The Dynamic Evolution of Twisted Magnetic Flux Tubes in a Three‐dimensional Convecting Flow. I. Uniformly Buoyant Horizontal Tubes

Abstract

We present three-dimensional numerical simulations of the dynamic evolution of uniformly buoyant, twisted horizontal magnetic flux tubes in a three-dimensional stratified convective velocity field. Our calculations are relevant to understanding how stratified convection in the deep solar convection zone may affect the rise and the structure of buoyant flux tubes that are responsible for the emergence of solar active regions. We find that in order for the magnetic buoyancy force of the tube to dominate the hydrodynamic force due to the convective downflows, the field strength B of the flux tube needs to be greater than ðH p =aÞ 1=2 B eq $ 3B eq , where H p is the pressure scale height, a is the tube radius, and B eq is the field strength in equipartition with the kinetic energy density of the strong downdrafts. For tubes of equipartition field strength (B ¼ B eq ), the dynamic evolution depends sensitively on the local condition of the convective flow. Sections of the tube in the paths of strong downdrafts are pinned down to the bottom despite their buoyancy, while the rise speed of sections within upflow regions is significantly boosted; -shaped emerging tubes can form between downdrafts. Although flux tubes with B ¼ B eq are found to be severely distorted by convection, the degree of distortion obtained from our simulations is not severe enough to clearly rule out the -tubes that are able to emerge between downdrafts as possible progenitors of solar active regions. As the initial field strength of the tube becomes higher than the critical value of $ðH p =aÞ 1=2 B eq given above, the dynamic evolution converges toward the results of previous simulations of the buoyant rise of magnetic flux tubes in a static, adiabatically stratified model solar convection zone. Tubes with 10 times the equipartition field strength are found to rise unimpeded by the downdrafts and are not significantly distorted by the three-dimensional convective flow.

Magnetic helicity accumulation and tilt angle evolution of newly emerging active regions

“…A certain amount of twist is needed to prevent the flux tube from being destroyed by the hydrodynamic vortex behind it during its emergence in the convection zone (Fan et al 1998). Simulations of flux tube emergence (Schüssler et al 1979;Moreno-Insertis & Emonet 1996;Emonet & Moreno-Insertis 1998;Fan et al 2003;Cheung et al 2006) also showed that untwisted flux tubes are very unlikely to emerge. So we consider the two situations H > 0 and H < 0.…”

Dynamo action and magnetic buoyancy in convection simulations with vertical shear

“…These values are small in comparison to the u rms values of the models (see Tables 1 and 2) which does not agree with the rise of a flux tube in a stratified atmosphere. For instance, Fan et al (2003) obtain a final rise velocity ≈5 times larger than the rms-velocity. We should point out that in the simulations here, the strong shear increases u rms by a factor of two or even more.…”

“…In most of the cases we find max(B y ) ≈ 5B eq , and only in the models with a thicker (Runs T04 and AR01) or a deeper shear layer (Run D04), max(B y ) can be somewhat greater than 6B eq . Fan et al (2003) argue that if B 0 > (H P /a) 1/2 B eq , B 0 being the field strength in the shear layer and H P the local pressure scale height, a buoyant flux-tube of radius a may rise without experiencing the convective drag force. Here, although the shape of the magnetic field is not a tube, we compute the same condition using a = d s .…”

“…Fan et al (2003) studied the evolution of an isolated twisted flux tube in a turbulent convection zone. They found that coherent rise is possible as far as the magnetic buoyant force overcomes the hydrodynamic force from convection, i.e., obeying the condition B 0 > (H P /a) 1/2 B eq , where B 0 is the initial magnetic field strength, H P is the pressure scale height, and a is the radius of the tube.…”

The Evolution of a Double Diffusive Magnetic Buoyancy Instability

“…Until fairly recently, such investigations have principally focussed on the evolution of pre-conceived, idealised buoyant structures (e.g. Parker (1955), Fan et al (1998), Emonet & Moreno-Insertis (1998), Hughes, Falle, & Joarder (1998), Hughes & Falle (1998), Wissink et al (2000), Fan et al (2003), Abbett et al (2004), Jouve & Brun (2009)). Recently attention turned to the problem of the self-consistent generation of such structures as well as their evolution, in particular using the dynamics that are expected to be available in the solar tachocline, i.e.…”