Turbulent Transport of Spray Droplets in the Vicinity of Moving Surface Waves

David H. Richter University of Notre Dame, Notre Dame, Indiana

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Anne E. Dempsey University of Notre Dame, Notre Dame, Indiana

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Peter P. Sullivan National Center for Atmospheric Research, Boulder, Colorado

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Abstract

A common technique for estimating the sea surface generation functions of spray and aerosols is the so-called flux–profile method, where fixed-height concentration measurements are used to infer fluxes at the surface by assuming a form of the concentration profile. At its simplest, this method assumes a balance between spray emission and deposition, and under these conditions the concentration profile follows a power-law shape. It is the purpose of this work to evaluate the influence of waves on this power-law theory, as well as investigate its applicability over a range of droplet sizes. Large-eddy simulations combined with Lagrangian droplet tracking are used to resolve the turbulent transport of spray droplets over moving, monochromatic waves at the lower surface. The wave age and the droplet diameter are varied, and it is found that droplets are highly influenced both by their inertia (i.e., their inability to travel exactly with fluid streamlines) and the wave-induced turbulence. Deviations of the vertical concentration profiles from the power-law theory are found at all wave ages and for large droplets. The dynamics of droplets within the wave boundary layer alter their net vertical fluxes, and as a result, estimates of surface emission based on the flux–profile method can yield significant errors. In practice, the resulting implication is that the flux–profile method may unsuitable for large droplets, and the combined effect of inertia and wave-induced turbulence is responsible for the continued spread in their surface source estimates.

© 2019 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: David H. Richter, david.richter.26@nd.edu

Abstract

A common technique for estimating the sea surface generation functions of spray and aerosols is the so-called flux–profile method, where fixed-height concentration measurements are used to infer fluxes at the surface by assuming a form of the concentration profile. At its simplest, this method assumes a balance between spray emission and deposition, and under these conditions the concentration profile follows a power-law shape. It is the purpose of this work to evaluate the influence of waves on this power-law theory, as well as investigate its applicability over a range of droplet sizes. Large-eddy simulations combined with Lagrangian droplet tracking are used to resolve the turbulent transport of spray droplets over moving, monochromatic waves at the lower surface. The wave age and the droplet diameter are varied, and it is found that droplets are highly influenced both by their inertia (i.e., their inability to travel exactly with fluid streamlines) and the wave-induced turbulence. Deviations of the vertical concentration profiles from the power-law theory are found at all wave ages and for large droplets. The dynamics of droplets within the wave boundary layer alter their net vertical fluxes, and as a result, estimates of surface emission based on the flux–profile method can yield significant errors. In practice, the resulting implication is that the flux–profile method may unsuitable for large droplets, and the combined effect of inertia and wave-induced turbulence is responsible for the continued spread in their surface source estimates.

© 2019 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: David H. Richter, david.richter.26@nd.edu
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  • Andreas, E. L, J. B. Edson, E. C. Monahan, M. P. Rouault, and S. D. Smith, 1995: The spray contribution to net evaporation from the sea: A review of recent progress. Bound.-Layer Meteor., 72, 352, https://doi.org/10.1007/BF00712389.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Andreas, E. L, L. Mahrt, and D. Vickers, 2015: An improved bulk air-sea surface flux algorithm, including spray-mediated transfer. Quart. J. Roy. Meteor. Soc., 141, 642654, https://doi.org/10.1002/qj.2424.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Balachandar, S., and J. K. Eaton, 2010: Turbulent dispersed multiphase flow. Annu. Rev. Fluid Mech., 42, 111133, https://doi.org/10.1146/annurev.fluid.010908.165243.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Banner, M. L., 1990: The influence of wave breaking on the surface pressure distribution in wind–wave interactions. J. Fluid Mech., 211, 463495, https://doi.org/10.1017/S0022112090001653.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Belcher, S. E., and J. C. R. Hunt, 1998: Turbulent flow over hills and waves. Annu. Rev. Fluid Mech., 30, 507538, https://doi.org/10.1146/annurev.fluid.30.1.507.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Blanchard, D. C., A. H. Woodcock, and R. J. Cipriano, 1984: The vertical distribution of the concentration of sea salt in the marine atmosphere near Hawaii. Tellus, 36B, 118125, https://doi.org/10.1111/j.1600-0889.1984.tb00233.x.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Buckles, J., T. J. Hanratty, and R. J. Adrian, 1984: Turbulent flow over large-amplitude wavy surfaces. J. Fluid Mech., 140, 2744, https://doi.org/10.1017/S0022112084000495.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Buckley, M. P., and F. Veron, 2016: Structure of the airflow above surface waves. J. Phys. Oceanogr., 46, 13771397, https://doi.org/10.1175/JPO-D-15-0135.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • De Angelis, V., P. Lombardi, and S. Banerjee, 1997: Direct numerical simulation of turbulent flow over a wavy wall. Phys. Fluids, 9, 2429, https://doi.org/10.1063/1.869363.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Deike, L., W. K. Melville, and S. Popinet, 2016: Air entrainment and bubble statistics in breaking waves. J. Fluid Mech., 801, 91129, https://doi.org/10.1017/jfm.2016.372.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • de Leeuw, G., 1986: Vertical profiles of giant particles close above the sea surface. Tellus, 38B, 5161, https://doi.org/10.1111/j.1600-0889.1986.tb00087.x.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • de Leeuw, G., E. L Andreas, M. D. Anguelova, C. W. Fairall, E. R. Lewis, C. D. O’Dowd, M. Schulz, and S. E. Schwartz, 2011: Production flux of sea spray aerosol. Rev. Geophys., 49, RG2001, https://doi.org/10.1029/2010RG000349.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Derakhti, M., and J. T. Kirby, 2014: Bubble entrainment and liquid-bubble interaction under unsteady breaking waves. J. Fluid Mech., 761, 464506, https://doi.org/10.1017/jfm.2014.637.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Druzhinin, O. A., Y. I. Troitskaya, and S. S. Zilitinkevich, 2012: Direct numerical simulation of a turbulent wind over a wavy water surface. J. Geophys. Res., 117, C00J05, https://doi.org/10.1029/2011JC007789.

