  Here we show that there exist internal gravity waves that are inherently
unstable, that is, they cannot exist in nature for a long time. The instability
mechanism is a one-way (irreversible) harmonic-generation resonance that
permanently transfers the energy of an internal wave to its higher harmonics.
We show that, in fact, there are countably infinite number of such unstable
waves. For the harmonic-generation resonance to take place, nonlinear terms in
the free surface boundary condition play a pivotal role, and the instability
does not obtain for a linearly-stratified fluid if a simplified boundary
condition such as rigid lid or linear form is employed. Harmonic-generation
resonance presented here also provides a mechanism for the transfer of the
energy of the internal waves to the higher-frequency part of the spectrum where
internal waves are more prone to breaking, hence losing energy to turbulence
and heat and contributing to oceanic mixing.
