One-dimensional models have been used extensively over the past decade
to study liquid columns. While the range of validity of these models
is well known in the linear limit, this is not the case when nonlinear
effects are important. By comparing results of a number of one-dimens
ional models with results based on a velocity-potential model in which
no approximations have been made, the present aim is to establish exa
ctly when the one-dimensional models are applicable. First of all it i
s shown how the Cosserat equations in the inviscid limit may be obtain
ed formally from the Euler equations. Subsequently, a linearized form
of the Cosserat equations is derived and results of this model are com
pared with results obtained by means of the well-established inviscid-
slice model and results obtained by the velocity-potential approach. I
t is found that the applicability of the inviscid-slice model is limit
ed by short-wavelength effects rather than amplitude effects. The rang
e of validity of the inviscid-slice model can be extended by including
radial momentum contributions. However, even with the inclusion of ra
dial momentum effects the one-dimensional models are not well suited t
o describe the behavior close to the bifurcation point.