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Ocean Science An interactive open-access journal of the European Geosciences Union

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doi:10.5194/os-2016-97
© Author(s) 2017. This work is distributed
under the Creative Commons Attribution 3.0 License.
Research article
18 Jan 2017
Review status
A revision of this discussion paper is under review for the journal Ocean Science (OS).
Simulations and observation of nonlinear waves on the continental shelf: KdV solutions
Kieran O'Driscoll and Murray Levine Department of Civil Engineering, Queen’s University Belfast, Belfast, BT9 1NN, Northern Ireland
Abstract. Numerical solutions of the Korteweg-de Vries (KdV) and extended Korteweg-de Vries (eKdV) equations are used to model the transformation of a sinusoidal internal tide as it propagates across the continental shelf. The ocean is idealized as being a two-layer fluid, justified by the fact that most of the oceanic internal wave signal is contained in the gravest mode. The model accounts for nonlinear and dispersive effects but neglects friction, rotation, and mean shear. The KdV model is run for a variety of idealized stratifications and unique realistic topographies to study the role of the nonlinear and dispersive effects. In all model solutions the internal tide steepens forming a sharp front from which a packet of nonlinear solitary-like waves evolves. Comparisons between KdV and eKdV solutions is explored. The model results for realistic topography and stratification are compared with observations made at moorings off Massachusetts in the Mid Atlantic Bight. Some features of the observations compare well with the model. The leading face of the internal tide steepens to form a shock like front, while nonlinear high frequency waves evolve shortly after the appearance of the jump. Although not rank ordered, the wave of maximum amplitude is always close to the jump. Some features of the observations are not found in the model. Nonlinear waves can be very widely spaced and persist over a tidal period.

Citation: O'Driscoll, K. and Levine, M.: Simulations and observation of nonlinear waves on the continental shelf: KdV solutions, Ocean Sci. Discuss., doi:10.5194/os-2016-97, in review, 2017.
Kieran O'Driscoll and Murray Levine
Kieran O'Driscoll and Murray Levine
Kieran O'Driscoll and Murray Levine

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Short summary
Studies of the propagation and evolution of non-linear internal waves as they cross the continental shelf are presented and discussed. The model simulations are based on wave theory, and the results are analysed and compared with observations. These waves are important because they transport momentum and energy through the ocean, they provide energy for vertical mixing, so that they carry nutrients onto the continental shelf. Important for sediment transport and for underwater operations.
Studies of the propagation and evolution of non-linear internal waves as they cross the...
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