Meandering Instability of a Vertical Plume

The meandering instability of a two-dimensional vertical plume is considered in this paper. The base flow profile is derived using boundary layer approximation and similarity hypothesis, in the spirit of Blasius boundary layer solution. Using linear stability analysis, we derive a modified version of the Orr-Sommerfeld equation governing the disturbances. The resulting eigenvalue problem is solved by the Galerkin method. It is found that a vertical plume is unstable to meandering, and in particular, three different wavelengths of meanders exist. A meandering instability of long wavelength ensues at the lowest portion of a vertically rising plume, where $\mathsf{R}<94$ . Beyond $\mathsf{R}=94$ and $\mathsf{R}=192$ , the most unstable wavelength shifts to an intermediate and to a short wavelength meandering during the course of rising motion.