Parametric interaction and intensification of nonlinear Kelvin waves

Observational evidence is presented for nonlinear interaction between mesoscale internal Kelvin waves at the tidal -- $\omega_t$ or the inertial -- $\omega_i$ frequency and oscillations of synoptic -- $\Omega$ frequency of the background coastal current of Japan/East Sea. Enhanced coastal currents at the sum -- $\omega_+$ and dif -- $\omega_-$ frequencies: $\omega_\pm =\omega_{t,i}\pm \Omega$ have properties of propagating Kelvin waves suggesting permanent energy exchange from the synoptic band to the mesoscale $\omega_\pm$ band. The interaction may be responsible for the greater than predicted intensification, steepen and break of boundary trapped and equatorially trapped Kelvin waves, which can affect El Ni\~{n}o. The problem on the parametric interaction of the nonlinear Kelvin wave at the frequency $\omega$ and the low-frequency narrow-band nose with representative frequency $\Omega\ll\omega$ is investigated with the theory of nonlinear week dispersion waves.