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In this paper we investigate the linear stability of an initially symmetric two-dimensional thin ridge of Newtonian fluid of finite width on a horizontal planar substrate acting under the influence of a symmetric two-dimensional jet of air normal to the substrate. Ridges both with and without a dry patch at their center are considered. For both problems we examine both the special case of quasistatic motion (corresponding to zero capillary number) analytically and the general case of nonzero capillary number numerically. In all cases the ridge is found to be unconditionally unstable, but the nature and location of the most unstable mode are found to depend on the details of the specific problem considered

The linear stability of a ridge of fluid subject to a jet of air