    • Search Google Scholar
    • Export Citation
  • Druzhinin, O. A., Y. I. Troitskaya, and S. S. Zilitinkevich, 2017: The study of droplet-laden turbulent airflow over waved water surface by direct numerical simulation. J. Geophys. Res. Oceans, 122, 17891807, https://doi.org/10.1002/2016JC012134.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Druzhinin, O. A., Y. I. Troitskaya, and S. S. Zilitinkevich, 2018: The study of momentum, mass, and heat transfer in a droplet-laden turbulent airflow over a waved water surface by direct numerical simulation. J. Geophys. Res. Oceans, 123, 83468365, https://doi.org/10.1029/2018JC014346.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Edson, J. B., and C. W. Fairall, 1994: Spray droplet modeling: 1. Lagrangian model simulation of the turbulent transport of evaporating droplets. J. Geophys. Res., 99, 25 29525 311, https://doi.org/10.1029/94JC01883.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Edson, J. B., and Coauthors, 2013: On the exchange of momentum over the open ocean. J. Phys. Oceanogr., 43, 15891610, https://doi.org/10.1175/JPO-D-12-0173.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Fairall, C. W., M. L. Banner, W. L. Peirson, W. Asher, and R. P. Morison, 2009: Investigation of the physical scaling of sea spray spume droplet production. J. Geophys. Res., 114, C10001, https://doi.org/10.1029/2008JC004918.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Fischer, H. B., 1973: Longitudinal dispersion and turbulent mixing in open-channel flow. Annu. Rev. Fluid Mech., 5, 5978, https://doi.org/10.1146/annurev.fl.05.010173.000423.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Freire, L. S., M. Chamecki, and J. A. Gillies, 2016: Flux-profile relationship for dust concentration in the stratified atmospheric surface layer. Bound.-Layer Meteor., 160, 249267, https://doi.org/10.1007/s10546-016-0140-2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Grachev, A. A., and C. W. Fairall, 2001: Upward momentum transfer in the marine boundary layer. J. Phys. Oceanogr., 31, 16981711, https://doi.org/10.1175/1520-0485(2001)031<1698:UMTITM>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Grare, L., L. Lenain, and W. Melville, 2013: Wave-coherent airflow and critical layers over ocean waves. J. Phys. Oceanogr., 43, 21562172, https://doi.org/10.1175/JPO-D-13-056.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hara, T., and P. P. Sullivan, 2015: Wavy boundary layer turbulence over surface waves in a strongly forced condition. J. Phys. Oceanogr., 45, 868883, https://doi.org/10.1175/JPO-D-14-0116.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Helgans, B., and D. H. Richter, 2016: Turbulent latent and sensible heat flux in the presence of evaporative droplets. Int. J. Multiph. Flow, 78, 111, https://doi.org/10.1016/j.ijmultiphaseflow.2015.09.010.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hoppel, W. A., G. M. Frick, and J. W. Fitzgerald, 2002: Surface source function for sea-salt aerosol and aerosol dry deposition to the ocean surface. J. Geophys. Res., 107, 4382, https://doi.org/10.1029/2001JD002014.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hristov, T. S., S. D. Miller, and C. A. Friehe, 2003: Dynamical coupling of wind and ocean waves through. Nature, 422, 5558, https://doi.org/10.1038/nature01382.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Jiang, Q., P. P. Sullivan, S. Wang, J. Doyle, and L. Vincent, 2016: Impact of swell on air–sea momentum flux and marine boundary layer under low-wind condition. J. Atmos. Sci., 73, 26832697, https://doi.org/10.1175/JAS-D-15-0200.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Jones, K. F., and E. L Andreas, 2012: Sea spray concentrations and the icing of fixed offshore structures. Quart. J. Roy. Meteor. Soc., 138, 131144, https://doi.org/10.1002/qj.897.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kind, R. J., 1992: One-dimensional aeolian suspension above beds of loose particles - A new concentration-profile equation. Atmos. Environ., 26A, 927931, https://doi.org/10.1016/0960-1686(92)90250-O.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Komori, S., K. Iwano, N. Takagaki, R. Onishi, R. Kurose, K. Takahashi, and N. Suzuki, 2018: Laboratory measurements of heat transfer and drag coefficients at extremely high wind speeds. J. Phys. Oceanogr., 48, 959974, https://doi.org/10.1175/JPO-D-17-0243.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kudryavtsev, V. N., and V. K. Makin, 2001: The impact of air-flow separation on the drag of the sea surface. Bound.-Layer Meteor., 98, 155171, https://doi.org/10.1023/A:1018719917275.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lenain, L., and W. K. Melville, 2017: Evidence of sea-state dependence of aerosol concentration in the marine atmospheric boundary layer. J. Phys. Oceanogr., 47, 6984, https://doi.org/10.1175/JPO-D-16-0058.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lewis, E. R., and S. E. Schwartz, 2004: Sea Salt Aerosol Production: Mechanisms, Methods, Measurements, and Models: A Critical Review. Geophys. Monogr., Vol. 152, Amer. Geophys. Union, 413 pp.

