Parametric interaction and intensification of nonlinear Kelvin waves

arXiv:0807.0479v1 [physics.ao-ph] 3 Jul 2008 GEOPHYSICAL RESEARCH LETTERS, VOL. ???, XXXX, DOI:10.1029/, Parametric interaction and intensification of nonlinear Kelvin waves Vadim Novotryasov and Dmitriy Stepanov V.I.Il’ichev Pacific Oceanological Institute, Vladivostok, Russia Observational evidence is presented for nonlinear inter- action between mesoscale internal Kelvin waves at the tidal – ωt or the inertial – ωi frequency and oscillations of syn- optic – Ωfrequency of the background coastal current of Japan/East Sea. Enhanced coastal currents at the sum – ω+ and dif – ω−frequencies: ω± = ωt,i ± Ωhave proper- ties of propagating Kelvin waves suggesting permanent en- ergy exchange from the synoptic band to the mesoscale ω± band. The interaction may be responsible for the greater than predicted intensification, steepen and break of bound- ary trapped and equatorially trapped Kelvin waves, which can affect El Ni˜no. The problem on the parametric inter- action of the nonlinear Kelvin wave at the frequency ω and the low-frequency narrow-band nose with representative fre- quency Ω≪ω is investigated with the theory of nonlinear week dispersion waves. 1. Introduction Internal Kelvin waves play a significant role in the dy- namics of the oceans. There are two basic types of the waves: equatorially trapped and boundary trapped. Kelvin waves propagating on the equatorial thermocline participate in the adjustment of the tropical ocean to wind stress forc- ing [Philander,1990]. Extensive data on Kelvin waves have been obtained recently, motivated in part by possible con- nection between the initial stages of El Ni˜no and equatorial nonlinear Kelvin waves which may precede this event. Any relaxation or reversal of the steady trade winds (the east- erlies) results in the excitation of a Kelvin wave, which can affect El Ni˜no. In other words Kelvin waves play a critical role in generating and sustaining of the Southern Oscillation [e.g.,Fedorov, 2000]. In the dynamics of the coastal oceans Kelvin waves are used to interpret such phenomena as the instability of along- shore currents, the generation and variability of wind cur- rents on the shelf, and upwelling [Brink, 1991]. Fedorov and Melville [1995, 1996] considered Kelvin waves trapped boundaries and showed that waves could manifest nonlinear properties that is steepen and overturn or break. A wave of depression deepens the thermocline and breaks on the for- ward face of the wave. A broken wave of depression can form a jump [also called shocks or fronts: Lighthill, 1978; Philan- der, 1990]. In turn, the breaking of Kelvin waves may be im- portant in mixing, momentum and energy transfer in coastal oceans. Other example of nonlinear Kelvin wave dynamics includes the problem of nonlinear geostrophic adjustment in the presence of a boundary [Helfrich et al., 1999; Reznik and Grimshaw, 2002]. Copyright 2018 by the American Geophysical Union. 0094-8276/18/$5.00 The spectrum represents one of the major characteristics of the waves. It is used as a representative statistical descrip- tion of the wave field in studies of nonlinear interaction [e.g., Hibiya et al., 1998], acoustic propagation [e.g., Colosi et al., 1998], and mixing parametrization [Polzin, 1995]. Filonov and Novotryasov [2005, 2007] studded the wave band of temperature fluctuation spectra in the coastal zone of Pa- cific Ocean and observed that in the high-frequency band of temperature spectra the spectral exponent tends to ∼ω−1 at the time of spring tide and on the western shelf of the Japan/East Sea, in the ωi ≪ω ≪N∗range, where N∗is the representative buoyancy frequency and ωi is the iner- tial frequency, the spectral exponent tends to ∼ω−3. These features Filonov and Novotryasov [2007] simulated by the model spectrum of nonlinear internal waves in the shallow water. They considered interaction of high-frequency waves with the wave at the tidal frequency and shown that the spectrum of high-frequency internal waves take the univer- sal form and the spectral exponent tends to ∼ω−1. In this paper, we present observational evidence for non- linear interaction between synoptic oscillations of the back- ground current at the representative frequency Ωand non- linear Kelvin waves at the tidal – ωt or the inertial – ωi frequencies. Findings are based on a well defined spec- tral peaks at the sum – ω+ and dif – ω−frequencies of inertial, semidiurnal and synoptic motions measured by current meters and temperature records collected in the coastal Japan/East Sea. We made rotary spectral analyses of these records and found that the clockwise rotary spec- trum for coastal currents measured at 35–m depth in the 1999 year has well-defined spectral peaks at the frequen- cies ωt ∼1/12.4(cph), Ω1,2 ∼1/64, 1/102(cph), as well as sym and difference frequencies ω± = ωs ± Ω1,2 and their overtones ωn = nω±(n = 1, 2, 3). Analyses of coastal tem- perature records collected in the 2004 year showed that the spectrum of temperature variations

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