Influence Of Differential Rotation Research Articles

The Sun’s Mean Line-of-sight Field

In this paper, I regard the Sun-as-a-star magnetic field (i.e., the mean field) as a filter for the spherical harmonic components of the photospheric field, and then calculate the transmission coefficients of this filter. The coefficients for each harmonic, Y l m , are listed in three tables according to their dependence on B 0, the observer’s latitude in the star’s polar coordinate system. These coefficients are used to interpret the 46 yr sequence of daily mean-field measurements at the Wilcox Solar Observatory. I find that the nonaxisymmetric part of the field originates in the , , and a combination of the and harmonic components. The axisymmetric part of the field originates in plus a B 0-dependent combination of the and components. The power spectrum of the field has peaks at frequencies corresponding to the ∼27 day synodic equatorial rotation period and its second and third harmonics. Each of these peaks has fine structure on its low-frequency side, indicating magnetic patterns that rotate slowly under the influence of differential rotation and meridional flow. The sidebands of the fundamental mode resolve into peaks corresponding to periods of ∼28.5 and ∼30 days, which tend to occur at the start of sunspot maximum, whereas the ∼27 day period tends to occur toward the end of sunspot maximum. We might expect similar rotational sidebands to occur in magnetic observations of other Sun-like stars and to be a useful complement to asteroseismology studies of convection and magnetic fields in those stars.

Bifurcations in rotating spherical shell convection under the influence of differential rotation.

The bifurcations of thermal convection in a rotating spherical shell heated from the inner sphere and driven by the buoyancy of a central gravity field are studied numerically. This model of spherical Rayleigh-Bénard convection describes large-scale convection in planets and in the outer zones of celestial bodies. In this work, the influence of an additionally imposed differential rotation of the inner sphere with respect to the outer one on the heat transfer and, more generally, on the whole bifurcation structure is investigated. In addition to numerical simulations, path-following techniques are applied in order to compute both stable and unstable solution branches. The dynamics and the heat transfer are essentially determined by a global bifurcation, which we have identified as a homoclinic bifurcation that consists of a collision of a stable modulated rotating with an unstable rotating wave.

About influence of differential rotation in convection zone of gaseous or fluid giant planet (Uranus) onto the parameters of orbits of satellites

Tidal interactions between Planet and its satellites are known to be the main phenomena, which are determining the orbital evolution of the satellites. We suggest in the current research to take into consideration the additional well-known effect of differential rotation which obviously takes place in the gaseous or fluid convection zone of primary giant Planet (indeed, the aforementioned effect exists even not depending on the orbital evolution of satellites around host Planet). Nevertheless, estimations for the contribution of the aforementioned effect of differential rotation in the Uranus system (including all its most massive satellites) let us exclude using such effect from calculations of mutual evolution of the eccentricity e along with the semi-major axis a for all satellites of Uranus (Planet of ice-type). It means that the Uranus can be considered in the analytic exploration of governing equations as to be the appropriate candidate for applying the modern ansatz [Efroimsky, 2015] (tidal dissipation effect depending on the tidal-flexure frequency) in regard to estimations of eccentricity e along with semi-major axis a for satellites of Uranus. We can see from the results of calculations in Section 3 that the combined system of governing equations (in the sense of combined contributions to the tidal dissipation from Uranus + from satellite) yields the really observed magnitudes of decelerations for semi-major axises of all the satellites of Uranus. Meanwhile, internal heat generation effects in the satellites (due to tidal dissipation effect) are much more than those which definitely take place in the Uranus, excepting the case of Ariel.

The angular momentum transport by unstable toroidal magnetic fields

We demonstrate with a nonlinear MHD code that angular momentum can be transported due to the magnetic instability of toroidal fields under the influence of differential rotation, and that the resulting effective viscosity may be high enough to explain the almost rigid-body rotation observed in radiative stellar cores. Only stationary current-free fields and only those combinations of rotation rates and magnetic field amplitudes which provide maximal numerical values of the viscosity are considered. We find that the dimensionless ratio of the effective over molecular viscosity, $\nu_T/\nu$;, linearly grows with the Reynolds number of the rotating fluid multiplied with the square-root of the magnetic Prandtl number - which is of order unity for the considered red sub-giant KIC 7341231. For the considered interval of magnetic Reynolds numbers - which is restricted by numerical constraints of the nonlinear MHD code - there is a remarkable influence of the magnetic Prandtl number on the relative importance of the contributions of the Reynolds stress and the Maxwell stress to the total viscosity, which is magnetically dominated only for Pm $\gtrsim$ 0.5. We also find that the magnetized plasma behaves as a non-Newtonian fluid, i.e. the resulting effective viscosity depends on the shear in the rotation law. The decay time of the differential rotation thus depends on its shear and becomes longer and longer during the spin-down of a stellar core.

