Abstract
The impacts of surface waves on the steady near-surface wind profiles in the marine atmospheric boundary layer (ABL) are studied based on the Ekman theory, modified by introducing a wave-induced component on the total stress. An analytic solution is presented for the wave-modified Ekman model for an eddy viscosity coefficient varying linearly with height. The solution can be determined by the two-dimensional wavenumber spectrum of ocean waves, the wave-growth or decay rate, the geostrophic wind velocity, the Coriolis parameter and the densities of air and water. Wind profiles are calculated as examples for two cases: one with a monochromatic wave and the other with a fully-developed wind-generated sea. The effects of the surface waves on the wind profiles in the marine ABL are illustrated, and solutions proposed are compared with those of the model where the wave-induced stress is neglected. The solutions are also compared with observations from a tower on Östergarnsholm Island in the Baltic Sea. Illustrative examples and the comparisons between observations and the theoretical predictions demonstrate that the surface waves have a considerable impact, not only on the near-surface mean wind profile, but also on the turbulence structure of the marine ABL, as they change qualitatively the structure of the ABL.







Similar content being viewed by others
References
Belcher SE, Hunt JCR (1993) Turbulent shear flow over slowly moving waves. J Fluid Mech 251:109–148
Benilov AY, Kuznetsov OA, Panin GN (1974) On the analysis of wind wave-induced disturbances in the atmospheric turbulent surface layer. Boundary-Layer Meteorol 6:269–285
Davidson KL, Frank AJ (1973) Wave-related fluctuations in the airflow above natural waves. J Phys Oceanogr 3:102–119
Donelan MA, Pierson WJP (1987) Radar scattering and equilibrium ranges in wind-generated waves with application to scatterometry. J Geophys Res 92:4971–5029
Donelan MA, Drennan WM, Katsaros KB (1997) The air-sea momentum flux in conditions of wind sea and swell. J Phys Oceanogr 27:2087–2099
Edson JB, Fairall CW (1998) Similarity relationships in the marine atmospheric surface layer for terms in the TKE and scalar variance budgets. J Atmos Sci 55:2311–2328
Grachev AA, Fairall CW (2001) Upward momentum transfer in the marine boundary layer. J Phys Oceanogr 31:1698–1711
Grachev AA, Fairall CW, Hare JE, Edson JB, Miller SD (2003) Wind stress vector over ocean waves. J Phys Oceanogr 33:2408–2429
Hanley KE, Belcher SE (2008) Wave-driven wind jets in the marine atmospheric boundary layer. J Atmos Sci 65:2646–2660
Harris DL (1966) The wave-driven wind. J Atmos Sci 23:688–693
Hasselmann S, Hasselmann K, Komen GK, Janssen P, Ewing JA, Cardone V (1988) The WAM model—a third generation ocean wave prediction model. J Phys Oceanogr 18:1775–1810
Högström U, Smedman A, Sahleé E, Drennan WM, Kahma KK, Pettersson H, Zhang F (2009) The atmospheric boundary layer during swell—a field study and interpretation of the turbulent kinetic energy budget for high wave ages. J Atmos Sci 66:2764–2779
Holland JZ, Chen W, Almazon JA, Elder FC (1981) Atmospheric boundary layer. In: Aubert EJ, Richards TL (eds) IFYGL: The International Field Year for the Great Lakes. NOAA, Ann Arbor, pp 109–167
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 81:5245–5248
Hristov TS, Miller SD, Friehe CA (2003) Dynamical coupling of wind and ocean waves through wave-induced air flow. Nature 422:55–58
Janssen PAEM (1989) Wave-induced stress and the drag of air flow over sea waves. J Phys Oceanogr 19:745–754
Kudryavtsev VN, Makin VK (2004) Impact of swell on marine atmospheric boundary layer. J Phys Oceanogr 34:934–949
Lewis DM, Belcher SE (2004) Time-dependent, coupled, Ekman boundary layer solutions incorporating Stokes drift. Dyn Atmos Oceans 37:313–351
Makin VK (2008) On the possible impact of a following-swell on the atmospheric boundary layer. Boundary-Layer Meteorol 129:469–478
Makin VK, Mastenbroek C (1996) Fluxes of momentum and heat above waves. In: Donelan MA, Hui WH, Plant WJ (eds) The air–sea interface. The University of Toronto Press, Toronto, pp 475–480
Makin VK, Kudryavtsev VN, Mastenbroek C (1995) Drag of the sea surface. Boundary-Layer Meteorol 73:159–182
Miller S, Friehe C, Hristov T, Edson J, Wetzel S (1999) Wind and turbulent profiles in the surface layer over ocean waves. In: Sajjadi SG, Thomas NH, Hunt JCR (eds) Wind-over-wave couplings. Oxford University Press, Oxford, pp 91–98
Rutgersson A, Smedman A-S, Högström U (2001) Use of conventional stability parameters during swell. J Geophys Res 106:27 117–27 134
Semedo A, Saetra Ø, Rutgersson A, Kahma KK, Pettersson H (2009) Wave-induced wind in the marine boundary layer. J Atmos Sci 66:2256–2271
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 68:2366–2384
Smedman A, Högström U, Sahlée E, Drennan WM, Kahma KK, Pettersson H, Zhang F (2009) Observational study of marine atmospheric boundary layer characteristics during swell. J Atmos Sci 66:2747–2763
Smedman AS, Tjernström M, Högström U (1994) The near neutral marine atmospheric boundary layer with no surface shearing stress: a case study. J Atmos Sci 51:3399–3411
Smedman AS, Högström U, Bergström H, Rutgersson A, Kahma KK, Pettersson H (1999) A case study of air–sea interaction during swell conditions. J Geophys Res 104:25 833–25 851
Smith SD (1992) Sea surface wind stress and drag coefficients: the HEXOS results. Boundary-Layer Meteorol 60:109–142
Song JB (2009) The effects of random surface waves on the steady Ekman current solutions. Deep-Sea Res Part I 56(5):659–671
Sullivan PP, McWilliams JC, Melville WK (2004) The oceanic boundary layer driven by wave breaking with stochastic variability. Part 1. Direct numerical simulations. J Fluid Mech 507:143–174
Sullivan PP, Edson JB, Hristov T, McWilliams JC (2008) Large eddy simulations and observations of atmospheric marine boundary layers above nonequilibrium surface waves. J Atmos Sci 65:1225–1245
Veron F, Melville WK, Lenain L (2008) Wave-coherent air–sea heat flux. J Phys Oceanogr 38:788–802
Volkov YA (1970) Turbulent flux of momentum and heat in the atmospheric surface layer over a disturbed sea surface. Izv Atmos Oceanic Phys 6:734–770
Acknowledgments
The research was supported by the National Basic Research Programs of China (Nos. 2011CB403501), the Strategic Priority Research Program of the Chinese Academy of Sciences (No. XDA11010104) and the National Natural Science Foundation of China (No. 41176016).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Song, J., Fan, W., Li, S. et al. Impact of Surface Waves on the Steady Near-Surface Wind Profiles over the Ocean. Boundary-Layer Meteorol 155, 111–127 (2015). https://doi.org/10.1007/s10546-014-9983-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10546-014-9983-6