Abstract
Investigation of damping of gravity–capillary waves (GCW) on the surface of turbulent fluid is a classical problem which geophysical applications are related to the problems of swell damping, interpretation of radar and optical images of ship wakes, development of physical mechanisms of wind wave suppression, etc. Analysis of the relevant literature reveals the necessity of setting reliable experiments to study the effect of damping of GCW due to turbulence. An original laboratory method of investigation of surface wave damping due to turbulence is described. The method is based on the parametric excitation of standing surface waves (so-called Faraday ripples) and simultaneous and independent generation of turbulence. The wave damping coefficient is determined by a threshold acceleration corresponding to the surface wave parametric excitation. The disadvantages of the previously used methods are eliminated or significantly reduced in the presented method, and the results are formulated in terms of eddy viscosity. It is revealed that the eddy viscosity coefficient is proportional to the rms velocity of turbulent pulsations, and achieves a maximum as a function of GCW frequency, when the GCW wavelengths are of order of the scales of turbulent eddies. This effect has never been mentioned in the literature, since the previous studies were focused on the investigation of wave damping due to small-scale (relative to the GCW wavelengths) turbulence. Applications of the obtained results to real-sea conditions are discussed.
Graphic abstract
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Adamczyk AA, Rimai L (1988) 2-Dimensional particle tracking velocimetry (PTV): technique and image processing algorithms. Exp Fluids 6(6):373–380
Adrian RJ (1991) Particle-imaging techniques for experimental fluid mechanics. Annu Rev Fluid Mech 23(1):261–304. https://doi.org/10.1146/annurev.fl.23.010191.001401
Ardhuin F, Jenkins AD (2006) On the interaction of surface waves and upper ocean turbulence. J Phys Oceanogr 36(3):551–557. https://doi.org/10.1175/JPO2862.1
Ardhuin F, Chapron B, Collard F (2009) Observation of swell dissipation across oceans. Geophys Res Lett. https://doi.org/10.1029/2008GL037030
Badulin SI, Voropaev SI, Kulikov AV, Rozenberg AD (1988) On the impact of turbulence on regular gravity waves of small amplitude. Okeanologiya 4:551–560
Beya J, Peirson W, Banner M (2011) Attenuation of gravity waves by turbulence. Coast Eng Proc 1(32):1–10
Beya JF, Peirson WL, Banner ML (2012) Turbulence beneath finite amplitude water waves. Exp Fluids 52(5):1319–1330
Boyev AG (1971) The damping of surface waves by intense turbulence. Izv Atmos Ocean Phys 7:31–36
Ermakov SA, Kijashko SV (2006) Laboratory study of the damping of parametric ripples due to surfactant films. In: Gade M, Hühnerfuss H, Korenowski GM (eds) Marine surface films. Springer, New York, pp 113–128 doi: 10.1007/3-540-33271-5_12
Ermakov S, Kapustin I, Lazareva T (2014a) Ship wake signatures in radar/optical images of the sea surface: observations and physical mechanisms. Proc SPIE 9240:92400N. https://doi.org/10.1117/12.2067367
Ermakov SA, Kapustin IA, Shomina OV (2014b) Laboratory investigation of damping of gravity-capillary waves on the surface of turbulized liquid. Izv Atmos Ocean Phys 50(2):204–212. https://doi.org/10.1134/S0001433814020042
Ermakova OS, Kapustin IA, Papko VV (2008) Turbulent-layer dynamics in homogeneous and stratified fluids. Izv Atmos Ocean Phys 44(5):583–593. https://doi.org/10.1134/S0001433808050046
Gade M, Byfield V, Ermakov S, Lavrova O, Mitnik L (2013) Slicks as indicators for marine processes. Oceanography 26(2):138–149
Green T, Medwin H, Paquin JE (1972) Measurements of surface wave decay due to underwater turbulence. Nat Phys Sci 237(77):115–117
