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An Eulerian model for sea spray transport and evaporation

Published online by Cambridge University Press:  09 June 2020

Fabrice Veron*
Affiliation:
School of Marine Science and Policy, University of Delaware, Newark, DE 19711, USA
Luc Mieussens
Affiliation:
Bordeaux INP, Univ. Bordeaux, CNRS, IMB, UMR 5251, F-33400Talence, France
*
Email address for correspondence: [email protected]

Abstract

Reliable estimates of the fluxes of momentum, heat and moisture at the air–sea interface are essential for accurate long-term climate projections, as well as the prediction of short-term weather events such as tropical cyclones. In recent years, it has been suggested that these estimates need to incorporate an accurate description of the transport of sea spray within the atmospheric boundary layer and the drop-induced fluxes of momentum, heat and moisture, so that the resulting effects on atmospheric flow can be evaluated. In this paper we propose a model based on a theoretical and mathematical framework inspired from kinetic gas theory. This approach reconciles the Lagrangian nature of spray transport with the Eulerian description of the atmosphere. In turn, this enables a relatively straightforward inclusion of the spray fluxes and the resulting spray effects on the atmospheric flow. A comprehensive dimensional analysis has led us to identify the spray effects that are most likely to influence the speed, temperature and moisture of the airflow. We also provide an example application to illustrate the capabilities of the model in specific environmental conditions. Finally, suggestions for future work are offered.

Type
JFM Papers
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

Adrian, R. J. 1991 Particle-imaging techniques for experimental fluid mechanics. Annu. Rev. Fluid Mech. 23 (1), 261304.CrossRefGoogle Scholar
Andreas, E. L.1989 Thermal and size evolution of sea spray droplets. Tech. Rep. 89-11. CRREL.Google Scholar
Andreas, E. L. 1990 Time constants for the evolution of sea spray droplets. Tellus B 42 (5), 481497.CrossRefGoogle Scholar
Andreas, E. L. 1992 Sea spray and the turbulent air–sea heat fluxes. J. Geophys. Res. 97 (C7), 1142911441.CrossRefGoogle Scholar
Andreas, E. L. 1998 A new sea spray generation function for wind speeds up to 32 m s-1. J. Phys. Oceanogr. 28 (11), 21752184.2.0.CO;2>CrossRefGoogle Scholar
Andreas, E. L. 2002 A review of the sea spray generation function for the open ocean. In Atmosphere-Ocean Interactions (ed. Perrie, W. A.), vol. 1, p. 146. WIT Press.Google Scholar
Andreas, E. L. 2004 Spray stress revisited. J. Phys. Oceanogr. 34 (6), 14291440.2.0.CO;2>CrossRefGoogle Scholar
Andreas, E. L. & DeCosmo, J. 1999 Sea spray production and influence on air–sea heat and moisture fluxes over the open ocean. In Air–Sea Exchange: Physics, Chemistry and Dynamics (ed. Geernaert, G. L.), pp. 327362. Kluwer.CrossRefGoogle Scholar
Andreas, E. L., Edson, J. B., Monahan, E. C., Rouault, M. P. & Smith, S. D. 1995 The spray contribution to net evaporation from the sea: a review of recent progress. Boundary-Layer Meteorol. 72 (1–2), 352.CrossRefGoogle Scholar
Andreas, E. L. & Emanuel, K. A. 2001 Effects of sea spray on tropical cyclone intensity. J. Atmos. Sci. 58 (24), 37413751.2.0.CO;2>CrossRefGoogle Scholar
Andreas, E. L., Jones, K. F. & Fairall, C. W. 2010 Production velocity of sea spray droplets. J. Geophys. Res. 115, C12065.CrossRefGoogle Scholar
Andreas, E. L., Persson, P. O. G. & Hare, J. E. 2008 A bulk turbulent air–sea flux algorithm for high-wind, spray conditions. J. Phys. Oceanogr. 38 (7), 15811596.CrossRefGoogle Scholar
