Approximate solution for Euler equations of stratified water via numerical solution of coupled KdV system
We consider Euler equations with stratified background state that is valid for internal water waves. The solution of the initial-boundary problem for Boussinesq approximation in the waveguide mode is presented in terms of the stream function. The orthogonal eigenfunctions describe a vertical shape o...
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| Format: | Article |
| Language: | English |
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Wiley
2003-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171203212242 |
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| author | A. A. Halim S. P. Kshevetskii S. B. Leble |
| author_facet | A. A. Halim S. P. Kshevetskii S. B. Leble |
| author_sort | A. A. Halim |
| collection | DOAJ |
| description | We consider Euler equations with stratified background state that
is valid for internal water waves. The solution of the
initial-boundary problem for Boussinesq approximation in the
waveguide mode is presented in terms of the stream function. The
orthogonal eigenfunctions describe a vertical shape of the
internal wave modes and satisfy a Sturm-Liouville problem. The
horizontal profile is defined by a coupled KdV system which is
numerically solved via a finite-difference scheme for which we
prove the convergence and stability. Together with the solution
of the Sturm-Liouville problem, the stream functions give the
internal waves profile. |
| format | Article |
| id | doaj-art-1a8407876b4d4d68900d874a7d2c430a |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2003-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-1a8407876b4d4d68900d874a7d2c430a2025-02-03T01:23:08ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252003-01-012003633979399310.1155/S0161171203212242Approximate solution for Euler equations of stratified water via numerical solution of coupled KdV systemA. A. Halim0S. P. Kshevetskii1S. B. Leble2Theoretical and Mathematical Physics Department, Gdansk University of Technology, Gdansk 80-952, PolandTheoretical Physics Department, Kaliningrad State University, Kaliningrad 236041, RussiaTheoretical and Mathematical Physics Department, Gdansk University of Technology, Gdansk 80-952, PolandWe consider Euler equations with stratified background state that is valid for internal water waves. The solution of the initial-boundary problem for Boussinesq approximation in the waveguide mode is presented in terms of the stream function. The orthogonal eigenfunctions describe a vertical shape of the internal wave modes and satisfy a Sturm-Liouville problem. The horizontal profile is defined by a coupled KdV system which is numerically solved via a finite-difference scheme for which we prove the convergence and stability. Together with the solution of the Sturm-Liouville problem, the stream functions give the internal waves profile.http://dx.doi.org/10.1155/S0161171203212242 |
| spellingShingle | A. A. Halim S. P. Kshevetskii S. B. Leble Approximate solution for Euler equations of stratified water via numerical solution of coupled KdV system International Journal of Mathematics and Mathematical Sciences |
| title | Approximate solution for Euler equations of
stratified water via numerical solution of coupled KdV system |
| title_full | Approximate solution for Euler equations of
stratified water via numerical solution of coupled KdV system |
| title_fullStr | Approximate solution for Euler equations of
stratified water via numerical solution of coupled KdV system |
| title_full_unstemmed | Approximate solution for Euler equations of
stratified water via numerical solution of coupled KdV system |
| title_short | Approximate solution for Euler equations of
stratified water via numerical solution of coupled KdV system |
| title_sort | approximate solution for euler equations of stratified water via numerical solution of coupled kdv system |
| url | http://dx.doi.org/10.1155/S0161171203212242 |
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