Nonlinear oscillations in three-armed tubes

We consider nonlinear gravitational oscillations of inviscid liquid in arrangements of three tubes joined at their bases, for which the dynamical system is four-dimensional and conservative. Though the problem of two joined tubes was solved in 1738, that of three tubes appears to have remained unstudied. We consider both weakly-nonlinear theory, which gives rise to coupled amplitude evolution equations; and also full numerical solutions. In this way, an understanding is reached of the strengths and limitations of the weakly-nonlinear approximation. Both the weakly-nonlinear approximation and the full system display amplitude modulations on a slow timescale; but only the full system captures a narrow region of chaos. (C) 2002 tditions scientifiques et medicales Elsevier SAS. All rights reserved.