Convective overstability in accretion disks: 3D linear analysis and nonlinear saturation

Recently, Klahr & Hubbard (2014) claimed that a hydrodynamical linear overstability exists in protoplanetary disks, powered by buoyancy in the presence of thermal relaxation. We analyse this claim, confirming it through rigorous compressible linear analysis. We model the system numerically, reproducing the linear growth rate for all cases studied. We also study the saturated properties of the overstability in the shearing box, finding that the saturated state produces finite amplitude fluctuations strong enough to trigger the subcritical baroclinic instability. Saturation leads to a fast burst of enstrophy in the box, and a large-scale vortex develops in the course of the next $\approx$100 orbits. The amount of angular momentum transport achieved is of the order of $\alpha \approx 10^{-3}$, as in compressible SBI models. For the first time, a self-sustained 3D vortex is produced from linear amplitude perturbation of a quiescent base state.Comment: 7 pages, 4 figures. ApJ, accepte

On the connection between the magneto-elliptic and magneto-rotational instabilities

It has been recently suggested that the magneto-rotational instability (MRI) is a limiting case of the magneto-elliptic instability (MEI). This limit is obtained for horizontal modes in the presence of rotation and an external vertical magnetic field, when the aspect ratio of the elliptic streamlines tends to infinite. In this paper we unveil the link between these previously unconnected mechanisms, explaining both the MEI and the MRI as different manifestations of the same Magneto-Elliptic-Rotational Instability (MERI). The growth rates are found and the influence of the magnetic and rotational effects is explained, in particular the effect of the magnetic field on the range of negative Rossby numbers at which the horizontal instability is excited. Furthermore, we show how the horizontal rotational MEI in the rotating shear flow limit links to the MRI by the use of the local shearing box model, typically used in the study of accretion discs. In such limit the growth rates of the two instability types coincide for any power-type background angular velocity radial profile with negative exponent corresponding to the value of the Rossby number of the rotating shear flow. The MRI requirement for instability is that the background angular velocity profile is a decreasing function of the distance from the centre of the disk which corresponds to the horizontal rotational MEI requirement of negative Rossby numbers. Finally a physical interpretation of the horizontal instability, based on a balance between the strain, the Lorentz force and the Coriolis force is given.Comment: 15 pages, 3 figures. Accepted for publication in the Journal of Fluid Mechanic

Interplay between spin frustration and thermal entanglement in the exactly solved Ising-Heisenberg tetrahedral chain

The spin-1/2 Ising-Heisenberg tetrahedral chain is exactly solved using its local gauge symmetry, which enables one to establish a rigorous mapping with the corresponding chain of composite Ising spins tractable within the transfer-matrix approach. Exact results derived for spin-spin correlation functions are employed to obtain the frustration temperature, at which a product of correlation functions along an elementary triangular plaquette becomes negative and the relevant spins experience a spin frustration. In addition, we have exactly calculated a concurrence quantifying thermal entanglement along with a threshold temperature, above which concurrence as a measure of thermal entanglement vanishes. It is shown that the frustration and threshold temperature coincide at sufficiently low temperatures, while they exhibit a very different behavior in the high-temperature region when tending towards completely different asymptotic limits. The threshold temperature additionally shows a notable reentrant behavior when it extends over a narrow temperature region above the classical ground state without any quantum correlations. It is demonstrated that the specific heat may display temperature dependence with or without an anomalous low-temperature peak for a relatively strong or weak Heisenberg interaction, respectively.Comment: 9 pages, 6 figure