Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-12-01T10:55:20.822Z Has data issue: false hasContentIssue false

Near-surface turbulence and buoyancy induced by heavy rainfall

Published online by Cambridge University Press:  03 October 2017

E. L. Harrison
Affiliation:
Naval Surface Warfare Center, Carderock Division, 9500 Macarthur Boulevard, West Bethesda, MD 20817, USA
F. Veron*
Affiliation:
University of Delaware, School of Marine Science and Policy, Newark, DE 19716, USA Université de Bordeaux, I2M, CNRS UMR 5295, 16 avenue Pey-Berland, 33607 Pessac, France
*
Email address for correspondence: fveron@udel.edu

Abstract

We present results from experiments designed to measure near-surface turbulence generated by rainfall. Laboratory experiments were performed using artificial rain falling at near-terminal velocity in a wind–wave channel filled with synthetic seawater. In this first series of experiments, no wind was generated and the receiving seawater was initially at rest. Rainfall rates from 40 to $190~\text{mm}~\text{h}^{-1}$ were investigated. Subsurface turbulent velocities of the order of $O(10^{-2})~\text{m}~\text{s}^{-1}$ are generated near the interface below the depth of the cavities generated by the rain drop impacts. The turbulence appears independent of rainfall rates. At depth larger than the size of the cavities, the turbulent velocity fluctuations decay as $z^{-3/2}$. Turbulent length scales also appear to scale with the size of the impact cavities. In these seawater experiments, a freshwater lens is established at the water surface due to the rain. At the highest rain rate studied, the resulting buoyancy flux appears to lead to a shallower subsurface mixed layer and a slight decrease of the turbulent kinetic energy dissipation. Finally, direct measurements and inertial estimates of the turbulent kinetic energy dissipation show that approximately 0.1–0.3 % of the kinetic energy flux from the rain is dissipated in the form of turbulence. This is consistent with existing freshwater measurements and suggests that high levels of dissipation occur at depths and scales smaller than those resolved here and/or that other phenomena dissipate a considerable amount of the total kinetic energy flux provided by rainfall.

Type
Papers
Copyright
© 2017 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Beya, J., Peirson, W. & Banner, M. 2011 Rainfall-generated, near-surface turbulence. In Gas Transfers at Water Surfaces 2010 (ed. Komori, S., McGillis, W. & Kurose, R.), pp. 90103. Kyoto University Press.Google Scholar
Bliven, L. F., Sobieski, P. W. & Craeye, C. 1997 Rain generated ring-waves: measurements and modelling for remote sensing. Intl J. Remote Sensing 18 (1), 221228.Google Scholar
Braun, N.2003 Untersuchungen zur radar-rückstreuung und wellendämpfung beregneter wasseroberflächen, dissertation, universität hamburg, fachbereich geowissenschaften, ‘on the radar backscattering and wave damping on water surfaces agitated by rain’. PhD dissertation, University of Hamburg.Google Scholar
Braun, N., Gade, M. & Lange, P. A. 2002 The effect of artificial rain on wave spectra and multi-polarisation x-band radar backscatter. Intl J. Remote Sensing 23 (20), 43054323.Google Scholar
