Air-Sea Gas Transfer: Schmidt Number Dependency and Intermittency

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1 Air-Sea Gas Transfer: Schmidt Number Dependency and Intermittency Bernd Jähne, Reinhard Nielsen, Christopher Pop, Uwe Schimpf, and Christoph Garbe Interdisziplinäres Zentrum für Wissenschaftliches Rechnen and Institut für Umweltphysik, Universität Heidelberg 37th International Lìege Colloquium on Ocean Dynamics Gas Transfer at Water Surfaces, 2 6 May 2005

2 Overview Introduction Impact of intermittency on gas transfer measurements A new (old) approach to active thermography Schmidt number dependency Future research plans and conclusions

3 Intermittency Wave slope image 33 cm 25 cm, Delft wind/wave flume , 2.5 m/s wind

4 Intermittency Wave slope image 33 cm 25 cm, Delft wind/wave flume , 2.5 m/s wind, 0.15 s later

5 Intermittency Wave slope image 33 cm 25 cm, Delft wind/wave flume , 3.6 m/s wind

6 Intermittency Wave slope image 33 cm 25 cm, Delft wind/wave flume , 3.6 m/s wind, 0.1 s later

7 Intermittency Wave slope image 33 cm 25 cm, Delft wind/wave flume , 3.6 m/s wind, 0.2 s later

8 Impact of intermittency on gas transfer measurements Flux density averaged over area A and time t: j = 1 j(x,t)d 2 x dt = j p(j) dp (1) A t A t Classical mass balance: unbiased estimate if c = const k = j/ c = k (2) averaging of transfer velocity

9 Active controlled flux technique: constant flux density, varying concentration difference k = j/ c = 1 c/j = 1 (3) 1/k averaging of reciprocal transfer velocity Active controlled flux technique: time constant constant flux density, varying concentration difference t = D/k 2 = D1/k 2 k = D/t = 1/1/k 2 (4) averaging of squared reciprocal transfer velocity

10 Illustration with simple example 20% of surface with three times mean gas transfer rate 80% of surface with half mean gas transfer rate Classical mass balance: k = k k = 6 10 k k = k 1.0k Active controlled flux technique: Time constant 1/k = k k = 2 30k k = 5 3k 0.6k 1/k 2 = k k 2 = 2 90k k 2 = k 9k Generally effects are related to relative variance of transfer velocity 1 (k + k ) 2 1 σ k k 2 k 2

11 Characteristic scales of transfer process across aqueous heat boundary layer

12 The original controlled flux technique

13 Experimental set up

14 Spectral response to rectangular signal (switching on and off)

15 Theoretical analysis I Modelling of transport across boundary layer: Solution of 1-D transport equation in Fourier space (frequency): turbulent diffusion iω + c + = [ (1 + α m+ z + m ) c ] + z + z + ( generalized surface renewal iω + + γ p+ z + p ) c + = 2 c + z+ 2 with ω + = ωt, all quantities indexed by + are dimensionless (5) Examples for solution: Model Amplitude damping Phase shift 1 1 Surface renewal model (1 + ω 2 +) 1/4 arctan ω+ 2 ( ) ( ) tanh( iω+ ) tanh( iω+ ) Film model R arg iω+ iω+

16 Theoretical analysis II General shape of solutions: Model ω + << 1 ω + >> 1 Amplitude damping 1 ω 1/2 + Phase shift φ( z + ) = κω + (1 + z + ) π/4 Linear phase shift for small ω + with 0.33 κ 0.55 (Compare with first-order low pass: κ = 1 and maximum phase shift of π/2 and amplitude damping ω 1 + )

17 Early experimental verification: amplitude damping

18 Early experimental verification: phase shift

19 Principal verification successful Conclusions (1988) Results too inaccurate for detailed studies, especially distinction of different models Technique could be used in laboratory facilities but not in the field

20 Spatiotemporal response at low wind speed (2.0 m/s) 0.5 s 1.0 s 1.5 s after switching on CO 2 laser

21 Spatiotemporal response at low wind speed (2.0 m/s) 2.0 s 2.5 s 3.0 s after switching on CO 2 laser

22 Spatiotemporal response at medium wind speed (7.0 m/s) 0.5 s 1.0 s 1.5 s after switching on CO 2 laser

23 Spatiotemporal response at medium wind speed (7.0 m/s) 2.0 s 2.5 s 3.0 s after switching on CO 2 laser

24 Experimental facility: Heidelberg Aeolotron Annular wind/wave facility especially designed for thermographic measurements

25 Experimental results 2004: amplitude damping amplitude frequency [Hz]

26 Experimental results 2004: phase shift

27 Experimental results 2004: phase shift

28 Conclusions and Outlook Spatiotemporal active thermography offers unprecedented insight into exchange processes at the water surface Potential to "lookïnto different depths of the boundary layer Potential to analyze concentration fields and velocity fields simultaneously

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