    • Crossref
    • Export Citation
  • Marchioli, C., V. Armenio, M. V. Salvetti, and A. Soldati, 2006: Mechanisms for deposition and resuspension of heavy particles in turbulent flow over wavy interfaces. Phys. Fluids, 18, 025102, https://doi.org/10.1063/1.2166453.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Mestayer, P., and C. Lefauconnier, 1988: Spray droplet generation, transport, and evaporation in a wind wave tunnel during the humidity exchange over the sea experiments in the simulation tunnel. J. Geophys. Res., 93, 572586, https://doi.org/10.1029/JC093iC01p00572.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Miles, J. W., 1957: On the generation of surface waves by shear flows. J. Fluid Mech., 3, 185204, https://doi.org/10.1017/S0022112057000567.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Moeng, C.-H., 1984: A large-eddy-simulation model for the study of planetary boundary-layer turbulence. J. Atmos. Sci., 41, 20522062, https://doi.org/10.1175/1520-0469(1984)041<2052:ALESMF>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Monahan, E. C., 1968: Sea spray as a function of low elevation wind speed. J. Geophys. Res., 73, 11271137, https://doi.org/10.1029/JB073i004p01127.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ortiz-Suslow, D. G., B. K. Haus, S. Mehta, and N. J. M. Laxague, 2016: Sea spray generation in very high winds. J. Atmos. Sci., 73, 39753995, https://doi.org/10.1175/JAS-D-15-0249.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Pan, Y., M. Chamecki, and S. A. Isard, 2013: Dispersion of heavy particles emitted from area sources in the unstable atmospheric boundary layer. Bound.-Layer Meteor., 146, 235256, https://doi.org/10.1007/s10546-012-9753-2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Peng, T., and D. Richter, 2017: Influence of evaporating droplets in the turbulent marine atmospheric boundary layer. Bound.-Layer Meteor., 165, 497518, https://doi.org/10.1007/s10546-017-0285-7.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Prandtl, L., 1952: Essentials of Fluid Dynamics with Applications to Hydraulics, Aeronautics, Meteorology, and Other Subjects. Hafner Publishing Company, 452 pp.

  • Reul, N., H. Branger, and J. P. Giovanangeli, 2008: Air flow structure over short-gravity breaking water waves. Bound.-Layer Meteor., 126, 477505, https://doi.org/10.1007/s10546-007-9240-3.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Richter, D. H., and P. P. Sullivan, 2013: Momentum transfer in a turbulent, particle-laden Couette flow. Phys. Fluids, 25, 053304, https://doi.org/10.1063/1.4804391.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Richter, D. H., and M. Chamecki, 2018: Inertial effects on the vertical transport of suspended particles in a turbulent boundary layer. Bound.-Layer Meteor., 167, 235256, https://doi.org/10.1007/s10546-017-0325-3.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Rouse, H., 1937: Modern conceptions of the mechanics of fluid turbulence. Trans. Amer. Soc. Civ. Eng., 102, 463505.

