Hostname: page-component-8448b6f56d-sxzjt Total loading time: 0 Render date: 2024-04-24T16:07:22.365Z Has data issue: false hasContentIssue false
  • English
  • Français

Direct numerical simulation of scalar transport in turbulent flows over progressive surface waves

Published online by Cambridge University Press:  18 April 2017

Di Yang  and
Lian Shen Open the ORCID record for Lian Shen [Opens in a new window]
Di Yang
Affiliation:
Department of Mechanical Engineering, University of Houston, Houston, TX 77204, USA
Lian Shen*
Affiliation:
Department of Mechanical Engineering and St. Anthony Falls Laboratory, University of Minnesota, Minneapolis, MN 55455, USA
*
†Email address for correspondence: shen@umn.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

The transport of passive scalars in turbulent flows over progressive water waves is studied using direct numerical simulation. A combined pseudo-spectral and finite-difference scheme on a wave-surface-fitted grid is used to simulate the flow and scalar fields above the wave surface. Three representative wave ages (i.e. wave-to-wind speed ratios) are considered, corresponding to slow, intermediate and fast wind-waves, respectively. For each wave condition, four Schmidt numbers are considered for the scalar transport. The presence of progressive surface waves is found to induce significant wave-phase-correlated variation to the scalar field, with the phase dependence varying with the wave age. The time- and plane-averaged profiles of the scalar over waves of various ages exhibit similar vertical structures as those found in turbulence over a flat wall, but with the von Kármán constant and effective wave surface roughness for the mean scalar profile exhibiting considerable variation with the wave age. The profiles of the root-mean-square scalar fluctuations and the horizontal scalar flux exhibit good scaling in the viscous sublayer that agrees with the scaling laws previously reported for flat-wall turbulence, but with noticeable wave-induced variation in the viscous wall region. The profiles of the vertical scalar flux in the viscous sublayer exhibit apparent discrepancies from the reported scaling law for flat-wall turbulence, due to a negative vertical flux region above the windward face of the wave crest. Direct observation and quadrant-based conditional averages indicate that the wave-dependent distributions of the scalar fluctuations and fluxes are highly correlated with the coherent vortical structures in the turbulence, which exhibit clear wave-dependent characteristics in terms of both shape and preferential location.

JFM classification

Turbulent Flows: Turbulent boundary layers Turbulent Flows: Turbulence simulation
Type
Papers
Information
Journal of Fluid Mechanics , Volume 819 , 25 May 2017 , pp. 58 - 103
Check for updates
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

