Non-exponential growth in density-stratified thin vertically isothermal discs

Linear instability of an equilibrium configuration with toroidal dominant magnetic field is studied in thin vertically-isothermal Keplerian discs. Solutions of the stability problem are found explicitly by asymptotic expansions in small aspect ratio of the disc. The perturbations are decoupled into in-plane and vertical modes, which are the inertia-Coriolis and magnetosonic waves. It is shown that the axisymmetric MRI is completely suppressed by dominant toroidal magnetic fields. Exhibiting spectral asymptotic stability, thin discs are nonetheless shown to host intensive activity in the shape of non modal growth of initial small perturbations. In pure hydrodynamic case two mechanisms that lead to such behavior are identified and studied, namely, non-resonant excitation of vertically confined sound waves by stable planar inertia-Coriolis modes that results in linear growth with time, as well as resonant coupling of those two modes that leads to a quadratic growth of the initial perturbations. It is further speculated that the non modal growth can give rise to secondary stratorotational instabilities and thus lead to a new route to turbulence generation in thin discs.