Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-25T01:52:02.292Z Has data issue: false hasContentIssue false
  • English
  • Français

The role of wave kinematics in turbulent flow over waves

Published online by Cambridge University Press:  18 October 2019

Espen Åkervik Open the ORCID record for Espen Åkervik [Opens in a new window]  and
Magnus Vartdal Open the ORCID record for Magnus Vartdal [Opens in a new window]
Espen Åkervik*
Affiliation:
Norwegian Defence Research Establishment (FFI), Instituttvn 20, 2007 Kjeller, Norway
Magnus Vartdal
Affiliation:
Norwegian Defence Research Establishment (FFI), Instituttvn 20, 2007 Kjeller, Norway
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The turbulent flow over monochromatic waves of moderate steepness is studied by means of wall resolved large eddy simulations. The simulations cover a range of wave ages and Reynolds numbers. At low wave ages the form drag is highly sensitive to Reynolds number changes, and the interaction between turbulent and wave-induced stresses increases with Reynolds number. At higher wave ages, the flow enters a quasi-laminar regime where wave-induced stresses are primarily balanced by viscous stresses, and the form drag displays a simple Reynolds number dependence. To exploit the quasi-laminar response to the wave kinematics, we split the flow field into a laminar wave-generated response and a turbulent shear flow. The former is driven by the non-homogeneous boundary conditions, whereas the latter is driven by the laminar solution as well as turbulent stresses. For high wave ages, the splitting enables approximate functional dependencies for the form drag to be formulated. In the low wave age regime, where the wave-induced stresses are tightly connected with higher harmonics in the turbulent stresses, the flow is more challenging to analyse. Nevertheless, the importance of higher harmonics in the turbulent stresses can be quantified by explicitly choosing which modes to include in the split-system forcing.

JFM classification

Geophysical and Geological Flows: Air/sea interactions Turbulent Flows: Turbulent boundary layers
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 880 , 10 December 2019 , pp. 890 - 915
Copyright
© 2019 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

