Growth and dissipation of typhoon-forced solitary continental shelf waves in the northern South China Sea

This study aims to gain insight into the sea level response to typhoon in the northern South China Sea using typhoon records from 1978 to 1997, simultaneous tidal gauge records and satellite altimeter along-track sea level data. We find that the ocean sea level response signatures in the deep water agree well with a single sea level soliton, of which the average soliton amplitude is (34 +/- 6) cm and the average characteristic half width is (115 +/- 12) km. Evolution of the single soliton as propagating across a shoaling bottom topography obeys solutions of the perturbed Korteweg and de Vries equation. The solutions reveal that forced by the hyperbolic-tangent-shaped topography, the single soliton evolves to a solitary wave packet consisting of a large leading soliton and smaller following waves in an oscillatory tail as approaching the shallow water. This phenomenon is verified by observed sea level signatures of 19 storm surges. The correlation coefficient between theoretical solution and observations is as high as 0.91. Meanwhile, the soliton amplitude grows with a soliton amplitude growth ratio (SAGR), which depends on the deep water and shallow water depths. However, without consideration of viscous effects, the SAGR model overestimates the soliton amplitude growth. Thus the vorticity equation for viscous fluid is adopted to solve this issue. The results indicate that turbulent viscosities are responsible to soliton amplitude decay concurring with the growth and causes dependence of the storm surge amplitude on the typhoon incident angle.