The Effects of Surfactants on Small-scale Waves 9.4
Chapter 9 THE INFLUENCE OF SURFACTANTS ON WATER WAVES AND. . .
(a) Logarithm of the 2D Power SpectrumS(⃗k). The numbers on the axes indicate the wave number vector components kx andky.
-14661 -8858 -3054 2749 8552 14355
14661 8934 3207 -2520 -8247 -13974
kx [px]
ky[px]
8 10 12 14 16 18 20 22
(b) Omnidirectional Power Spectrum S(k)
101 102 103 104
10−10 10−7 10−4
(c) Omnidirectional Saturation Spectrum B(k)
101 102 103 104
10−3 10−2 10−1
Figure 9.10.:Comparison of some different types of spectra. Data of 30/04/2013 (1mg/l Dextran) for a wind speed of8.42m/s.
Compared to the measurements with Triton X-100 as evaluated by Kiefhaber [2014], the wave suppression at low wave numbers (below 100 rad/m) is less promi-nent. Apparently, wave suppression is less effective for the surfactants studied here compared to Triton X-100.
It is noticeable that the red curve (lowest wind speed 1.48 m/s) displays character-istic “bumps” at ak of about 2×102and 5×102for the first three surfactant cases. It is not visible for the last surfactant condition, which is essentially the same as the third one. It is likely to be an artifact from data evaluation without physical origin in the wave field.
For comparison, the spectra at a wind speed of 3.88 m/s and 5.11 m/s are given for all surfactant cases inFigure 9.12(seesection A.5for the other conditions). As
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The Effects of Surfactants on Small-scale Waves 9.4
(a)Data of 30/04/2013, 1mg/L Dextran.
101 102 103 104
10−6 10−5 10−4 10−3 10−2
k [rad/m]
B(k)
(b) Data of 03/05/2013,2mg/L Dextran.
101 102 103 104
10−6 10−5 10−4 10−3 10−2
k [rad/m]
B(k)
(c) Data of 08/05/2013, full mix.
101 102 103 104
10−6 10−5 10−4 10−3 10−2
k [rad/m]
B(k)
(d) Data of 10/05/2013, full mix.
101 102 103 104
10−6 10−5 10−4 10−3 10−2
k [rad/m]
B(k)
Figure 9.11.:Omnidirectional saturation spectraB(k) =S(k) ⋅k2plotted over kfor the different surfactant conditions. Wind speed increases from condition 1 to condition 7 in the order red ( 1.48m/s), blue( 2.20m/s), yellow(
2.89m/s), green( 3.88m/s), dark blue( 5.11m/s), violet( 6.77m/s), black( 8.42m/s). The dashed line gives the noise level (white noise inS(k)).
Chapter 9 THE INFLUENCE OF SURFACTANTS ON WATER WAVES AND. . .
mentioned in the previous section, the curves of the two Dextran cases appear to be the wrong way round because the spectral energy content is higher for the case with more surfactant. As before, an explanation for this phenomenon could be the pollution of the water with additional substances due to not skimming the surface.
The curves for the two full mix cases were recorded on different days, but with the same surfactant concentration. Thus, they are almost identical as expected.
Furthermore,Figure 9.12illustrates that for a wind speed of 3.88 m/s, the spectral energy content for the two Dextran cases (30/04/2013 & 03/05/2013) is much higher than that for the two full mix cases (08/05/2013 & 10/05/2013). When the surface film has ruptured for the full mix cases at a wind speed of 5.11 m/s the spectral energy content of the Dextran cases and of the full mix cases becomes almost the same, indicating that the influence of the surfactant becomes independent of the type of surfactant present4.
All in all, the analysis of the omnidirectional saturation spectra shows that the two types of surfactant have different influences on the water waves for the concentrations used. In the full mix cases, waves are suppressed more effectively (especially in the high wave number range) than in the Dextran cases. This might be due to the insoluble components of the full mix surfactant which are not as easily mixed into the bulk water.
4Probably due to mixing into the bulk water.