Belcher, S. E. & Hunt, J. C. R. 1993 Turbulent shear flow over slowly moving waves. J. Fluid Mech. 251, 109–148.Google Scholar
Belcher, S. E. & Hunt, J. C. R. 1998 Turbulent flows over hills and waves. Annu. Rev. Fluid Mech. 30, 507–538.Google Scholar
Boyd, J. P. 2001 Chebyshev and Fourier Spectral Methods. Dover.Google Scholar
Buckley, M. P. & Veron, F. 2016 Structure of the airflow above surface waves. J. Phys. Oceanogr. 46 (5), 1377–1397.Google Scholar
Cess, R. D.1958 A survey of the literature on heat transfer in turbulent tube flow. Res. Rep. 8–0529-R24. Westinghouse Research.Google Scholar
Cohen, J. E. & Belcher, S. E. 1999 Turbulent shear flow over fast-moving waves. J. Fluid Mech. 386, 345–371.Google Scholar
Donelan, M. A. 1998 Air–water exchange processes. In Physical Processes in Lakes and Oceans (ed. Imberger, J.), Coastal and Estuarine Studies, vol. 54, pp. 19–36. American Geophysical Union.Google Scholar
Edson, J., Crawford, T., Crescenti, J., Farrar, T., Frew, N., Gerbi, G., Helmis, C., Hristov, T., Khelif, D., Jessup, A. et al. 2007 The coupled boundary layers and air–sea transfer experiment in low winds. Bull. Am. Meteorol. Soc. 88 (3), 341–356.Google Scholar
Gent, P. R. & Taylor, P. A. 1976 A numerical model of the air flow above water waves. J. Fluid Mech. 77 (1), 105–128.Google Scholar
Grare, L., Peirson, W. L., Branger, H., Walker, J. W., Giovanangeli, J.-P. & Makin, V. 2013 Growth and dissipation of wind-forced, deep-water waves. J. Fluid Mech. 722, 5–50.Google Scholar
Ham, F. & Iaccarino, G. 2004 Energy conservation in collocated discretization schemes on unstructured meshes. In CTR Annu. Res. Briefs 2004, pp. 3–14. Center for Turbulence Research.Google Scholar
Ham, F., Mattsson, K. & Iaccarino, G. 2006 Accurate and stable finite volume operators for unstructured flow solvers. In CTR Annu. Res. Briefs 2006, pp. 243–261. Center for Turbulence Research.Google Scholar
Ham, F., Mattsson, K., Iaccarino, G. & Moin, P. 2007 Towards time-stable and accurate LES on unstructured grids. In Complex Effects in Large Eddy Simulations (ed. Kassinos, S. C., Langer, C. A., Iaccarino, G. & Moin, P.), Lecture Notes in Computational Science and Engineering, vol. 56, pp. 235–249. Springer.Google Scholar
Hara, T. & Sullivan, P. P. 2015 Wave boundary layer turbulence over surface waves in a strongly forced condition. J. Phys. Oceanogr. 45, 868–883.Google Scholar
Harrison, W. J. 1908 The influence of viscosity on the oscillations of superposed fluids. Proc. R. Soc. Lond. A 2 (1), 396–405.Google Scholar
Hasselmann, K., Barnett, T. P., Bouws, E., Carlson, H., Cartwright, D. E., Enke, K., Ewing, J. A., Gienapp, H., Hasselmann, D. E., Kruseman, P. et al. 1973 Measurements of wind-wave growth and swell decay during the Joint North Sea Wave Project (JONSWAP). Erg. Deutsch. Hydrogr. Z. 12 (A8), 1–95. Deutches Hydrographisches Institut.Google Scholar
Hoepffner, J., Popinet, S., Lagreé, P. Y., Balestra, G., Gallino, G., Valcke, P., De Guyon, G. & Bernardos, L.2019 Easystab. Available at: http://www.basilisk.fr/sandbox/easystab/README.Google 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), 5245–5248.Google Scholar
Hristov, T. S., Miller, S. D. & Friehe, C. A. 2003 Dynamical coupling of wind and ocean waves through wave-induced air flow. Nature 422, 55–58.Google Scholar
Hussain, A. K. M. F. & Reynolds, W. C. 1970 The mechanics of an organized wave in turbulent shear flow. J. Fluid Mech. 41, 241–258.Google Scholar
Hussain, A. K. M. F. & Reynolds, W. C. 1972a The mechanics of an organized wave in turbulent shear flow. Part 2. Experimental results. J. Fluid Mech. 54 (2), 241–261.Google Scholar
Hussain, A. K. M. F. & Reynolds, W. C. 1972b The mechanics of an organized wave in turbulent shear flow. Part 3. Theoretical models and comparsion with experiments. J. Fluid Mech. 54, 263–288.Google Scholar
