Existence Of The Magnetorotational Instability

By posing and solving a global axisymmetric eigenvalue problem on an infinite domain with modes vanishing at zero and infinity for a differentially rotating MHD plasma, the conditions for the occurrence of a purely growing low-frequency mode known as the magnetorotational instability (MRI) are mapped. It is shown that the MRI criterion drawn from the "local dispersion relation" is at best inadequate and may even be misleading. The physics of the MRI is rather nuanced. It is dictated by the details of the radial profile of the rotation velocity Omega(r) and not just by the sign and the magnitude of its gradient, Omega'. The salient features of the class of profiles for which the MRI-like eigenmodes may occur are given along with the eigenspectrum. For a variety of other profiles, it is shown that an unstable magnetorotational mode is not a valid eigensolution.Institute for Fusion Studie

Weak and strong regimes of incompressible magnetohydrodynamic turbulence

It is shown that in the framework of the weak turbulence theory, the autocorrelation and cascade timescales are always of the same order of magnitude. This means that, contrary to the general belief, any model of turbulence which implies a large number of collisions among wave packets for an efficient energy cascade (such as the Iroshnikov-Kraichnan model) are not compatible with the weak turbulence theory.Comment: Accepted to Phys. Plasma

Controlling the partial coalescence of a droplet on a vertically vibrated bath

A new method is proposed to stop the cascade of partial coalescences of a droplet laid on a liquid bath. The strategy consists in vibrating the bath in the vertical direction in order to keep small droplets bouncing. Since large droplets are not able to bounce, they partially coalesce until they reach a critical size. The system behaves as a low pass filter : droplets smaller than the critical size are selected. This size has been investigated as a function of the acceleration and the frequency of the bath vibration. Results suggest that the limit size for bouncing is related to the first mode of the droplet deformation.Comment: 4 pages, 3 figures, accepted in Phys. Rev.