposition of a background magnetic field aligned with the direction of rotation. Understanding the physics behind the suppression may be important in systems found in astrophysical fluid dynamics, such as stellar interiors. However, the mechanism of suppression has not yet been explained. In the idealized setting of a magnetized beta plane, we provide a theoretical explanation that shows how magnetic fluctuations directly counteract the growth of weak zonal flows. Two distinct calculations yield consistent conclusions. The first, which is simpler and more physically transparent, extends the Kelvin-Orr shearing wave to include magnetic fields and shows that a weak, long-wavelength shear flow organizes magnetic fluctuations to absorb energy from the mean flow. The second calculation, based on the quasilinear, statistical CE2 framework, is valid for arbitrary wavelength zonal flow and predicts a self-consistent growth rate of the zonal flow. We find that a background magnetic field suppresses zonal flow if the bare Alfvén frequency is comparable to or larger than the bare Rossby frequency. However, suppression can occur for even smaller magnetic fields if the resistivity is sufficiently small enough to allow sizable magnetic fluctuations. Our calculations reproduce the scaling that describes the boundary of zonation, as found in previous work, and we explicitly link this scaling to the amplitude of magnetic fluctuations.

AB - Zonal flows in rotating systems have been previously shown to be suppressed by the imposition of a background magnetic field aligned with the direction of rotation. Understanding the physics behind the suppression may be important in systems found in astrophysical fluid dynamics, such as stellar interiors. However, the mechanism of suppression has not yet been explained. In the idealized setting of a magnetized beta plane, we provide a theoretical explanation that shows how magnetic fluctuations directly counteract the growth of weak zonal flows. Two distinct calculations yield consistent conclusions. The first, which is simpler and more physically transparent, extends the Kelvin-Orr shearing wave to include magnetic fields and shows that a weak, long-wavelength shear flow organizes magnetic fluctuations to absorb energy from the mean flow. The second calculation, based on the quasilinear, statistical CE2 framework, is valid for arbitrary wavelength zonal flow and predicts a self-consistent growth rate of the zonal flow. We find that a background magnetic field suppresses zonal flow if the bare Alfvén frequency is comparable to or larger than the bare Rossby frequency. However, suppression can occur for even smaller magnetic fields if the resistivity is sufficiently small enough to allow sizable magnetic fluctuations. Our calculations reproduce the scaling that describes the boundary of zonation, as found in previous work, and we explicitly link this scaling to the amplitude of magnetic fluctuations.

KW - Sun: interior

KW - Sun: magnetic fields

KW - instabilities

KW - magnetohydrodynamics (MHD)

KW - turbulence

UR - http://www.scopus.com/inward/record.url?scp=85051467979&partnerID=8YFLogxK

U2 - 10.3847/1538-4357/aace53

DO - 10.3847/1538-4357/aace53

M3 - Article

SN - 0004-637X

VL - 863

JO - Astrophysical Journal

JF - Astrophysical Journal

IS - 1

M1 - 46

ER -