Anis, A. & Moum, J. N. 1995 Surface wave-turbulence interactions: scaling 𝜖(z) near the sea surface. J. Phys. Oceanogr. 25, 346366.2.0.CO;2>CrossRefGoogle Scholar
Bao, J. W., Fairall, C. W., Michelson, S. A. & Bianco, L. 2011 Parameterizations of sea-spray impact on the air–sea momentum and heat fluxes. Mon. Wealth. Rev. 139, 37813797.CrossRefGoogle Scholar
Bao, J. W., Wilczak, J. M., Choi, J.-K. & Kantha, L. H. 2000 Numerical simulations of air–sea interaction under high wind conditions using a coupled model: a study of hurricane development. Mon. Wealth. Rev. 128, 21902210.2.0.CO;2>CrossRefGoogle Scholar
Barenblatt, G. I., Chorin, A. J. & Prostokishin, V. M. 2005 A note concerning the lighthill ‘sandwich model’ of tropical cyclones. Proc. Natl Acad. Sci. USA 102, 1114811150.CrossRefGoogle Scholar
Bell, M. M., Montgomery, M. T. & Emanuel, K. A. 2012 Air–sea enthalpy and momentum exchange at major hurricane wind speeds observed during cblast. J. Atmos. Sci. 69 (3), 31973222.CrossRefGoogle Scholar
Bianco, L., Bao, J.-W., Fairall, C. W. & Michelson, S. A. 2011 Impact of sea-spray on the atmospheric surface layer. Boundary-Layer Meteorol. 140 (3), 361.CrossRefGoogle Scholar
Blanchard, D. C. 1989 The size and height to which jet drops are ejected from bursting bubbles in sea water. J. Geophys. Res. 94 (C8), 1099911002.CrossRefGoogle Scholar
Carruthers, D. J. & Choularton, T. W. 1986 The microstructure of hill cap clouds. Q. J. R. Meteorol. Soc. 112 (471), 113129.CrossRefGoogle Scholar
Clift, R. & Gauvin, W. H. 1970 The motion of particles in turbulent gas-streams. Proc. Chemeca’70 1, 14.Google Scholar
Davies, C. N. 1945 Definitive equations for the fluid resistance of spheres. Proc. Phys. Soc. Lond. 57 (Pt.4), 259270.CrossRefGoogle Scholar
Desjardins, O., Fox, R. O. & Villedieu, P. 2008 A quadrature-based moment method for dilute fluid-particle flows. J. Comput. Phys. 227 (4), 25142539.CrossRefGoogle Scholar
Desvillettes, L., Golse, F. & Ricci, V. 2008 The mean-field limit for solid particles in a Navier–Stokes flow. J. Stat. Phys. 131 (5), 941967.CrossRefGoogle Scholar
Domelevo, K. & Villedieu, P. 2007 A hierarchy of models for turbulent dispersed two-phase flows derived from a kinetic equation for the joint particle-gas pdf. Commun. Math. Sci. 5 (2), 331353.CrossRefGoogle Scholar
Donelan, M. A., Haus, B. K., Reul, N., Plant, W. J., Stiassnie, M., Graber, H. C., Brown, O. B. & Saltzman, E. S. 2004 On the limiting aerodynamic roughness of the ocean in very strong winds. Geophys. Res. Lett. 31 (18), L18306.CrossRefGoogle Scholar
Drennan, W. M., Zhang, J. A., French, J. R., McCormick, C. & Black, P. G. 2007 Turbulent fluxes in the hurricane boundary layer. Part II. Latent heat flux. J. Atmos. Sci. 64 (4), 11031115.CrossRefGoogle Scholar
Edson, J. B., Anquetin, S., Mestayer, P. G. & Sini, J. F. 1996 Spray droplet modeling. 2. An interactive Eulerian–Lagrangian model of evaporating spray droplets. J. Geophys. Res. 101, 12791293.CrossRefGoogle Scholar
Edson, J. B. & Fairall, C. W. 1998 Similarity relationships in the marine surface layer. J. Atmos. Sci. 55, 23112328.2.0.CO;2>CrossRefGoogle Scholar
Edson, J. B. & Fairall, C. W. 1994 Spray droplet modeling. 1. Lagrangian model simulation of the turbulent transport of evaporating droplets. J. Geophys. Res. 99 (C12), 2529525311.CrossRefGoogle Scholar
Erinin, M. A., Wang, S. D., Liu, R., Towle, D., Liu, X. & Duncan, J. H. 2019 Spray generation by a plunging breaker. Geophys. Res. Lett. 46 (14), 82448251.CrossRefGoogle Scholar
