Rayleigh–Taylor instability with spatially varying acceleration: An illustration

An illustrative but realistic case of Taylor instability in an atmosphere in which the density increases exponentially with height and the gravitational acceleration varies with height, g(z)=g1+g2 exp(±kgz), is considered. This model problem is of interest both in astrophysical contexts (e.g., an extended accretion disk) and magnetically accelerated configurations in which the field may diffuse into the material being accelerated. Both bounded and unbounded atmospheres are considered. For the case g=g0 exp(−kgz), the growth rate is reduced compared to the case with constant g=g1=g0 exp(−kgzm), where zm is the height of the maximum of the velocity eigenfunction, by more than would be expected.