6 research outputs found
Brief communication: Multiscaled solitary waves
It is analytically shown how competing nonlinearities yield multiscaled
structures for internal solitary waves in stratified shallow fluids. These
solitary waves only exist for large amplitudes beyond the limit of
applicability of the Korteweg–de Vries (KdV) equation or its usual
extensions. The multiscaling phenomenon exists or does not exist for almost
identical density profiles. The trapped core inside the wave prevents the
appearance of such multiple scales within the core area. The structural
stability of waves of large amplitudes is briefly discussed. Waves of large
amplitudes displaying quadratic, cubic and higher-order nonlinear terms have
stable and unstable branches. Multiscaled waves without a vortex core are
shown to be structurally unstable. It is anticipated that multiscaling
phenomena will exist for solitary waves in various physical contexts
Brief communication "On one mechanism of low frequency variability of the Antarctic Circumpolar Current"
In this paper we present a simple analytical model for low frequency and large scale variability of the Antarctic Circumpolar Current (ACC). The physical mechanism of the variability is related to temporal and spatial variations of the cyclonic mean flow (ACC) due to circularly propagating nonlinear barotropic Rossby wave trains. It is shown that the Rossby wave train is a fundamental mode, trapped between the major fronts in the ACC. The Rossby waves are predicted to rotate with a particular angular velocity that depends on the magnitude and width of the mean current. The spatial structure of the rotating pattern, including its zonal wave number, is defined by the specific form of the stream function-vorticity relation. The similarity between the simulated patterns and the Antarctic Circumpolar Wave (ACW) is highlighted. The model can predict the observed sequence of warm and cold patches in the ACW as well as its zonal number