Triad resonance between a surface-gravity wave and two high frequency hydro-acoustic waves

A new class of resonant triad in the family of gravity–acoustic waves has been found. I show that a hydro-acoustic wave interacting with a surface-gravity wave may generate a second hydro-acoustic wave. Interestingly, the two acoustic waves propagate in the same direction with similar wavelengths, that are almost double of that of the gravity wave. The evolution of the wave triad amplitudes is periodic and it is derived analytically, in terms of Jacobian elliptic functions and elliptic integrals. The physical importance of this type of triad interactions is the modulation of pertinent hydro-acoustic signals, leading to inaccurate signal perceptions.