Nonlinear internal tidal waves in a semi-enclosed sea (Gulf of California)

Abstract

This paper studies the nonlinear transformation of the semidiurnal internal tidal waves in the northern Gulf of California, based on spectral analysis of temperature and current fluctuations from moored instruments, and analytical simulation. Observations showed that: (a) The spectrum presented a quasilinear structure with peaks at frequencies w n = n w 0, where w 0 is the frequency of the tidal harmonic M 2 and n = 1, 2.. is the subharmonics number. (b) The amplitudes of the even subharmonics M 4 and M 8 were of the same order, as were those of the odd subharmonics M 6 and M 10, but the last two were larger. (c) The energy of the subharmonics decreased as w -3 with increasing n. These features were simulated by an analytical model spectrum of nonlinear internal waves; it produced a line structure formed by the harmonics whose energy depends on the distance traveled by the wave from the area of generation. In the approximation of quadratic nonlinearity, the spectrum of nonlinear long internal waves in the zone of wave breaking is asymptotically ∼w n -2,6. Allowance for cubic nonlinearity leads to a non-monotonic decay of subharmonics energy depending on their number n, similar to the observed spectrum, which indicates that the internal semidiurnal tide in the northern Gulf of California is a cubically nonlinear wave. Copyright 2011 by the American Geophysical Union.