Observations of highly nonlinear internal solitons over the continental shelf

Abstract

Abstract. Surface disturbances caused by strong, near-surface internal waves are widely seen in coastal regions as bands of slick and rough water propagating shoreward. These surface slicks are typically manifestations of optical and radar backscatter properties above internal solitons, and have strong surface current pulses associated with them. During a recent experiment studying coastal internal waves, extremely strong solitary internal wave packets were observed over a three week period on a very shallow and strongly stratified pycnocline off Northern Oregon. During periods of strongest tidal forcing, solitons were consistently observed on the leading edge of a semidiurnal internal tide bore, with pycnocline displacements up to 25m downward from a 7m initial depth in the first few solitons. The extreme nonlinearity of these internal waves is believed to be unique in ocean observations. This note characterizes these highly nonlinear Solitary Internal Waves (SIW) and presents a second order KdV model which reproduces the form of the displacements, and the small change in soliton width with amplitude predicted by this model.

Beyond the KdV: Post-explosion development

“…8), which shows a long sequence of tide-generated solitary impulses. 66 As seen from Fig. 8, the depression of the sharp pycnocline (often approximated by a density jump in theory) reaches a depth 5-6 times its initial position (from 5 to 30 m in Fig.…”

“…66, the Gardner equation was used beyond its formal range of applicability as a fit for the shape of an individual soliton. In Ref.…”

Instability in internal solitary waves with trapped cores

“…[1][2][3][4] In the open ocean, typically, the waves are highly nonlinear and may attain very large amplitudes. [5][6][7] It is well known that at such large amplitudes, ISWs of depression (elevation) may exhibit trapped cores if the density gradient at the surface (bottom) of the water column is finite (and waves are supported in which the local horizontal fluid velocity exceeds the wave speed). As well as in the ocean, 8,9 waves of this type have been observed in the atmosphere, 10-12 the laboratory, 13,14 and in theoretical studies.…”

Models for strongly-nonlinear evolution of long internal waves in a two-layer stratification

“…The wide-spread appearance of packets of long internal waves in the shallow, stratified waters of the coastal ocean and lakes is firmly established (Osborne and Burch, 1980;Apel et al, 1985;Scotti and Pineda, 2004;Ostrovsky and Stepanyants, 1989;Stanton and Ostrovsky, 1998;Antenucci et al, 2000;Duda et al, 2004;Helfrich and Melville, 2006). These long-wave packets in many contexts are decidedly nonlinear, containing waves with amplitudes that are equal to and greater in magnitude than the controlling length scale of the problem, which is typically the scale of the uppermixed layer depth.…”

“…That is, although α 1 tends to zero with , what are the sign and magnitude of α 3 , etc., for small values of | |. The issue is readily addressed through use of a recent result by Slunyaev et al (2003) where, based on earlier work by Ostrovsky and Grue (2003), an analytic expression for the fully-nonlinear, longwave propagation speed for a wave moving in one direction was derived (see Eq. 45 in Ostrovsky and Stepanyants, 2005):…”