Structure of Large-Amplitude Internal Solitary Waves

Vasiliy Vlasenko Marine Hydrophysical Institute, Sevastopol, Ukraine

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Peter Brandt Institut für Meereskunde, Universität Hamburg, Hamburg, Germany

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Angelo Rubino Institut für Meereskunde, Universität Hamburg, Hamburg, Germany

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Abstract

The horizontal and vertical structure of large-amplitude internal solitary waves propagating in stratified waters on a continental shelf is investigated by analyzing the results of numerical simulations and in situ measurements. Numerical simulations aimed at obtaining stationary, solitary wave solutions of different amplitudes were carried out using a nonstationary model based on the incompressible two-dimensional Euler equations in the frame of the Boussinesq approximation. The numerical solutions, which refer to different density stratifications typical for midlatitude continental shelves, were obtained by letting an initial disturbance evolve according to the numerical model. Several intriguing characteristics of the structure of the simulated large-amplitude internal solitary waves like, for example, wavelength–amplitude and phase speed–amplitude relationship as well as form of the locus of zero horizontal velocity emerge, consistent with those obtained previously using stationary Euler models. The authors’ approach, which tends to exclude unstable oceanic internal solitary waves as they are filtered out during the evolution process, was also employed to perform a detailed comparison between model results and characteristics of large-amplitude internal solitary waves found in high-resolution in situ data acquired north and south of the Strait of Messina, in the Mediterranean Sea. From this comparison the importance of using higher-order theoretical models for a detailed description of large-amplitude internal solitary waves observed in the real ocean emerge. Implications of the results showing the complexity related to a possible inversion of sea surface manifestations of oceanic internal solitary waves into characteristics of the interior ocean dynamics are finally discussed.

* Current affiliation: Institut für Mechanik, Technische Universität Darmstadt, Darmstadt, Germany.

+ Current affiliation: Institut für Meereskunde, Universität Kiel, Kiel, Germany.

# Current affiliation: Dipartimento di Dipartimento di Scienze Ambientali, Università di Venezia, Venice, Italy.

Corresponding author address: Peter Brandt, Institut für Meereskunde, Universität Hamburg, Troplowitzstr. 7, D-22529 Hamburg, Germany.

brandt@ifm.uni-hamburg.de

Abstract

The horizontal and vertical structure of large-amplitude internal solitary waves propagating in stratified waters on a continental shelf is investigated by analyzing the results of numerical simulations and in situ measurements. Numerical simulations aimed at obtaining stationary, solitary wave solutions of different amplitudes were carried out using a nonstationary model based on the incompressible two-dimensional Euler equations in the frame of the Boussinesq approximation. The numerical solutions, which refer to different density stratifications typical for midlatitude continental shelves, were obtained by letting an initial disturbance evolve according to the numerical model. Several intriguing characteristics of the structure of the simulated large-amplitude internal solitary waves like, for example, wavelength–amplitude and phase speed–amplitude relationship as well as form of the locus of zero horizontal velocity emerge, consistent with those obtained previously using stationary Euler models. The authors’ approach, which tends to exclude unstable oceanic internal solitary waves as they are filtered out during the evolution process, was also employed to perform a detailed comparison between model results and characteristics of large-amplitude internal solitary waves found in high-resolution in situ data acquired north and south of the Strait of Messina, in the Mediterranean Sea. From this comparison the importance of using higher-order theoretical models for a detailed description of large-amplitude internal solitary waves observed in the real ocean emerge. Implications of the results showing the complexity related to a possible inversion of sea surface manifestations of oceanic internal solitary waves into characteristics of the interior ocean dynamics are finally discussed.

* Current affiliation: Institut für Mechanik, Technische Universität Darmstadt, Darmstadt, Germany.

+ Current affiliation: Institut für Meereskunde, Universität Kiel, Kiel, Germany.

# Current affiliation: Dipartimento di Dipartimento di Scienze Ambientali, Università di Venezia, Venice, Italy.

Corresponding author address: Peter Brandt, Institut für Meereskunde, Universität Hamburg, Troplowitzstr. 7, D-22529 Hamburg, Germany.

brandt@ifm.uni-hamburg.de

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