Gutiérrez P, Aumaître S (2016) Surface waves propagating on a turbulent flow. Phys Fluids 28:025107. https://doi.org/10.1063/1.4941425
Johannessen OM, Johannessen JA, Jenkins AD, Davidson K, Lyzenga DR, Shuchman R, Samuel P, Espedal HA, Knulst J, Dano E, Reistad M (1996) COAST WATCH-95: ERS-1/2 SAR applications of mesoscale upper ocean and atmospheric boundary layer processes off the coast of Norway. In: IGARSS'96. International geoscience and remote sensing symposium 2: pp 1158–1161. Doi: 10.1109/IGARSS.1996.516600
Kitaigorodskii SA, Lumley JL (1983) Wave-turbulence interactions in the upper ocean. Part I: the energy balance of the interacting fields of surface wind waves and wind-induced three-dimensional turbulence. J Phys Oceanogr 13(11):1977–1987. https://doi.org/10.1175/1520-0485(1983)013<1988:WTIITU>2.0.CO;2
Landau LD, Lifshits EM (1959) Fluid Mechanics: Transl. from the Russian by JB Sykes and WH Reid. Addison-Wesley, Boston
Landau LD, Lifshitz EM (1960) Course of theoretical physics. vol. 1: Mechanics. Oxford
McKenna SP, McGillis WR (2004) The role of free-surface turbulence and surfactants in air–water gas transfer. Int J Heat Mass Transf 47(3):539–553. https://doi.org/10.1016/j.ijheatmasstransfer.2003.06.001
Meinhart CD, Prasad AK, Adrian RJ (1993) A parallel digital processor system for particle image velocimetry. Meas Sci Technol 4(5):619–626. https://doi.org/10.1088/0957-0233/4/5/013
Milgram JH (1998) Short wave damping in the simultaneous presence of a surface film and turbulence. J Geophys Res: Oceans 103(8):15717–15727. https://doi.org/10.1029/98JC01191
Milgram JH, Peltzer RD, Griffin OM (1993) Suppression of short sea waves in ship wakes: measurements and observations. J Geophys Res: Oceans 98(44):7103–7114. https://doi.org/10.1029/92JC02612
Mitnik L, Dubina V, Konstantinov O, Fischenko V, Darkin D (2009) Remote sensing of surface films as a tool for the study of oceanic dynamic processes. Ocean Polar Res 31(1):111–119
Monin AS, Yaglom AM (2013) Statistical fluid mechanics, volume II: mechanics of turbulence. Dover publications Inc, Mineola
Olmez HS, Milgram JH (1992) An experimental study of attenuation of short water waves by turbulence. J Fluid Mech 239:133–156. https://doi.org/10.1017/S002211209200435X
Phillips OM (1959) The scattering of gravity waves by turbulence. J Fluid Mech 5(2):177–192. https://doi.org/10.1017/S0022112059000143
Phillips OM (1977) The dynamics of the upper ocean. Cambridge University Press, Melbourne
Rapp RJ, Melville WK (1990) Laboratory measurements of deep-water breaking waves. Philos Trans R Soc Lond Ser A Math Phys Sci 331(1622):735–800. https://doi.org/10.1098/rsta.1990.0098
Scoda JD (1972) The interaction of waves and turbulence in water. Dissertation, University of California
Shomina OV, Kapustin IA, Ermakov SA (2019) Damping of surface waves due to turbulence in application to the problem of ocean remote sensing. In: Proceedings of SPIE 11150, Remote Sensing of the Ocean, Sea Ice, Coastal Waters, and Large Water Regions 2019, 111501M. https://doi.org/10.1117/12.2533223
Teixeira MAC, Belcher SE (2002) On the distortion of turbulence by a progressive surface wave. J Fluid Mech 458:229–267. https://doi.org/10.1017/S0022112002007838
Variano EA, Cowen EA (2008) A random-jet-stirred turbulence tank. J Fluid Mech 604:1–32
Willert CE, Gharib M (1991) Digital particle image velocimetry. Exp Fluids 10(4):181–193
Acknowledgements
We are grateful to Tatiana Lazareva for her help in the experiment. This research was funded by the Russian Science Foundation (Project RSF 18-77-10066).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Shomina, O., Kapustin, I. & Ermakov, S. Damping of gravity–capillary waves on the surface of turbulent fluid. Exp Fluids 61, 184 (2020). https://doi.org/10.1007/s00348-020-03022-5
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/s00348-020-03022-5