Anderson, D. A., Tannehill, J. C. & Pletcher, R. H. 1984 Computational Fluid Mechanics and Heat Transfer. McGraw Hill.Google Scholar
Antonia, R. A. & Kim, J. 1991 Turbulent Prandtl number in the near-wall region of a turbulent channel flow. Intl J. Heat Mass Transfer 34, 1905–1908.CrossRefGoogle Scholar
Aydin, E. M. & Leutheusser, H. J. 1991 Plane-Couette flow between smooth and rough walls. Exp. Fluids 11, 302–312.Google Scholar
Banner, M. L. & Melville, W. K. 1976 On the separation of air flow over water waves. J. Fluid Mech. 77, 825–842.Google Scholar
Belcher, S. E. & Hunt, J. C. R. 1998 Turbulent flow over hills and waves. Annu. Rev. Fluid Mech. 30, 507–538.CrossRefGoogle Scholar
Bourassa, M. A., Vincent, D. G. & Wood, W. L. 1999 A flux parameterization including the effects of capillary waves and sea state. J. Atmos. Sci. 56, 1123–1139.2.0.CO;2>CrossRefGoogle Scholar
Buckley, M. P. & Veron, F. 2016 Structure of the airflow above surface waves. J. Phys. Oceanogr. 46, 1377–1397.CrossRefGoogle Scholar
Charnock, H. 1955 Wind stress on a water surface. Q. J. R. Meteorol. Soc. 81, 639–640.Google Scholar
Choi, H. S. & Suzuki, K. 2005 Large eddy simulation of turbulent flow and heat transfer in a channel with one wavy wall. Intl J. Heat Fluid Flow 26, 681–694.CrossRefGoogle Scholar
Craft, T. J. & Launder, B. E. 1996 A Reynolds stress closure designed for complex geometries. Intl J. Heat Fluid Flow 17, 245–254.CrossRefGoogle Scholar
De Angelis, V., Lombardi, P. & Banerjee, S. 1997 Direct numerical simulation of turbulent flow over a wavy wall. Phys. Fluids 9, 2429–2442.CrossRefGoogle Scholar
Dean, R. G. & Dalrymple, R. A. 1991 Water Wave Mechanics for Engineers and Scientists. World Scientific.CrossRefGoogle Scholar
Debusschere, B. & Rutland, C. J. 2004 Turbulent scalar transport mechanisms in plane channel and Couette flows. Intl. J. Heat Mass Transfer 47, 1771–1781.CrossRefGoogle Scholar
DeCosmo, J., Katsaros, K. B., Smith, S. D., Anderson, R. J., Oost, W. A., Bumke, K. & Chadwick, H. 1996 Air–sea exchange of water vapor and sensible heat: the humidity exchange of the sea experiment (HEXOS) results. J. Geophys. Res. 101 (C5), 12001–12016.CrossRefGoogle Scholar
Dellil, A. Z., Azzi, A. & Jubran, B. A. 2004 Turbulent flow and convective heat transfer in a wavy wall channel. Heat Mass Transfer 40, 793–799.Google Scholar
Dommermuth, D. G. & Yue, D. K. P. 1987 A high-order spectral method for the study of nonlinear gravity waves. J. Fluid Mech. 184, 267–288.CrossRefGoogle Scholar
Donelan, M. A. 1990 Air-sea interaction. In The Sea (ed. LeMehaute, B. & Hanes, D. M.), vol. 9, pp. 239–292. Wiley-Interscience.Google Scholar
Donelan, M. A., Babanin, A. V., Young, I. R. & Banner, M. L. 2006 Wave-follower field measurements of the wind-input spectral function. Part II. Parameterization of the wind input. J. Phys. Oceanogr. 36, 1672–1689.Google Scholar
Druzhinin, O. A., Troitskaya, Y. I. & Zilitinkevich, S. S. 2012 Direct numerical simulation of a turbulent wind over a wavy water surface. J. Geophys. Res. 117, C00J05.Google Scholar
Druzhinin, O. A., Troitskayaa, Y. I. & Zilitinkevich, S. S. 2016 Stably stratified airflow over a waved water surface. Part 1: stationary turbulence regime. Q. J. R. Meteorol. Soc. 142, 759–772.CrossRefGoogle Scholar
Eckelmann, H. 1974 The structure of the viscous sublayer and the adjacent wall region in a turbulent channel flow. J. Fluid Mech. 65, 439–459.CrossRefGoogle 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, 342–356.Google Scholar
Edson, J. B., Zappa, C. J., Ware, J. A., McGillis, W. R. & Hare, J. E. 2004 Scalar flux profile relationships over the open ocean. J. Geophys. Res. 109, C08S09.Google Scholar
El Telbany, M. M. M. & Reynolds, A. J. 1982 The structure of turbulent plane Couette. Trans. ASME J. Fluids Engng 104, 367–372.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, 3747–3764.Google Scholar
Gent, P. R. & Taylor, P. A. 1976 A numerical model of the air flow above water waves. J. Fluid Mech. 77, 105–128.CrossRefGoogle Scholar
Gent, P. R. & Taylor, P. A. 1977 A note on ‘separation’ over short wind waves. Boundary-Layer Meteorol. 11, 65–87.CrossRefGoogle 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
Hasegawa, Y. & Kasagi, N. 2008 Systematic analysis of high Schmidt number turbulent mass transfer across clean, contaminated and solid interfaces. Intl J. Heat Fluid Flow 29, 765–773.Google Scholar
Hoyas, S. & Jiménez, J. 2006 Scaling of the velocity fluctuations in turbulent channels up to Re 𝜏 = 2003. Phys. Fluids 18, 011702.CrossRefGoogle 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.CrossRefGoogle ScholarPubMed
Jähne, B. & Haußecker, H. 1998 Air–water gas exchange. Annu. Rev. Fluid Mech. 30, 443–468.CrossRefGoogle Scholar
Jeong, J. & Hussain, F. 1995 On the identification of a vortex. J. Fluid Mech. 285, 69–94.CrossRefGoogle Scholar
Johnson, H. K., Høstrup, J., Vested, H. J. & Larsen, S. E. 1998 On the dependence of sea surface roughness on wind waves. J. Phys. Oceanogr. 28, 1702–1716.2.0.CO;2>CrossRefGoogle Scholar
Kader, B. A. 1981 Temperature and concentration profiles in fully turbulent boundary layers. Intl J. Heat Mass Transfer 24, 1541–1544.Google Scholar
