7. Conclusion and Outlook
A new analysis of dierent methods to determine the wave slope distribution from the series of light speckle images is made. It shows that a simple position detection of the light speckles is not sucient, though the light speckle properties 'area' and 'intensity' have to be taken into account. The overall uncertainty of the total mean square slope values can be estimated to be less than 10 % from an intercomparison of the dierent analysis methods.
The height measurement is calibrated to an ultrasonic distance sensor and yields an error of less than 2 mm for a at water surface. However, for a rough water surface, the measured water height is biased, so unrealistic height values appear. Lens eects due to the high curvature at the surface and fast changes of the wave slope can be an explanation for a dierent light speckle shape in corresponding IR and RED images and an additional variation of the light intensity in the images. This error cannot be corrected for, so the small wave amplitudes in the ume represent a relatively small signal compared to the noise due to the lens eects and fast slope changes. For a better understanding of the lens eects an exact ray tracing model at the water surface would be necessary. Changes of the slope between two images could be avoided with an even shorter time period between the two LED pulses. Limiting the t range to realistic values, the root mean square wave height can still be estimated from the height probability distribution with a Gaussian t.
A characterization of the wave eld in the new linear wave ume is accomplished. Waves start to develop abruptly at a wind speed of 3.5m/s or a water side friction velocity of 0.7cm/s. A measurement at a wind speed of 5.0m/s shows that the wave eld develops within the rst 1.40 m of the fetch and remains constant from there to the beach concerning the parameters mean square wave slope and rms wave height. At the maximum wind speed of 6.7m/s and a fetch of 2.38 m the mean square slope is 0.059 and the rms wave height is 6 mm.
In addition to the usual use of the wave gauge at the linear wave ume, the wave gauge will be tested at the large circular ume, where the dominant wave height is higher by a factor of up to 100. Therefore the height measurement has a better signal to noise ratio and is expected to yield correct wave height values of the dominant gravity waves.
The height values are needed in the large ume to correct the height dependent slope measurement. A correlation analysis of the height of the large scale waves and the slope can provide information about the long wave - short wave interaction.
A Reective Slope Gauge (RSG) is planned to accompany heat transfer measurements in the eld in 2009-2010. The detailed analysis of the single light speckle images shown in this study allows for a determination of the speckle properties. The ndings can improve a quantitative evaluation of the RSG measurements.
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Erklärung:
Ich versichere, dass ich diese Arbeit selbständig verfasst und keine anderen als die angegebenen Quellen und Hilfsmittel benutzt habe.
Heidelberg, 03.09.2008
Danksagung
Besonders bedanken möchte ich mich bei Prof. Dr. Bernd Jähne, der diese Arbeit betreut und sie erst möglich gemacht hat. Ein groÿer Dank geht auch an Prof. Dr.
Platt für die Übernahme der Zweitkorrektur.
Auÿerdem möchte ich noch meinen Dank aussprechen
Roland Rocholz, der mir seine Zeit geopfert hat für ausführliche Diskussionen und wertvolle Tipps,
der ganzen Arbeitsgruppe "Gasaustausch und Wellen" am Institut für Umweltphysik in Heidelberg für ihre tolle Unterstützung meiner Arbeit, der Beantwortung der vielen Fragen und die allzeit nette Stimmung im Windkanal Labor,
der Institutswerkstatt im IUP und Herrn Spiegel in der Diplomandenwerkstatt für die freundliche Beratung in technischen Fragen,
und nicht zuletzt meiner Freundin und meinen Eltern dafür, dass sie immer da sind.
Appendices
A. Calculations
A.1. Water height amplitude from IR and RED speckle intensities
The slant absorption lengthlin water is
l = − 1
(αIR−αRED) ln IIR
IRED
+C (A.1)
l = b+C (A.2)
with measured IR intensity IIR and RED intensity IRED of the same speckle. C is a constant length.
The correction from the slant absorption lengthl to the vertical water heightη is
η =l cosθ2 (A.3)
withθ2 as dened in Fig. 3.1.
landcosθ2are not totally uncorrelated, but the error is small, hlcosθ2i−hlihcoshηi θ2i = 0.1%, so
d2 = hηi=hlcosθ2i ≈ hlihcosθ2i (A.4) hli ≈ hηi
hcosθ2i = d2
hcosθ2i (A.5)
with the mean water heighthηi=d2. Hence,
l− hli = b− hbi+C− hCi (A.6)
l = b− hbi+hli (A.7)
l = b− hbi+ d2
hcosθ2i (A.8)
So with Eq. A.3 and Eq. A.8 the water surface amplitudehbecomes
h = η− hηi (A.9)
= l cosθ2−d2 (A.10)
=
b− hbi+ d2
hcosθ2i
cosθ2−d2 (A.11)