Rayleigh-Taylor instability with spatially varying acceleration - An illustration

Physics

Scientific paper

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Acceleration (Physics), Accretion Disks, Gravitational Fields, Taylor Instability, Atmospheres, Eddy Viscosity, Eigenvalues

Scientific paper

Consideration is given to a simple but realistic model for density and acceleration profiles that is simply soluble and comparable to the classic exponential atmosphere instability problem solved by Lord Rayleigh. The model problem is thought to be of interest both in astrophysical contexts (for example, an extended accretion disk) and in magnetically accelerated configurations in which the field may diffuse into the material being accelerated. Both bounded and unbounded atmospheres are treated. A determination is made of the growth rates and eigenmodes for Rayleigh-Taylor instability in the case of density and gravitational acceleration varying in the vertical direction with differing constant scale heights for each. It is found that allowing the gravitational acceleration to vary in a layer subject to Rayleigh-Taylor instability has the expected qualitative effects on growth rate and shifts the eigenvalue maximum toward larger values of g. In a quantitative sense, however, the change in g growth rate is larger than might be expected.

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