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.