Cai, Y. K. 1989 Phenomena of a liquid drop falling to a liquid surface. Exp. Fluids 7 (6), 388394.CrossRefGoogle Scholar
Caldwell, D. R. & Elliott, W. P. 1971 Surface stresses produced by rainfall. J. Phys. Oceanogr. 1 (2), 145148.2.0.CO;2>CrossRefGoogle Scholar
Chapman, D. S. & Critchlow, P. R. 1967 Formation of vortex rings from falling drops. J. Fluid Mech. 29 (01), 177185.CrossRefGoogle Scholar
Ching, B., Golay, M. W. & Johnson, T. J. 1984 Droplet impacts upon liquid surfaces. Science 226 (4674), 535537.Google Scholar
Cole, D.2007 The splashing morphology of liquid–liquid impacts. PhD thesis, James Cook University.Google Scholar
Craeye, C. 1998 Rainfall on the sea: surface renewals and wave damping. Boundary-Layer Meteorol. 89 (2), 349355.CrossRefGoogle Scholar
Cresswell, R. W. & Morton, B. R. 1995 Drop-formed vortex rings – the generation of vorticity. Phys. Fluids 7 (6), 13631370.Google Scholar
Dooley, B. S., Warncke, A. E., Gharib, M. & Tryggvason, G. 1997 Vortex ring generation due to the coalescence of a water drop at a free surface. Exp. Fluids 22 (5), 369374.Google Scholar
Engel, O. G. 1966 Crater depth in fluid impacts. J. Appl. Phys. 37 (4), 17981808.Google Scholar
Fedorchenko, A. I. & Wang, A.-B. 2004 On some common features of drop impact on liquid surfaces. Phys. Fluids 16 (5), 13491365.CrossRefGoogle Scholar
Fofonoff, N. P. & Millard, R. C.1983 Algorithms for computation of fundamental properties of seawater. Tech. Rep. 44. UNESCO.Google Scholar
Gill, A. 1982 Atmosphere-Ocean Dynamics. Academic.Google Scholar
Green, T. & Houk, D. F. 1979 The mixing of rain with near-surface water. J. Fluid Mech. 90, 569588.CrossRefGoogle Scholar
Harrison, E. L.2012 The effects of rainfall in the ocean surface at low to moderate wind speed. PhD dissertation, University of Delaware.Google Scholar
Harrison, E. L., Veron, F., Ho, D. T., Reid, M. S., Orton, P. & McGillis, W. R. 2012 Nonlinear interaction between rain- and wind-induced air–water gas exchange. J. Geophys. Res. 117, C03034.CrossRefGoogle Scholar
Ho, D. T., Asher, W. E., Bliven, L. F., Schlosser, P. & Gordan, E. L. 2000 On mechanisms of rain-induced air–water gas exchange. J. Geophys. Res. 105 (C10), 2404524057.Google Scholar
Ho, D. T., Veron, F., Harrison, E., Bliven, L. F., Scott, N. & McGillis, W. R. 2007 The combined effect of rain and wind on air–water gas exchange: a feasibility study. J. Mar. Syst. 66 (1–4), 150160.Google Scholar
Ho, D. T., Zappa, C. J., McGillis, W. R., Bliven, L. F., Ward, B., Dacey, J. W. H., Schlosser, P. & Hendricks, M. B. 2004 Influence of rain on air–sea gas exchange: lessons from a model ocean. J. Geophys. Res. 109, C08S18.Google Scholar
Holthuijsen, L. H., Powell, M. D. & Pietrzak, J. D. 2012 Wind and waves in extreme hurricanes. J. Geophys. Res. 117, C09003.Google Scholar
Houk, D. F. & Green, T. 1976 A note on surface waves due to rain. J. Geophys. Res. 81 (24), 44824484.Google Scholar
Jayaratne, O. W. & Mason, B. J. 1964 The coalescence and bouncing of water drops at an air/water interface. Proc. R. Soc. Lond. A 280, 545565.Google Scholar
de Jong, J., Cao, L., Woodward, S. H., Salazar, J. P. L. C., Collins, L. R. & Meng, H. 2008 Dissipation rate estimation from piv in zero-mean isotropic turbulence. Exp. Fluids 46 (3), 499.Google Scholar
