Analysis Of Non-Stationary Evolution Of The Gardner-Eguation Solitons Of Intense Internal Wave.
Gorshkov, Konstantin1; Ermoshkin, Alexey2; Dubina, Vyacheslav3; Troitskaya, Yuliya1; Rybushkina, Galina1; Zaitseva, Nataliya1; Soustova, Irina4
1Institute of Applied Physics, RUSSIAN FEDERATION; 2Institute of Applied Physics, RUSSIAN FEDERATION; 3Pacific Oceanological Institute, RUSSIAN FEDERATION; 4RUSIAN ACADEMY OF SCIENCES INSTITUTE OF APPLIED PHYSICS, RUSSIAN FEDERATION
Analysis data recorded by MODIS radiometer (MODerate resolution Imaging Spectro-radiometer) of the Terra and Aqua satellites and synthetic aperture radar ASAR of the Envisat leads to the conclusion that in the area of interest internal waves are primarily nonlinear. Consequently, the Gardner equation is chosen for analysis of their dynamics taking into consideration variations of the shelf zone depth. The dynamics of intense IW in the shelf zone will be calculated using a modified approximate approach developed by the authors¡¦ research team earlier. The approach is based on representing the group of intense IWs near the shelf by a population of table-shaped solitons whose amplitude is close to the amplitude of limiting solitons of the Gardner equation (Korteweg-de Vries equation with cubic nonlinearity) with variable parameters. The quasi-stationary soliton evolution in media with slowly varying (compared to the IW scale) parameters has been well studied by now. The quasi-stationary behavior of the wave process allows the solution to be regarded to be close to a stationary solitary wave a soliton with slowly varying parameters, thus, reducing description of solitary wave field transformation to a much simpler problem, namely, to description of the dynamics of a finite number of independent soliton parameters. For soliton parameters comparable with (or exceeding) the scale of medium changes, soliton field transformation becomes nonstationary and more diverse. This concerns, in particular, wide fÁ-shaped solitons with maximum amplitude that arise in the course of IW evolution on the shelf. The keystone in the construction of the proposed approximate solution for description of dynamics of such intense IW solitons is their compound structure. These solitons have a form of a plateau of arbitrary length, bounded by relatively narrow field kinks of different polarity that are, together with the solitons, stationary solutions of Gardner equation with constant parameters. We will consider in our paper the situations when, at variable cubic or square nonlinearity, the quasi-stationary conditions are not fulfilled for a rather extended soliton upon the whole, but are met for kinks forming the front and rear of the evolving quasi-soliton. The obtained approximate solution is compared with the results of the previous direct numerical integration of this problem and experimental dates of different authors? concerning of investigation of intense internal wave in the shelf zone of the East Coastal of the Pacific Ocean.