  • Sullivan, P. P., and J. C. McWilliams, 2010: Dynamics of winds and currents coupled to surface waves. Annu. Rev. Fluid Mech., 42, 1942, https://doi.org/10.1146/annurev-fluid-121108-145541.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sullivan, P. P., J. C. McWilliams, and C.-H. Moeng, 1996: A grid nesting method for large-eddy simulation of planetary boundary-layer flows. Bound.-Layer Meteor., 80, 167202, https://doi.org/10.1007/BF00119016.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sullivan, P. P., J. C. McWilliams, and C.-H. Moeng, 2000: Simulation of turbulent flow over idealized water waves. J. Fluid Mech., 404, 4785, https://doi.org/10.1017/S0022112099006965.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sullivan, P. P., J. B. Edson, T. Hristov, and J. C. McWilliams, 2008: Large-eddy simulations and observations of atmospheric marine boundary layers above nonequilibrium surface waves. J. Atmos. Sci., 65, 12251245, https://doi.org/10.1175/2007JAS2427.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sullivan, P. P., J. C. McWilliams, and E. G. Patton, 2014: Large-eddy simulation of marine atmospheric boundary layers above a spectrum of moving waves. J. Atmos. Sci., 71, 40014027, https://doi.org/10.1175/JAS-D-14-0095.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sullivan, P. P., M. L. Banner, R. P. Morison, and W. L. Peirson, 2018a: Impacts of wave age on turbulent flow and drag of steep waves. Procedia IUTAM, 26, 174183, https://doi.org/10.1016/j.piutam.2018.03.017.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sullivan, P. P., M. L. Banner, R. P. Morison, and W. L. Peirson, 2018b: Turbulent flow over steep steady and unsteady waves under strong wind forcing. J. Phys. Oceanogr., 48, 327, https://doi.org/10.1175/JPO-D-17-0118.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tamura, H., W. M. Drennan, C. O. Collins, and H. C. Graber, 2018: Turbulent airflow and wave-induced stress over the ocean. Bound.-Layer Meteor., 169, 4766, https://doi.org/10.1007/s10546-018-0359-1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tang, S., Z. Yang, C. Liu, Y.-H. Dong, and L. Shen, 2017: Numerical study on the generation and transport of spume droplets in wind over breaking waves. Atmosphere, 8, 248, https://doi.org/10.3390/atmos8120248.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Troitskaya, Y., A. Kandaurov, O. Ermakova, D. Kozlov, D. Sergeev, and S. Zilitinkevich, 2017: Bag-breakup fragmentation as the dominant mechanism of sea-spray production in high winds. Sci. Rep., 7, 14, https://doi.org/10.1038/s41598-017-01673-9.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Troitskaya, Y., A. Kandaurov, O. Ermakova, D. Kozlov, D. Sergeev, and S. Zilitinkevich, 2018a: The “Bag Breakup” spume droplet generation mechanism at high winds. Part I: Spray generation function. J. Phys. Oceanogr., 48, 21672188, https://doi.org/10.1175/JPO-D-17-0104.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Troitskaya, Y. I., O. Druzhinin, D. Kozlov, and S. Zilitinkevich, 2018b: The “Bag Breakup” spume droplet generation mechanism at high winds. Part II: Contribution to momentum and enthalpy transfer. J. Phys. Oceanogr., 48, 21892207, https://doi.org/10.1175/JPO-D-17-0105.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Veron, F., 2015: Ocean spray. Annu. Rev. Fluid Mech., 47, 507538, https://doi.org/10.1146/annurev-fluid-010814-014651.

  • Veron, F., C. Hopkins, E. L. Harrison, and J. A. Mueller, 2012: Sea spray spume droplet production in high wind speeds. Geophys. Res. Lett., 39, L16602, https://doi.org/10.1029/2012GL052603.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wanninkhof, R., W. E. Asher, D. T. Ho, C. S. Sweeney, and W. R. McGillis, 2009: Advances in quantifying air-sea gas exchange and environmental forcing. Annu. Rev. Mar. Sci., 1, 213244, https://doi.org/10.1146/annurev.marine.010908.163742.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Weil, J. C., P. P. Sullivan, and C.-H. Moeng, 2004: The use of large-eddy simulations in Lagrangian particle dispersion models. J. Atmos. Sci., 61, 28772887, https://doi.org/10.1175/JAS-3302.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Yang, D., and L. Shen, 2010: Direct-simulation-based study of turbulent flow over various waving boundaries. J. Fluid Mech., 650, 131180, https://doi.org/10.1017/S0022112009993557.

    • Crossref
    • Search Google Scholar
    • Export Citation
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