Nonlinear harmonic generation by diurnal tides

•Nonlinear refraction by pycnocline stratification is proposed as a possible explanation for a transient double-frequency harmonic of the diurnal internal tide observed in the South China Sea.•Weakly nonlinear theory shows that harmonics of the observed amplitude can be produced by refraction without the need for wave–wave interactions or topographic effects.•The harmonic amplitude depends strongly on the pycnocline characteristics, which may explain the transient nature of the observed harmonic.

Recent observations from the South China Sea have demonstrated that semi-diurnal tides sometimes generate a double-frequency harmonic. Similar harmonic generation has been found in laboratory experiments and numerical simulations of internal wave beams refracting into a pycnocline. Here, a weakly nonlinear theory of internal wave refraction is applied to oceanic internal tides in an idealized stratification profile. The steady state harmonic amplitude is calculated as a function of the tidal frequency and the pycnocline characteristics. The results indicate that harmonic generation by nonlinear refraction of semi-diurnal tides is consistent with the South China Sea observations.