  In this paper, we present an experimental study of weakly non-linear
interaction of axisymmetric internal gravity waves in a resonant cavity,
supported by theoretical considerations. Contrary to plane waves in Cartesian
coordinates, for which self-interacting terms are null in a linear
stratifiation, the non-linear self-interaction of an internal wave mode in
axisymmetric geometry is found to be efficient at producing super-harmonics,
i.e. waves whose frequencies are integer multiples of the excitation frequency.
Due to the range of frequencies tested in our experiments, the first harmonic
frequency is below the cut-off imposed by the stratification so the lowest
harmonic created can always propagate. The study shows that the super-harmonic
wave field is a sum of standing waves satisfying both the dispersion relation
for internal waves and the boundary conditions imposed by the cavity walls,
while conserving the axisymmetry.

Fluid Dynamics;Geophysics