Janssen, P. A. E. M. 1991 Quasi-linear theory of wind-wave generation applied to wave forecasting. J. Phys. Ocean. 21 (11), 1631–1642.Google Scholar
Jeffreys, H. 1925 On the formation of water waves by wind. Proc. R. Soc. Lond. A 107 (742), 189–206.Google Scholar
Kahma, K. K., Donelan, M. A., Drennan, W. M. & Terray, E. A. 2016 Evidence of energy and momentum flux from swell to wind. J. Phys. Oceanogr. 46 (7), 2143–2156.Google Scholar
Kelvin, Lord 1880 On a disturbing infinity in Lord Rayleigh’s solution for waves in a plane vortex stratum. Nature 23, 45–46.Google Scholar
Kihara, N., Mizuya, T. & Ueda, H. 2007 Relationship between airflow at the critical height and momentum transfer to the traveling waves. Phys. Fluids 19, 015102.Google Scholar
Kudryavtsev, V. N. & Makin, V. K. 2004 Impact of swell on the marine atmospheric boundary layer. J. Phys. Oceanogr. 34 (4), 934–949.Google Scholar
Kudryavtsev, V. N., Makin, V. K. & Meirink, J. F. 2001 Simplified model of the air flow above waves. Boundary-Layer Meteorol. 100, 63–90.Google Scholar
Lamb, H. 1932 Hydrodynamics. Cambridge University Press.Google Scholar
Li, P. Y., Xu, D. & Taylor, P. A. 2000 Numerical modelling of turbulent airflow over water waves. Boundary-Layer Meteorol. 95 (3), 397–425.Google Scholar
Mahesh, K., Constantinescu, G. & Moin, P. 2004 A numerical method for large-eddy simulation in complex geometries. J. Comput. Phys. 197, 215–240.Google Scholar
Mastenbroek, C., Makin, V. K., Garat, M. H. & Giovanangeli, J.-P. 1996 Experimental evidence of the rapid distortion of turbulence in the air flow over water waves. J. Fluid Mech. 318, 273–302.Google Scholar
Meirink, J. F. & Makin, V. K. 2000 Modelling low-Reynolds-number effects in the turbulent air flow over water waves. J. Fluid Mech. 415, 155–174.Google Scholar
Miles, J. W. 1957 On the generation of surface waves by shear flows. J. Fluid Mech. 3, 185–204.Google Scholar
Miles, J. W. 1959 On the generation of surface waves by shear flows. Part 2. J. Fluid Mech. 6 (4), 568–582.Google Scholar
Phillips, O. M. 1957 On the generation of waves by turbulent wind. J. Fluid Mech. 2 (5), 417–445.Google Scholar
Plant, W. J. 1982 A relationship between wind stress and wave slope. J. Geophys. Res. Oceans 87 (C3), 1961–1967.Google Scholar
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.Google Scholar
Pujals, G., García-Villalba, M., Cossu, C. & Depardon, S. 2009 A note on optimal transient growth in turbulent channel flows. Phys. Fluids 21, 015109.Google Scholar
Reynolds, W. C. & Tiederman, W. G. 1967 Stability of turbulent channel flow, with application to Malkus’s theory. J. Fluid Mech. 27 (2), 253–272.Google Scholar
Semedo, A., Saetra, Ø, Rutgersson, A., Kahma, K. K. & Pettersson, H. 2009 Wave-induced wind in the marine boundary layer. J. Atmos. Sci. 66 (8), 2256–2271.Google Scholar
Sullivan, P. P., Edson, J. B., Hristov, T. & McWilliams, J. C. 2008 Large-eddy simulations and observations of atmospheric marine boundary layers above nonequillibrium surface waves. J. Atmos. Sci. 65, 1225–1245.Google Scholar
Sullivan, P. P., McWilliams, J. C. & Moeng, C.-H. 2000 Simulation of turbulent flow over idealized waves. J. Fluid Mech. 404, 47–85.Google Scholar
Van Duin, C. A. & Janssen, P. A. E. M. 1992 An analytic model of the generation of surface gravity waves by turbulent air flow. J. Fluid Mech. 236, 197–215.Google Scholar
Weideman, J. A. & Reddy, S. C. 2000 A matlab differentiation matrix suite. ACM Trans. Math. Softw. (TOMS) 26 (4), 465–519.Google Scholar
Yang, D., Meneveau, C. & Shen, L. 2013 Dynamic modelling of sea-surface roughness for large-eddy simulation of wind over ocean wavefield. J. Fluid Mech. 726, 62–99.Google Scholar
Yang, D. & Shen, L. 2009 Characteristics of coherent vortical structures in turbulent flows over progressive waves. Phys. Fluids 21, 125106.Google Scholar
Yang, D. & Shen, L. 2010 Direct-simulation-based study of turbulent flow over various waving boundaries. J. Fluid Mech. 650, 131–180.Google Scholar