Analytical studies of sloshing in half-cylindrical tanks

The technically important problem of two-dimensional inviscid standing-wave motion of a fluid in a semi-cylindrical vessel is examined using a variety of the Boussinesq wave equation as well as the directed fluid sheet technique. The associated eigenvalue problems are dealt with by employing perturbative procedures and series expansions. The predictions were compared with the outcome of laboratory tank experiments and also with 'exact' results. The Boussinesq equation perturbative scheme based on an approximate representation of the vessel geometry not only gave the best results, but was also the most straightforward to apply. Furthermore, it yielded practically useful explicit formulae for the frequencies at which sloshing may be initiated. A limitation is, however, that this formalism is only applicable to systems with comparatively small fill ratios.