Linear Rayleigh-Taylor instability of rotating viscous fluids
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The Rayleigh-Taylor instability is studied for the viscous and non-viscous case of two fluids of finite thickness, subjected to rotation around an axis perpendicular to the direction of acceleration. The effect of surface tension is also considered for both cases. In contrast of the non-viscous case where the combined effect of finite thickness and rotation modify the cut-off wave number due to surface tension, for the viscous case, the cut-off wave number remains unchanged. Likewise, it is verified that the wavelength of the mode of maximum instability reaches a limit value due to the action of surface tension. These computations are performed as a 1D problem assuming the other two directions as periodic, but the results are confirmed in 2D when a rectangular domain is used.