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| Titel |
Energetics of tidally generated internal waves for nonuniform stratification |
| VerfasserIn |
Mondheur Zarroug, Jonas Nycander, Kristofer Döös |
| Konferenz |
EGU General Assembly 2010
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 12 (2010) |
| Datensatznummer |
250034282
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| Zusammenfassung |
| In theoretical work on the generation of internal waves from tides, the WKB-approximation
is often used when considering nonuniform stratification. As a result, the rate of energy
conversion to internal waves is proportional to the buoyancy frequency at the bottom, NB.
The WKB-approximation requires that the vertical wave length of the internal waves is
shorter than the characteristic length scale for variations of the buoyancy frequency
N(z). This is true for higher vertical wave modes, but not for the low modes. For
example, the wave length of the lowest mode is of the same order as the entire ocean
depth.
In order to understand the effect of nonuniform stratification on the generation of the
lowest modes, a homogenization technique is here used. This approach is based on the
assumption that the vertical wave length of the internal waves is longer than the characteristic
length scale for variations of N(z), i.e. it is valid in the opposite regime as the
WKB-approximation. N(z) is then replaced by the homogenized profile Nh(z), which is
obtained by averaging N2 over the homogenization scale. The result is that the energy
conversion is proportional to NBh, i.e. to N(z) homogenized approximately over a vertical
wavelength from the bottom. For the lowest mode, N2(z) is thus averaged over the
entire ocean depth. With a realistic stratification, NBh is much larger than NB. The
WKB-approximation therefore severely underestimates the energy conversion for the lowest
modes.
The energy conversion at a simple ridge is calculated for different values of the ridge
width, using a realistic profile of N(z). The results are obtained both numerically (the exact
result), and using the WKB-approximation and the homogenization technique, repectively.
When the WKB-approximation is used (or when the stratification is uniform), the energy
conversion is largest in the limit of zero width, as has been noted previously. However, the
numerical result shows that the conversion in fact has a maximum for an intermediate width,
of the order 10 km. The reason is that a wider ridge projects more strongly onto the
lowest modes, and the conversion into these modes depend on the value of N(z)
higher up in the water column, where it is larger than near the bottom. This effect is
missed entirely by the WKB-approximation. For a still wider ridge, the conversion
again decreases, since it becomes too wide to project strongly onto even the lowest
mode. |
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