Journal cover Journal topic
Ocean Science An interactive open-access journal of the European Geosciences Union
Ocean Sci., 13, 749-763, 2017
https://doi.org/10.5194/os-13-749-2017
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.
Research article
21 Sep 2017
Simulations and observation of nonlinear internal waves on the continental shelf: Korteweg–de Vries and extended Korteweg–de Vries solutions
Kieran O'Driscoll1 and Murray Levine 1Department of Civil Engineering, Queen's University Belfast, Belfast, BT9 1NN, Northern Ireland
deceased
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 number 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 evolve. Comparisons between KdV and eKdV solutions are made. The model results for realistic topography and stratification are compared with observations made at moorings off Massachusetts in the Middle 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 internal waves on the continental shelf: Korteweg–de Vries and extended Korteweg–de Vries solutions, Ocean Sci., 13, 749-763, https://doi.org/10.5194/os-13-749-2017, 2017.
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Short summary
Studies of the propagation and evolution of the internal tide and development of non-linear internal waves as they cross the continental shelf are presented. Model simulations are based on wave theory, and the results are analyzed and compared with observations during the Coastal Mixing and Optics experiment. These waves are important: they transport momentum and energy, provide energy for vertical mixing, carry nutrients onto the continental shelf and resuspend and moving sediment.
Studies of the propagation and evolution of the internal tide and development of non-linear...
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