Fairall, C. W., Banner, M. L., Peirson, W. L., Asher, W. & Morison, R. P. 2009 Investigation of the physical scaling of sea spray spume droplet production. J. Geophys. Res. 114 (C10), C10001.CrossRefGoogle Scholar
Fairall, C. W., Bradley, E. F., Rogers, D. P., Edson, J. B. & Young, G. S. 1996 Bulk parameterization of air–sea fluxes for tropical ocean-global atmosphere coupled-ocean atmosphere response experiment. J. Geophys. Res. 101, 37473764.CrossRefGoogle Scholar
Fairall, C. W., Kepert, J. D. & Holland, G. J. 1994 The effect of sea spray on surface energy transports over the ocean. Global Atmos. Ocean Syst. 2, 121142.Google Scholar
Feireisl, E. & Novotný, A. 2009 Singular Limits in Thermodynamics of Viscous Fluids. Birkhäuser.CrossRefGoogle Scholar
Fox, R. O., Laurent, F. & Vié, A. 2018 Conditional hyperbolic quadrature method of moments for kinetic equations. J. Comput. Phys. 365, 269293.CrossRefGoogle Scholar
Fuentes, E., Coe, H., Green, D., de Leeuw, G. & McFiggans, G. 2010 Laboratory-generated primary marine aerosol via bubble-bursting and atomization. Atmos. Meas. Technol. 3 (1), 141162.CrossRefGoogle Scholar
Hare, J. E., Hara, T., Edson, J. B. & Wilczack, J. M. 1997 A similarity analysis of the structure of airflow over surface waves. J. Phys. Oceanogr. 27, 10181037.2.0.CO;2>CrossRefGoogle Scholar
Helgans, B. & Richter, D. H. 2016 Turbulent latent and sensible heat flux in the presence of evaporative droplets. Intl J. Multiphase Flow 78, 111.CrossRefGoogle Scholar
Hristov, T., Friehe, C. & Miller, S. 1998 Wave-coherent fields in air flow over ocean waves: identification of cooperative behavior buried in turbulence. Phys. Rev. Lett. 81 (23), 5245.CrossRefGoogle Scholar
Koga, M. 1981 Direct production of droplets from breaking wind-waves, its observation by a multi-colored overlapping exposure photographing technique. Tellus 33, 552563.CrossRefGoogle Scholar
de Leeuw, G., Andreas, E. L., Anguelova, M. D., Fairall, C. W., Lewis, E. R., O’Dowd, C., Shultz, M. & Schwartz, S. E. 2011 Production flux of sea spray aerosol. Rev. Geophys. 49, RG2001.Google Scholar
Lewis, E. R. & Schwartz, S. E. 2004 Sea Salt Aerosol Production: Mechanisms, Methods, Measurements and Models – A Critical Review, Geophysical Monograph Series, 152. American Geophysical Union.Google Scholar
Liu, B., Liu, H., Xie, L., Guan, C. & Zhao, D. 2010 A coupled atmosphere–wave–ocean modeling system: simulation of the intensity of an idealized tropical cyclone. Mon. Wealth. Rev. 139 (1), 132152.CrossRefGoogle Scholar
Makin, V. K. 1998 Air–sea exchange of heat in the presence of wind waves and spray. J. Geophys. Res. 103, 11371152.CrossRefGoogle Scholar
Marchiso, E. & Fox, R. O. 2013 Computational Models for Polydisperse Particulate and Multiphase Systems. Cambridge University Press.CrossRefGoogle Scholar
Marmottant, P. H. & Villermaux, E. 2004 On spray formation. J. Fluid Mech. 498, 73111.CrossRefGoogle Scholar
Melville, W. K. 1994 Energy dissipation by breaking waves. J. Phys. Oceanogr. 24, 20412049.2.0.CO;2>CrossRefGoogle Scholar
Melville, W. K. 1996 The role of surface-wave breaking in air–sea interaction. Annu. Rev. Fluid Mech. 28, 279321.CrossRefGoogle Scholar
Mestayer, P. G., Van Eijk, A. M. J., De Leeuw, G. & Tranchant, B. S. 1996 Numerical simulation of the dynamics of sea spray over the waves. J. Geophys. Res. 101, 2077120797.CrossRefGoogle Scholar
Michaelides, E. E. & Feng, Z. 1994 Heat transfer from a rigid sphere in a nonuniform flow and temperature field. Intl J. Heat Mass Transfer 37 (14), 20692076.CrossRefGoogle Scholar
