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Oblique spatial dispersive shock waves in nonlinear Schrodinger flows
In dispersive media, hydrodynamic singularities are resolved by coherent wavetrains known as dispersive shock waves (DSWs). Only dynamically expanding, temporal DSWs are possible in one-dimensional media. The additional degree of freedom inherent in two-dimensional media allows for the generation of...
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| Format: | Default Article |
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2017
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| Online Access: | https://hdl.handle.net/2134/24663 |
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| _version_ | 1805990998177742848 |
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| author | M.A. Hoefer Gennady El A.M. Kamchatnov |
| author_facet | M.A. Hoefer Gennady El A.M. Kamchatnov |
| author_sort | M.A. Hoefer (7160972) |
| collection | Figshare |
| description | In dispersive media, hydrodynamic singularities are resolved by coherent wavetrains known as dispersive shock waves (DSWs). Only dynamically expanding, temporal DSWs are possible in one-dimensional media. The additional degree of freedom inherent in two-dimensional media allows for the generation of time-independent DSWs that exhibit spatial expansion. Spatial oblique DSWs, dispersive analogs of oblique shocks in classical media, are constructed utilizing Whitham modulation theory for a class of nonlinear Schrodinger boundary value problems. Self-similar, simple wave solutions of the modulation equations yield relations between the DSW’s orientation and the upstream/downstream flow fields. Time dependent numerical simulations demonstrate a convective or absolute instability of oblique DSWs in supersonic flow over obstacles. The convective instability results in an effective stabilization of the DSW. |
| format | Default Article |
| id | rr-article-9389204 |
| institution | Loughborough University |
| publishDate | 2017 |
| record_format | Figshare |
| spelling | rr-article-93892042017-01-01T00:00:00Z Oblique spatial dispersive shock waves in nonlinear Schrodinger flows M.A. Hoefer (7160972) Gennady El (1258536) A.M. Kamchatnov (7160297) Other mathematical sciences not elsewhere classified untagged Mathematical Sciences not elsewhere classified In dispersive media, hydrodynamic singularities are resolved by coherent wavetrains known as dispersive shock waves (DSWs). Only dynamically expanding, temporal DSWs are possible in one-dimensional media. The additional degree of freedom inherent in two-dimensional media allows for the generation of time-independent DSWs that exhibit spatial expansion. Spatial oblique DSWs, dispersive analogs of oblique shocks in classical media, are constructed utilizing Whitham modulation theory for a class of nonlinear Schrodinger boundary value problems. Self-similar, simple wave solutions of the modulation equations yield relations between the DSW’s orientation and the upstream/downstream flow fields. Time dependent numerical simulations demonstrate a convective or absolute instability of oblique DSWs in supersonic flow over obstacles. The convective instability results in an effective stabilization of the DSW. 2017-01-01T00:00:00Z Text Journal contribution 2134/24663 https://figshare.com/articles/journal_contribution/Oblique_spatial_dispersive_shock_waves_in_nonlinear_Schrodinger_flows/9389204 CC BY-NC-ND 4.0 |
| spellingShingle | Other mathematical sciences not elsewhere classified untagged Mathematical Sciences not elsewhere classified M.A. Hoefer Gennady El A.M. Kamchatnov Oblique spatial dispersive shock waves in nonlinear Schrodinger flows |
| title | Oblique spatial dispersive shock waves in nonlinear Schrodinger flows |
| title_full | Oblique spatial dispersive shock waves in nonlinear Schrodinger flows |
| title_fullStr | Oblique spatial dispersive shock waves in nonlinear Schrodinger flows |
| title_full_unstemmed | Oblique spatial dispersive shock waves in nonlinear Schrodinger flows |
| title_short | Oblique spatial dispersive shock waves in nonlinear Schrodinger flows |
| title_sort | oblique spatial dispersive shock waves in nonlinear schrodinger flows |
| topic | Other mathematical sciences not elsewhere classified untagged Mathematical Sciences not elsewhere classified |
| url | https://hdl.handle.net/2134/24663 |