Sunspot activity and the long‐term variation of the Sun's open magnetic flux

The interplanetary magnetic field (IMF) originates in open magnetic regions of the Sun (coronal holes), which in turn form mainly through the emergence and dispersal of active region fields. The radial IMF strength is proportional to the total open flux Φopen, which can be estimated from source surface extrapolations of the measured photospheric field, after correction for magnetograph saturation effects. We derive the long‐term variation of Φopen during 1971–2000 and discuss its relation to sunspot activity. The average value of Φopen was ∼20–30% higher during 1976–1996 than during 1971–1976 and 1996–2000, with major peaks occurring in 1982 and 1991. Near sunspot minimum, most of the open flux resides in the large polar coronal holes, whereas at sunspot maximum it is rooted in relatively small, low‐latitude holes located near active regions and characterized by strong footpoint fields; since the decrease in the total area occupied by holes is offset by the increase in their average field strengths, Φopen remains roughly constant between activity minimum and maximum, unlike the total photospheric flux Φtot. The long‐term variation of Φopen approximately follows that of the Sun's total dipole strength, with a contribution from the magnetic quadrupole around sunspot maximum. Global fluctuations in sunspot activity lead to increases in the equatorial dipole strength and hence to enhancements in Φopen and the IMF strength lasting typically ∼1 year. We employ simulations to clarify the role of active region emergence and photospheric transport processes in the evolution of the open flux. Representing the initial field configuration by one or more bipolar magnetic regions (BMRs), we calculate its subsequent evolution under the influence of differential rotation, supergranular convection, and a poleward bulk flow. The initial value of Φopen is determined largely by the equatorial dipole strength, which in turn depends on the longitudinal phase relations between the BMRs. As the surface flow carries the BMR flux to higher latitudes, the equatorial dipole is annihilated on a timescale of ∼1 year by the combined effect of rotational shearing and turbulent diffusion. The remaining flux becomes concentrated around the poles, and Φopen approaches a limiting value that depends on the axisymmetric dipole strengths of the original BMRs. The polar coronal holes thus represent the long‐lived, axisymmetric remnant of the active regions that emerged earlier in the cycle.

Formation of a Switchback During the Rising Phase of Solar Cycle 21

The customary notion that high-latitude filaments arise from magnetic flux originating in the active-region belts finds its modern expression in numerical models that generate filament channels from flux patterns migrating from active latitudes to the polar caps. Polarity inversions underlying high-latitude filament channels are swept into distinct patterns called `switchbacks' under the joint influence of differential rotation, supergranular diffusion, and meridional flow. The numerical model of Mackay and van Ballegooijen (2001) predicts a heretofore unsuspected solar-cycle dependence to the hemispheric pattern of filament magnetic fields. Observations presented here of a switchback formed early in cycle 21 confirm some key aspects of their model. In this remarkable example the flux diffusing out of the source region migrates to the opposite side of the Sun before it encounters another active region with which to create the quadrupolar field configuration wherein a return arm forms to complete the switchback.

Magnetic stability under the magnetostrophic approximation

We determine the stability of s- and z-dependent basic fields under the magnetostrophic approximation in a cylindrical geometry. The geostrophic flow V G is the dominant nonlinearity in the nonlinear regime. This work assesses the impact of the geostrophic flow at critical linear stability Λ= Λ c by imposing V G as a differential rotation. Here, the Elsasser number Λ is the appropriate nondimensional measure of imposed field strength. Fearn et al. [Fearn, D.R., Lamb, C.J., McLean, D.R., Ogden, R.R., 1997. The influence of differential rotation on magnetic instability and nonlinear magnetic instability in the magnetostrophic limit. Geophys. Astrophys. Fluid Dyn. 86, 173–200] showed that for simple s-dependent basic fields, certain imposed differential rotations could lower Λ c. McLean and Fearn [McLean, D.R., Fearn, D.R., 1999. The geostrophic nonlinearity and its effect on magnetic instability. Geophys. Astrophys. Fluid Dyn., In Press.] then showed that the geostrophic flow-induced subcritical behaviour in the most unstable mode for various combinations of basic fields and aspect ratios. Here, both linear and nonlinear results are new; previous analyses only considered radially ( s-)dependent basic fields. We will derive a consistency condition necessary for the existence of solutions before investigating whether subcriticality exists under a dipolar basic field configuration.

Instabilities of magnetic flux tubes in a stellar convection zone I. Equatorial flux rings in differentially rotating stars

Abstract The stability properties of magnetic flux tubes in stellar convection zones including overshoot regions is of considerable interest in connection with the problems of magnetic flux storage and hydromagnetic dynamo action in the Sun and other cool stars. We have developed a general formalism based on the approximation of thin flux tubes which provides a basis for a linear stability analysis of arbitrary flux tube equilibria. As a first application, the stability of axisymmetric, toroidal flux tubes (flux rings) located in the equatorial plane of a star under the influence of differential rotation and stratification has been considered. Arbitrary angular velocity differences between the interior of the flux ring and its environment are permitted. It is found that the linear evolution of radial and azimuthal perturbations (i.e., within the equatorial plane) is decoupled from that of latitudinal perturbations (perpendicular to the plane). The latitudinal instability (‘poleward slip’) is found to be s...

The influence of differential rotation on the equatorial component of the sun's magnetic dipole field

This paper examines the effect that solar differential rotation would have on a hypothetical large-scale equatorial dipole field. The evolving large-scale field pattern is expressed as a series of non-axisymmetric moments. As time increases, power is transferred to progressively higher order moments. In the 27d rotating coordinate system, each moment undergoes a small retrograde drift which remains nearly uniform until that mode begins to fade. The synodic rotation periods of the first few moments are comparable to the observed 28.5d period of the sun's large-scale field near sunspot maximum. Differential rotation may be the source of this 28.5d period, but the eruption of new flux is necessary to keep the pattern going.

Free oscillations of the giant planets

We present the results of theoretical calculations of adiabatic oscillations of Jupiter and Saturn. The influence of differential rotation is analyzed using a second-order perturbation theory.