Monahan, E. C., Spiel, D. E. & Davidson, K. L. 1986 A model of marine aerosol generation via whitecaps and wave disruption. In Oceanic Whitecaps (ed. Monahan, E. C. & Niocaill, G. M.), Oceanographic Sciences Library, vol. 2, pp. 167174. Springer.CrossRefGoogle Scholar
Mueller, J. A. & Veron, F. 2009a A Lagrangian stochastic model for heavy particle dispersion in the atmospheric marine boundary layer. Boundary-Layer Meteorol. 130 (2), 229247.CrossRefGoogle Scholar
Mueller, J. A. & Veron, F. 2009b A sea state–dependent spume generation function. J. Phys. Oceanogr. 39, 23632372.CrossRefGoogle Scholar
Mueller, J. & Veron, F. 2010a A Lagrangian stochastic model for sea-spray evaporation in the atmospheric marine boundary layer. Boundary-Layer Meteorol. 137, 135152.CrossRefGoogle Scholar
Mueller, J. A. & Veron, F. 2010b Bulk formulation of the heat and water vapor fluxes at the air–sea interface, including nonmolecular contributions. J. Atmos. Sci. 67, 234247.CrossRefGoogle Scholar
Mueller, J. A. & Veron, F. 2014a Impact of sea spray on air–sea fluxes. Part I. Results from stochastic simulations of sea spray drops over the ocean. J. Phys. Oceanogr. 44 (11), 28172834.CrossRefGoogle Scholar
Mueller, J. A. & Veron, F. 2014b Impact of sea spray on air–sea fluxes. Part II. Feedback effects. J. Phys. Oceanogr. 44 (11), 28352853.CrossRefGoogle Scholar
Ortiz-Suslow, D. G., Haus, B. K., Mehta, S. & Laxague, N. J. M. 2016 Sea spray generation in very high winds. J. Atmos. Sci. 73 (10), 39753995.CrossRefGoogle Scholar
Peng, T. & Richter, D. 2017 Influence of evaporating droplets in the turbulent marine atmospheric boundary layer. Boundary-Layer Meteorol. 165 (3), 497518.CrossRefGoogle Scholar
Peng, T. & Richter, D. 2019 Sea spray and its feedback effects: assessing bulk algorithms of air–sea heat fluxes via direct numerical simulations. J. Phys. Oceanogr. 49 (6), 14031421.CrossRefGoogle Scholar
Pruppacher, H. R. & Klett, J. D. 1996 Microphysics of Clouds and Precipitation, vol. 18. Springer Science & Business Media.Google Scholar
Pruppacher, H. R. & Klett, J. D. 1978 Microphysics of Clouds and Precipitation. D. Riedel.CrossRefGoogle Scholar
Ranz, W. E. & Marshall, W. R. 1952 Evaporation from drops. Chem. Engng Prog. 48 (3), 141146.Google Scholar
Richter, D. H. 2015 Turbulence modification by inertial particles and its influence on the spectral energy budget in planar Couette flow. Phys. Fluids 27 (6), 063304.CrossRefGoogle Scholar
Richter, D. H., Dempsey, A. E. & Sullivan, P. P. 2019 Turbulent transport of spray droplets in the vicinity of moving surface waves. J. Phys. Oceanogr. 49 (7), 17891807.CrossRefGoogle Scholar
Richter, D. H., Garcia, O. & Astephen, C. 2016 Particle stresses in dilute, polydisperse, two-way coupled turbulent flows. Phys. Rev. E 93, 013111.Google ScholarPubMed
Richter, D. H. & Sullivan, P. P. 2013a Momentum transfer in a turbulent, particle-laden Couette flow. Phys. Fluids 25, 053304.CrossRefGoogle Scholar
Richter, D. H. & Sullivan, P. P. 2013b Sea surface drag and the role of spray. Geophys. Res. Lett. 40 (3), 656660.CrossRefGoogle Scholar
Richter, D. H. & Sullivan, P. P. 2014 Modification of near-wall coherent structures by inertial particles. Phys. Fluids 26, 103304.CrossRefGoogle Scholar
Rosenfeld, D., Woodley, W. L., Khain, A., Cotton, W. R., Carrio, G., Ginis, I. & Golden, J. H. 2012 Aerosol effects on microstructure and intensity of tropical cyclones. Bull. Amer. Meterol. Soc 93, 9871001.CrossRefGoogle Scholar
