Publication
The influence of magnetic field on shortwavelength instability of Riemann ellipsoids 

Mizerski K.A., Bajer K. 
Publication type:

Physica D: Nonlinear Phenomena240 (20), 2011, 16291635, 10.1016/j.physd.2011.02.006 
Organization unit:

We address the question of stability of the socalled Stype Riemann ellipsoids, i.e. a family of Euler flows in gravitational equilibrium with the vorticity and background rotation aligned along the principal axis perpendicular to the flow. The Riemann ellipsoids are the simplest models of selfgravitating, tidally deformed stars in binary systems, with the ellipticity of the flow modelling the tidal deformation. By the use of the WKB theory we show that mathematically the problem of stability of Riemann ellipsoids with respect to shortwavelength perturbations can be reduced to the problem of magnetoelliptic instability in rotating systems, studied previously by Mizerski and Bajer [K.A. Mizerski, K. Bajer, The magnetoelliptic instability of rotating systems, J. Fluid Mech. 632 (2009) 401–430]. In other words the equations describing the evolution of shortwavelength perturbations of the Riemann ellipsoids considered in Lagrangian variables are the same as those for the evolution of the magnetoellipticrotational (MER) waves in unbounded domain. This allowed us to use the most unstable MER eigenmodes found in Mizerski et al. [K.A. Mizerski, K. Bajer, H.K. Moffatt, The effect associated with elliptical instability, J. Fluid Mech., 2010 (in preparation)] to provide an estimate of the characteristic tidal synchronization time in binary star systems. We use the idea of Tassoul [J.L. Tassoul, On synchronization in earlytype binaries, Astrophys. J. 322 (1987) 856–861] and that the interactions between perturbations significantly increase the effective viscosity and hence the energy dissipation in an Ekmantype boundary layer at the surface of the star. The results obtained suggest that if the magnetic field generated by (say) the secondary component of a binary system is strong enough to affect the flow dynamics in the primary, nonmagnetized component, the characteristic tidal synchronization time can be significantly reduced.