Katsaros, K. & Buettner, K. J. K. 1969 Influence of rainfall on temperature and salinity of the ocean surface. J. Appl. Meteorol. 8 (1), 1518.2.0.CO;2>CrossRefGoogle Scholar
Lange, P. A., Graaf, G. V. D. & Gade, M. 2000 Rain-induced subsurface turbulence measured using image processing methods. In Proceedings IEEE 2000 International Geoscience and Remote Sensing Symposium (IGARSS 2000), vol. 7, pp. 31753177. IEEE, ID: 1.Google Scholar
Lavoie, P., Avallone, G., De Gregorio, F., Romano, G. P. & Antonia, R. A. 2007 Spatial resolution of piv for the measurement of turbulence. Exp. Fluids 43 (1), 3951.Google Scholar
Le Méhauté, B. 1988 Gravity-capillary rings generated by water drops. J. Fluid Mech. 197, 415427.Google Scholar
Le Méhauté, B. & Khangaonkar, T. 1990 Dynamic interaction of intense rain with water waves. J. Phys. Oceanogr. 20 (12), 18051812.Google Scholar
Lemaire, D., Bliven, L. F., Craeye, C. & Sobieski, P. 2002 Drop size effects on rain-generated ring-waves with a view to remote sensing applications. Intl J. Remote Sensing 23 (12), 23452357.CrossRefGoogle Scholar
Lemoine, F., Wolff, M. & Lebouche, M. 1996 Simultaneous concentration and velocity measurements using combined laser-induced flourescence and laser doppler velocimetry: application to turbulent transport. Exp. Fluids 20, 521544.Google Scholar
Lesieur, M. 2008 Turbulence in Fluids. Springer.Google Scholar
Liow, J. L. 2001 Splash formation by spherical drops. J. Fluid Mech. 427, 73105.Google Scholar
Liu, H. & Lin, J. 1982 On the spectra of high-frequency wind waves. J. Fluid Mech. 123, 165185.CrossRefGoogle Scholar
Macklin, W. C. & Metaxas, G. J. 1976 Splashing of drops on liquid layers. J. Appl. Phys. 47 (9), 39633970.Google Scholar
Manton, M. J. 1973 On the attenuation of sea waves by rain. Geophys. Astrophys. Fluid Dyn. 5, 249260.Google Scholar
Marshall, J. S. & Palmer, W. M. K. 1948 The distribution of raindrops with size. J. Meteorol. 5, 165166.Google Scholar
Morton, D., Rudman, M. & Liow, J.-L. 2000 An investigation of the flow regimes resulting from splashing drops. Phys. Fluids 12 (4), 747763.Google Scholar
Nystuen, J. A. 1990 A note on the attenuation of surface gravity waves by rainfall. J. Geophys. Res. 95 (C10), 1835318355.Google Scholar
Oguz, H. N. & Prosperetti, A. 1990 Bubble entrainment by the impact of drops on liquid surfaces. J. Fluid Mech. 219, 143179.Google Scholar
Pawlak, G. & Armi, L. 1998 Vortex dynamics in a spatially accelerating shear layer. J. Fluid Mech. 376, 135.Google Scholar
Peck, B. & Sigurdson, L. 1994 The three-dimensional vortex structure of an impacting water drop. Phys. Fluids 6 (2), 564576.Google Scholar
Peirson, W. L., Beya, J. F., Banner, M. L., Peral, J. S. & Azarmsa, S. A. 2013 Rain-induced attenuation of deep-water waves. J. Fluid Mech. 724, 535.Google Scholar
Poon, Y. K., Tang, S. & Wu, J. 1992 Interactions between rain and wind waves. J. Phys. Oceanogr. 22 (9), 976987.Google Scholar
Prosperetti, A. & Oguz, H. N. 1993 The impact of drops on liquid surfaces and the underwater noise of rain. Annu. Rev. Fluid Mech. 25, 577602.Google Scholar
Prosperetti, A. & Oguz, H. N. 1997 Air entrainment upon liquid impact. Phil. Trans. R. Soc. Lond. 355, 491506.Google Scholar