Rouault, M. P., Mestayer, P. G. & Schiestel, R. 1991 A model of evaporating spray droplet dispersion. J. Geophys. Res. 96, 71817200.CrossRefGoogle Scholar
Shpund, J., Pinsky, M. & Khain, A. 2011 Microphysical structure of the marine boundary layer under strong wind and spray formation as seen from simulations using a 2D explicit microphysical model. Part I. The impact of large eddies. J. Atmos. Sci. 68 (10), 23662384.CrossRefGoogle Scholar
Shpund, J., Zhang, J. A., Pinsky, M. & Khain, A. 2012 Microphysical structure of the marine boundary layer under strong wind and spray formation as seen from simulations using a 2D explicit microphysical model. Part II. The role of sea spray. J. Atmos. Sci. 69 (12), 35013514.CrossRefGoogle Scholar
Slinn, S. A. & Slinn, W. G. N. 1980 Prediction for particle deposition on natural waters. Atmos. Environ. 14 (9), 10131016.CrossRefGoogle Scholar
Smith, M. H., Park, P. M. & Consterdine, I. E. 1993 Marine aerosol concentration and estimated fluxes over the sea. Q. J. R. Meteorol. Soc. 119, 809824.CrossRefGoogle Scholar
Spiel, D. E. 1995 On the births of jet drops from bubbles bursting on water surfaces. J. Geophys. Res. 100 (C3), 49955006.CrossRefGoogle Scholar
Spiel, D. E. 1997 More on the births of jet drops from bubbles bursting on seawater surfaces. J. Geophys. Res. 102 (C3), 58155821.CrossRefGoogle Scholar
Spiel, D. E. 1998 On the births of film drops from bubbles bursting on seawater surfaces. J. Geophys. Res. 103 (C11), 2490724918.CrossRefGoogle Scholar
Terray, E. A., Donelan, M. A., Agrawal, Y. C., Drennan, W. M., Kahama, K. K., Williams, A. J. III, Hwang, P. A. & Kitaigorodskii, S. A. 1996 Estimates of kinetic energy dissipation under breaking waves. J. Phys. Oceanogr. 26, 792807.2.0.CO;2>CrossRefGoogle Scholar
Thorpe, S. A. 1993 Energy loss by breaking waves. J. Phys. Oceanogr. 23, 24982502.2.0.CO;2>CrossRefGoogle Scholar
Troitskaya, Y., Kandaurov, A., Ermakova, O., Kozlov, D., Sergeev, D. & Zilitinkevich, S. 2018 The bag breakup spume droplet generation mechanism at high winds. Part I. Spray generation function. J. Phys. Oceanogr. 48 (9), 21672188.CrossRefGoogle Scholar
Van Eijk, A. M. J., Tranchant, B. S. & Mestayer, P. G. 2001 Seacluse: numerical simulation of evaporating sea spray droplets. J. Geophys. Res. 106, 25732588.CrossRefGoogle Scholar
Veron, F. 2015 Ocean spray. Annu. Rev. Fluid Mech. 47, 507538.CrossRefGoogle Scholar
Veron, F., Hopkins, C., Harrison, E. L. & Mueller, J. A. 2012 Sea spray spume droplet production in high wind speeds. Geophys. Res. Lett. 39 (16), L16602.CrossRefGoogle Scholar
Veron, F. & Melville, W. K. 2001 Experiments on the stability and transition of wind-driven water surfaces. J. Fluid Mech. 446, 2565.CrossRefGoogle Scholar
Walls, P. L. L., Henaux, L. & Bird, J. C. 2015 Jet drops from bursting bubbles: how gravity and viscosity couple to inhibit droplet production. Phys. Rev. E 92 (2), 021002.Google ScholarPubMed
Wang, X., Deane, G. B., Moore, K. A., Ryder, O. S., Stokes, M. D., Beall, C. M., Collins, D. B., Santander, M. V., Burrows, S. M., Sultana, C. M. et al. 2017 The role of jet and film drops in controlling the mixing state of submicron sea spray aerosol particles. Proc. Natl Acad. Sci. USA 114 (27), 69786983.CrossRefGoogle ScholarPubMed
Wu, J. 2002 Jet drops produced by bubbles bursting at the surface of seawater. J. Phys. Oceanogr. 32, 32863290.2.0.CO;2>CrossRefGoogle Scholar
Zhang, J. A., Black, P. G., French, J. R. & Drennan, W. M. 2008 First direct measurements of enthalpy flux in the hurricane boundary layer: the CBLAST results. Geophys. Res. Lett. 35 (14), L14813.CrossRefGoogle Scholar