Internal-wave reflection from uniform slopes: higher harmonics and Coriolis effects
Weakly nonlinear reflection of internal waves from uniform slopes produces higher harmonics and mean fields; the expressions are here derived for constant stratification and with Coriolis effects fully included, i.e. the horizontal component <IMG WIDTH='14' HEIGHT='38...
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| Format: | Article |
| Language: | English |
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Copernicus Publications
2006-01-01
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| Series: | Nonlinear Processes in Geophysics |
| Online Access: | http://www.nonlin-processes-geophys.net/13/265/2006/npg-13-265-2006.pdf |
| _version_ | 1819113074359009280 |
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| author | T. Gerkema |
| author_facet | T. Gerkema |
| author_sort | T. Gerkema |
| collection | DOAJ |
| description | Weakly nonlinear reflection of internal waves from uniform slopes produces higher harmonics and mean fields; the expressions are here derived for constant stratification and with Coriolis effects fully included, i.e. the horizontal component <IMG WIDTH='14' HEIGHT='38' ALIGN='MIDDLE' BORDER='0' src='http://www.nonlin-processes-geophys.net/13/265/2006/npg-13-265-2006-1.gif' ALT='$ilde{f}$'> of the earth rotation vector (referred to as 'non-traditional'') is taken into account. Uniformity in one of the horizontal directions is assumed. It is shown that solutions can be as readily derived with as without <IMG WIDTH='14' HEIGHT='38' ALIGN='MIDDLE' BORDER='0' src='http://www.nonlin-processes-geophys.net/13/265/2006/npg-13-265-2006-1.gif' ALT='$ilde{f}$'>; hence there is no need to make the so-called Traditional Approximation. Examples of reflecting internal-wave beams are presented for super-inertial, inertial and sub-inertial frequencies. The problem of resonant and non-resonant forcing of the second harmonic is studied for single plane waves; unlike under the Traditional Approximation, the problem of reflection from a horizontal bottom no longer forms a singular case. Non-traditional effects are favourable to resonant forcing at near-tidal rather than near-inertial frequencies, and generally increase the intensity of the second harmonic. Strong stratification tends to suppress non-traditional effects, but a near-total suppression is only attained for high values of stratification that are characteristic of the seasonal thermocline; in most parts of the ocean, non-traditional effects can therefore be expected to be important. |
| first_indexed | 2024-12-22T04:23:37Z |
| format | Article |
| id | doaj.art-66f3ddbd2f8b478abf231b28f78456bf |
| institution | Directory Open Access Journal |
| issn | 1023-5809 1607-7946 |
| language | English |
| last_indexed | 2024-12-22T04:23:37Z |
| publishDate | 2006-01-01 |
| publisher | Copernicus Publications |
| record_format | Article |
| series | Nonlinear Processes in Geophysics |
| spelling | doaj.art-66f3ddbd2f8b478abf231b28f78456bf2022-12-21T18:39:12ZengCopernicus PublicationsNonlinear Processes in Geophysics1023-58091607-79462006-01-01133265273Internal-wave reflection from uniform slopes: higher harmonics and Coriolis effectsT. GerkemaWeakly nonlinear reflection of internal waves from uniform slopes produces higher harmonics and mean fields; the expressions are here derived for constant stratification and with Coriolis effects fully included, i.e. the horizontal component <IMG WIDTH='14' HEIGHT='38' ALIGN='MIDDLE' BORDER='0' src='http://www.nonlin-processes-geophys.net/13/265/2006/npg-13-265-2006-1.gif' ALT='$ilde{f}$'> of the earth rotation vector (referred to as 'non-traditional'') is taken into account. Uniformity in one of the horizontal directions is assumed. It is shown that solutions can be as readily derived with as without <IMG WIDTH='14' HEIGHT='38' ALIGN='MIDDLE' BORDER='0' src='http://www.nonlin-processes-geophys.net/13/265/2006/npg-13-265-2006-1.gif' ALT='$ilde{f}$'>; hence there is no need to make the so-called Traditional Approximation. Examples of reflecting internal-wave beams are presented for super-inertial, inertial and sub-inertial frequencies. The problem of resonant and non-resonant forcing of the second harmonic is studied for single plane waves; unlike under the Traditional Approximation, the problem of reflection from a horizontal bottom no longer forms a singular case. Non-traditional effects are favourable to resonant forcing at near-tidal rather than near-inertial frequencies, and generally increase the intensity of the second harmonic. Strong stratification tends to suppress non-traditional effects, but a near-total suppression is only attained for high values of stratification that are characteristic of the seasonal thermocline; in most parts of the ocean, non-traditional effects can therefore be expected to be important.http://www.nonlin-processes-geophys.net/13/265/2006/npg-13-265-2006.pdf |
| spellingShingle | T. Gerkema Internal-wave reflection from uniform slopes: higher harmonics and Coriolis effects Nonlinear Processes in Geophysics |
| title | Internal-wave reflection from uniform slopes: higher harmonics and Coriolis effects |
| title_full | Internal-wave reflection from uniform slopes: higher harmonics and Coriolis effects |
| title_fullStr | Internal-wave reflection from uniform slopes: higher harmonics and Coriolis effects |
| title_full_unstemmed | Internal-wave reflection from uniform slopes: higher harmonics and Coriolis effects |
| title_short | Internal-wave reflection from uniform slopes: higher harmonics and Coriolis effects |
| title_sort | internal wave reflection from uniform slopes higher harmonics and coriolis effects |
| url | http://www.nonlin-processes-geophys.net/13/265/2006/npg-13-265-2006.pdf |
| work_keys_str_mv | AT tgerkema internalwavereflectionfromuniformslopeshigherharmonicsandcorioliseffects |