Asymptotic estimates for two-dimensional sloshing modes

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