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The Effects of Surfactants on Small-scale Waves 9.4
(a) Condition 4. Wind speed of 3.88m/s
101 102 103 104
10−6 10−5 10−4 10−3 10−2
k [rad/m]
B(k)
30/04/2013 03/05/2013 08/05/2013 10/05/2013
(b) Condition 5. Wind speed of 5.11m/s
101 102 103 104
10−6 10−5 10−4 10−3 10−2
k [rad/m]
B(k)
30/04/2013 03/05/2013 08/05/2013 10/05/2013
Figure 9.12.:Omnidirectional saturation spectraB(k) =S(k) ⋅k2 plotted overk for conditions 4 and 5. The color code for the wind speeds is the same as inFigure 9.11.
10
Conclusion and Outlook
10.1 Conclusion
The ISG at the Heidelberg Aeolotron
In this work, the new high speed Imaging Slope Gauge at the Heidelberg Aeolotron (chapter 4andsection 5.2) has successfully been put into operation for the first time.
Moreover, a data evaluation routine (chapter 7) similar to that described byRocholz [2008] has been implemented for the new setup.
Regarding the ISG setup, the brightness of the illumination source (section 5.4) has been increased compared to the first tests described inFahle[2013]. This allows for measurements with smaller aperture1and hence with improved image quality in terms of depth of field.
For the calibration procedure, a method based on a lens float calibration target (see section 5.6) has been adapted (chapter 7) and investigated (section 8.3).
The setup has been characterized regarding the range of wave numbers which can be resolved in saturation spectra (section 8.1). Thanks to the new high speed camera (section 5.3) which is installed as part of the ISG setup it is now possible to record both components of water surface slope with an unprecedented frame rate of more than 1500 Hz. With the current setup, waves with wave numbers up to 2660 rad/m can be included into saturation spectra without aliasing effects. Detection limits for slope and mean square slope (section 2.4) have been explored for the current setup (section 8.2). Compared to the old CISG setup of 2011, the detection limit for mean square slope is lowered by a factor of≈10 and assumes a value of 3.2×10−4. Slope
1At the moment, measurements at an f-stop of 8 are possible.
Chapter 10 CONCLUSION AND OUTLOOK
values between±0.965 in alongwind and crosswind direction are covered by the new setup.
A spatial dependency of the calibration method remains due to the non-ideal optical imaging characteristics of the Fresnel lens, yet the resulting error appears negligible (Sections 8.4to8.5).
Waves and Gas Exchange in the Laboratory
The influence of different types of natural and synthetic surface films (section 2.6) on water waves has been analysed using mean square slope time series and wave number saturation spectra. Data was recorded for seven wind speed conditions with reference wind speeds between 1.48 m/s to 8.42 m/s for each surfactant.
The effect of a mixture of nature-like surfactants on water wave surface slopes has been shown to be larger2than that of Dextran (section 9.1) for wind speeds up to 5.11 m/s. Up to this wind speed, nature-like surfactants have been found to suppress waves, especially short- and medium-scale waves, very effectively.
The averaging time necessary to obtain a stable estimate for mean square slope was found to lie in between 100 s and 250 s (section 9.2). Furthermore, mean square slope data has been compared with data from a previous experiment at the Aeolotron with a different surfactant and clean water. The results give further evidence that, when waves are present, mean square slope is better suited for parametrizing gas transfer velocities than friction velocity is (section 9.3). In the literature, evidence is given which demands for a replacement of existing wind speed parametrizations for gas transfer velocities with other models. The present work supports with mean square slope.
For the higher wind speeds covered, the relation between mean square slope and transfer velocities has been shown to be similar for several types of soluble and insoluble surfactants.
The damping effect of surfactants on water waves has been studied using a spectral description of the wave field through wave slope saturation spectra (section 2.3, section 9.4). All in all, the results were found to be consistent with findings reported inRocholz[2008];Kiefhaber[2014].
2with the chosen reference concentrations
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Outlook 10.2