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Linear stability of a cylindrical falling film

The problem of a cylindrical falling film, descending vertically outside an infinitely long cylinder is considered. The linear stability of the fully developed flow is studied, first with a perturbation technique for small wavenumbers, and then by direct numerical computation. The numerical results are in agreement with other published values for the cylindrical jet and flat plate limits. The study shows that the cylindrical falling film is unstable for all Reynolds numbers, Weber numbers and radius ratios. Stability and amplification curves are calculated for different values of the parameters. With increasing curvature of the film the range of unstable wavenumbers and the wavenumber of the most amplified wave increase. For low curvature the wavenumber of the most amplified wave decreases with Reynolds number or Weber number, while for high curvatures it increases.