Pumphrey, H. C. & Crum, L. A. 1990 Free oscillations of near-surface bubbles as a source of the underwater noise of rain. J. Acoust. Soc. Am. 87 (1), 142148.Google Scholar
Pumphrey, H. C. & Elmore, P. A. 1990 Entrainment of bubbles by drop impacts. J. Fluid Mech. 220, 539567.Google Scholar
Ray, B., Biswas, G. & Sharma, A. 2010 Generation of secondary droplets in coalescence of a drop at a liquid–liquid interface. J. Fluid Mech. 655, 72104.Google Scholar
Ray, B., Biswas, G. & Sharma, A. 2015 Regimes during liquid drop impact on a liquid pool. J. Fluid Mech. 768, 492523.Google Scholar
Rein, M. 1993 Phenomena of liquid drop impact on solid and liquid surfaces. Fluid Dyn. Res. 12 (2), 6193.CrossRefGoogle Scholar
Rein, M. 1996 The transitional regime between coalescing and splashing drops. J. Fluid Mech. 306, 145165.Google Scholar
Rodriguez, F. & Mesler, R. 1988 The penetration of drop-formed vortex rings into pools of liquid. J. Colloid Interface Sci. 121 (1), 121129.Google Scholar
San Lee, J., Park, S. J., Lee, J. H., Weon, B. M., Fezzaa, K. & Je, J. H. 2015 Origin and dynamics of vortex rings in drop splashing. Nat. Commun. 6, 8187.Google Scholar
Santini, M., Fest-Santini, S. & Cossali, G. E. 2013 LDV characterization and visualization of the liquid velocity field underneath an impacting drop in isothermal conditions. Exp. Fluids 54 (9), 1593.Google Scholar
Shankar, P. N. & Kumar, M. 1995 Vortex rings generated by drops just coalescing with a pool. Phys. Fluids 7 (4), 737746.Google Scholar
Takagaki, N. & Komori, S. 2007 Effects of rainfall on mass transfer across the air–water interface. J. Geophys. Res. 112 (C6), C06006.Google Scholar
Takagaki, N. & Komori, S. 2014 Air–water mass transfer mechanism due to the impingement of a single liquid drop on the air–water interface. Intl J. Multiphase Flow 60, 3039.Google Scholar
Tsimplis, M. & Thorpe, S. A. 1989 Wave damping by rain. Nature 342, 893895.Google Scholar
Tsimplis, M. N. 1992 The effect of rain in calming the sea. J. Phys. Oceanogr. 22 (4), 404412.Google Scholar
Vander Wal, R. L., Berger, G. M. & Mozes, S. D. 2006 Droplets splashing upon films of the same fluid of various depths. Exp. Fluids 40 (1), 3352.Google Scholar
Veron, F. & Mieussens, L. 2016 A kinetic model for particle–surface interaction applied to rain falling on water waves. J. Fluid Mech. 796, 767787.Google Scholar
Ward, B. 2006 Near-surface ocean temperature. J. Geophys. Res. 111, C02004.Google Scholar
Worthington, A. M. 1908 A Study of Splashes. Longmans, Green, and Company.Google Scholar
Worthington, A. M. & Cole, R. S. 1897 Impact with a liquid surface, studied by the aid of instantaneous photography. Phil. Trans. R. Soc. Lond. A 189, 137148.Google Scholar
Xu, D. & Chen, J. 2013 Accurate estimate of turbulent dissipation rate using PIV data. Exp. Therm. Fluid Sci. 44, 662672.Google Scholar
Yang, Z., Tang, S. & Wu, J. 1997 An experimental study of rain effects on fine structures of wind waves. J. Phys. Oceanogr. 27 (3), 419430.Google Scholar
Yarin, A. L. 2006 Drop impact dynamics: splashing, spreading, receding, bouncing. Annu. Rev. Fluid Mech. 38, 159192.Google Scholar
Zappa, C. J., Ho, D. T., McGillis, W. R., Banner, M. L., Dacey, J. W. H., Bliven, L. F., Ma, B. & Nystuen, J. 2009 Rain-induced turbulence and air–sea gas transfer. J. Geophys. Res. 114, C07009.Google Scholar