We perform idealized numerical simulations of magnetic buoyancy instabilities in three dimensions, solving the equations of compressible magnetohydrodynamics in a model of the solar tachocline. In ...particular, we study the effects of including a highly simplified model of magnetic flux pumping in an upper layer ('the convection zone') on magnetic buoyancy instabilities in a lower layer ('the upper parts of the radiative interior - including the tachocline'), to study these competing flux transport mechanisms at the base of the convection zone. The results of the inclusion of this effect in numerical simulations of the buoyancy instability of both a preconceived magnetic slab and a shear-generated magnetic layer are presented. In the former, we find that if we are in the regime that the downward pumping velocity is comparable with the Alfvén speed of the magnetic layer, magnetic flux pumping is able to hold back the bulk of the magnetic field, with only small pockets of strong field able to rise into the upper layer.
In simulations in which the magnetic layer is generated by shear, we find that the shear velocity is not necessarily required to exceed that of the pumping (therefore the kinetic energy of the shear is not required to exceed that of the overlying convection) for strong localized pockets of magnetic field to be produced which can rise into the upper layer. This is because magnetic flux pumping acts to store the field below the interface, allowing it to be amplified both by the shear and by vortical fluid motions, until pockets of field can achieve sufficient strength to rise into the upper layer. In addition, we find that the interface between the two layers is a natural location for the production of strong vertical gradients in the magnetic field. If these gradients are sufficiently strong to allow the development of magnetic buoyancy instabilities, strong shear is not necessarily required to drive them (cf. previous work by Vasil & Brummell). We find that the addition of magnetic flux pumping appears to be able to assist shear-driven magnetic buoyancy in producing strong flux concentrations that can rise up into the convection zone from the radiative interior.
ABSTRACT
We consider the 3D instability of a layer of horizontal magnetic field in a polytropic atmosphere where, contrary to previous studies, the field lines in the initial state are not ...unidirectional. We show that if the twist is initially concentrated inside the unstable layer, the modifications of the instability reported by several authors are only observed when the calculation is restricted to two dimensions. In three dimensions, the usual interchange instability occurs in the direction fixed by the field lines at the interface between the layer and the field‐free region. We therefore introduce a new configuration: the instability now develops in a weakly magnetized atmosphere where the direction of the field can vary with respect to the direction of the strong unstable field below, the twist being now concentrated at the upper interface. Both linear stability analysis and non‐linear direct numerical simulations are used to study this configuration. We show that from the small‐scale interchange instability, large‐scale twisted coherent magnetic structures are spontaneously formed, with possible implications to the formation of active regions from a deep‐seated solar magnetic field.
Motivated by the interface model for the solar dynamo, this paper explores the complex magnetohydrodynamic interactions between convective flows and shear-driven instabilities. Initially, we consider ...the dynamics of a forced shear flow across a convectively stable polytropic layer, in the presence of a vertical magnetic field. When the imposed magnetic field is weak, the dynamics are dominated by a shear flow (Kelvin–Helmholtz type) instability. For stronger fields, a magnetic buoyancy instability is preferred. If this stably stratified shear layer lies below a convectively unstable region, these two regions can interact. Once again, when the imposed field is very weak, the dynamical effects of the magnetic field are negligible and the interactions between the shear layer and the convective layer are relatively minor. However, if the magnetic field is strong enough to favour magnetic buoyancy instabilities in the shear layer, extended magnetic flux concentrations form and rise into the convective layer. These magnetic structures have a highly disruptive effect upon the convective motions in the upper layer.
A-type stars have a complex internal structure with the possibility of multiple convection zones. If not sufficiently separated, such zones will interact through the convectively stable regions that ...lie between them. It is therefore of interest to ask whether the typical conditions that exist within such stars are such that these convection zones can ever be considered as disjoint. In this paper, we present results from numerical simulations that help in understanding how increasing the distance between the convectively unstable regions affects the interaction. We go on to discuss the effect of varying the stiffness of the stable layer that lies between the unstable regions. We show that in A-type stars the convectively unstable regions are likely to interact through the stable region that separates them. This has profound implications for mixing and transport within these stars.
Aquatic treadmill exercise has traditionally been used for aerobic training during rehabilitation; however, its ability to elicit comparable cardiorespiratory stress compared with land exercise is ...unclear. The purpose of this study was to investigate the cardiorespiratory (CR) responses elicited during maximal-effort protocols using an aquatic treadmill (ATM) and a land treadmill (TM).
Twenty-three college runners participated in two continuous, incremental peak oxygen consumption protocols (ATM and TM) until volitional exhaustion. For the ATM protocol, subjects were submerged in 28 degrees C water to the xiphoid process. ATM speed was increased incrementally to 206.8+/-23.1 m.min, and water jet resistance was increased 10% every minute thereafter. For the TM protocol, speed was increased to 205.3+/-22.3 m.min, and grade was increased 2% every minute thereafter. Rest between sessions was at least 48 h. Oxygen consumption (VO2), heart rate (HR), minute ventilation (VE), tidal volume (VT), breathing frequency (f), and respiratory exchange ratio (RER) were measured continuously, with peak values used for analysis. Rating of perceived exertion (RPE) was recorded immediately after each test, and blood lactate (LA) was measured 3 min afterward.
VE and f were significantly greater in ATM versus TM; however, VO2, HR, VT, RER, LA, RPE, speed, and exercise times were similar for both protocols.
Despite differences in VE and f, it seems that the fluid resistance created by water and jets in an ATM elicits peak CR responses comparable with those seen with inclined TM. These findings suggest that ATM running may be as effective as TM running for aerobic conditioning in fit individuals.
Recently, Silvers et al. (2009b), using numerical simulations, confirmed the existence of a double diffusive magnetic buoyancy instability of a layer of horizontal magnetic field produced by the ...interaction of a shear velocity field with a weak vertical field. Here, we demonstrate the longer term nonlinear evolution of such an instability in the simulations. We find that a quasi two-dimensional interchange instability rides (or “surfs”) on the growing shear-induced background downstream field gradients. The region of activity expands since three-dimensional perturbations remain unstable in the wake of this upward-moving activity front, and so the three-dimensional nature becomes more noticeable with time.
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