Articles | Volume 18, issue 1
Research article
14 Feb 2011
Research article |  | 14 Feb 2011

Strongly nonlinear, simple internal waves in continuously-stratified, shallow fluids

L. A. Ostrovsky and K. R. Helfrich

Abstract. Strongly nonlinear internal waves in a layer with arbitrary stratification are considered in the hydrostatic approximation. It is shown that "simple waves" having a variable vertical structure can emerge from a wide class of initial conditions. The equations describing such waves have been obtained using the isopycnal coordinate as a variable. Emergence of simple waves from an initial Gaussian impulse is numerically investigated for different density profiles, from two- and three-layer structure to the continuous one. Besides the first mode, examples of second- and third-mode simple waves are given.