Asymptotic estimates for two-dimensional sloshing modes

Estimates for the natural frequencies of linear two-dimensional sloshing mo des in channels composed of two planar walls, either opening or closing at the bottom, are derived using conformal transformation techniques. The resu lts are asymptotic in the sense that the wavelength of surface waves are as sumed small in comparison to the horizontal extent of the quiescent free su rface. An experiment was constructed to test the asymptotic theory for odd sloshing modes in two symmetric and three asymmetric containers. Good corro boration between measurement and theory is obtained when the increase in fr equency due to surface tension, not accounted for in the theoretical analys is, is estimated and removed from the experimental data. (C) 2000 American Institute of Physics. [S1070-6631(00)00904-1].