| Summary: | We present an investigation of the resonance conditions governing triad interactions
of cylindrical internal waves, i.e. Kelvin modes, described by Bessel functions. Our
analytical study, supported by experimental measurements, is performed both in confined
and unconfined axisymmetric domains. We are interested in two conceptual questions:
can we find resonance conditions for a triad of Kelvin modes? What is the impact of the
boundary conditions on such resonances? In both the confined and unconfined cases, we
show that sub-harmonics can be spontaneously generated from a primary wave field if they
satisfy at least a resonance condition on their frequencies of the form ω0 = ±ω1 ± ω2. We
demonstrate that the resulting triad is also spatially resonant, but that the resonance in the
radial direction may not be exact in confined geometries due to the prevalence of boundary
conditions – a key difference compared with Cartesian plane waves.
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