Katsouvas, G. D., Helmis, C. G. & Wang, Q. 2007 Quadrant analysis of the scalar and momentum fluxes in the stable marine atmospheric surface layer. Boundary-Layer Meteorol. 124, 335–360.Google Scholar
Katul, G. G., Sempreviva, A. M. & Cava, D. 2008 The temperature–humidity covariance in the marine surface layer: a one-dimensional analytical model. Boundary-Layer Meteorol. 126, 263–278.CrossRefGoogle Scholar
Kawamura, H., Ohsaka, K., Abe, H. & Yamamoto, K. 1998 DNS of turbulent heat transfer in channel flow with low to medium-high Prandtl number fluid. Intl J. Heat Fluid Flow 19, 482–491.CrossRefGoogle Scholar
Kihara, N., Hanazaki, H., Mizuya, T. & Ueda, H. 2007 Relationship between airflow at the critical height and momentum transfer to the traveling waves. Phys. Fluids 19, 015102.CrossRefGoogle Scholar
Kim, J. & Moin, P 1986 The structure of the vorticity field in turbulent channel flow. Part 2. Study of ensemble-averaged fields. J. Fluid Mech. 162, 339–363.CrossRefGoogle Scholar
Kim, J. & Moin, P. 1989 Transport of passive scalars in a turbulent channel flow. In Turbulent Shear Flows 6 (ed. André, J.-C., Cousteix, J., Durst, F., Launder, B. E., Schmidt, F. W. & Whitelaw, J. H.), pp. 85–96. Springer.Google Scholar
Kim, J., Moin, P. & Moser, R. 1987 Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133–166.Google Scholar
Kitaigorodskii, S. A. & Donelan, M. A. 1984 Wind–wave effects on gas transfer. In Gas Transfer at Water Surfaces (ed. Brutsaert, W. & Jirka, G. H.). Reidel.Google Scholar
Lee, M. & Moser, R. D. 2015 Direct numerical simulation of turbulent channel flow up to Re 𝜏 ≈ 5200. J. Fluid Mech. 774, 416–442.CrossRefGoogle Scholar
Li, P. Y., Xu, D. & Taylor, P. A. 2000 Numerical modeling of turbulent airflow over water waves. Boundary-Layer Meteorol. 95, 397–425.Google Scholar
Lighthill, M. J. 1962 Physical interpretation of the mathematical theory of wave generation by wind. J. Fluid Mech. 14, 385–398.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
Moser, R. D., Kim, J. & Mansour, N. N. 1999 Direct numerical simulation of turbulent channel flow up to Re 𝜏 = 590. Phys. Fluids 11, 943–945.Google Scholar
Na, Y., Papavassiliou, D. V. & Hanratty, T. J. 1999 Use of direct numerical simulation to study the effect of Prandtl number on temperature fields. Intl J. Heat Fluid Flow 20, 187–195.CrossRefGoogle Scholar
Papavassiliou, D. V. & Hanratty, T. J. 1997 Interpretation of large-scale structures observed in a turbulent plane Couette flow. Intl J. Heat Fluid Flow 18, 55–69.Google Scholar
Park, T. S., Choi, H. S. & Suzuki, K. 2004 Nonlinear k–𝜖–f 𝜇 model and its application to the flow and heat transfer in a channel having one undulant wall. Intl J. Heat Mass Transfer 47, 2403–2415.CrossRefGoogle Scholar
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.Google Scholar
Robinson, S. K. 1991 Coherent motions in the turbulent boundary layer. Annu. Rev. Fluid Mech. 23, 601–639.CrossRefGoogle Scholar
Rossi, R. 2010 A numerical study of algebraic flux models for heat and mass transport simulation in complex flows. Intl J. Heat Mass Transfer 53, 4511–4524.Google Scholar
Rutgersson, A. & Sullivan, P. P. 2005 The effect of idealized water waves onthe turbulence structure and kinetic energy budgets in the overlying airflow. Dyn. Atmos. Ocean 38, 147–171.Google Scholar
Schwartz, L. W. 1974 Computer extension and analytic continuation of Stokes’ expansion for gravity waves. J. Fluid Mech. 62, 553–578.CrossRefGoogle Scholar
Shaw, D. A. & Hanratty, T. J. 1977 Turbulent mass transfer to a wall for large Schmidt numbers. AIChE J. 23, 28–37.CrossRefGoogle Scholar
Smith, S. D. 1988 Coefficients for sea surface wind stress, heat flux and wind profiles as a function of wind speed and temperature. J. Geophys. Res. 93, 15467–15472.CrossRefGoogle Scholar
Stewart, R. H. 1970 Laboratory studies of the velocity field over deep-water waves. J. Fluid Mech. 42, 733–754.CrossRefGoogle Scholar
Stokes, G. G. 1847 On the theory of oscillatory waves. Trans. Camb. Phil. Soc. 8, 441–455.Google Scholar
Sullivan, P. P., Edson, J. B., Hristov, T. S. & McWilliams, J. C. 2008 Large-eddy simulations and observations of atmospheric marine boundary layers above nonequilibrium surface waves. J. Atmos. Sci. 65, 1225–1245.CrossRefGoogle Scholar
Sullivan, P. P. & McWilliams, J. C. 2002 Turbulent flow over water waves in the presence of stratification. Phys. Fluids 14, 1182–1194.Google Scholar
Sullivan, P. P. & McWilliams, J. C. 2010 Dynamics of winds and currents coupled to surface waves. Annu. Rev. Fluid Mech. 42, 19–42.CrossRefGoogle Scholar
Sullivan, P. P., McWilliams, J. C. & Moeng, C.-H. 2000 Simulation of turbulent flow over idealized water waves. J. Fluid Mech. 404, 47–85.CrossRefGoogle Scholar
Toba, Y., Smith, S. D. & Ebuchi, N. 2001 Historical drag expressions. In Wind Stress over the Ocean. (ed. Jones, I. S. F. & Toba, Y.), pp. 35–53. Cambridge University Press.Google Scholar
Tseng, Y.-H. & Ferziger, J. H. 2003 A ghost-cell immersed boundary method for flow in complex geometry. J. Comput. Phys. 192, 593–623.Google Scholar
Vinokur, M. 1974 Conservation equations of gas-dynamics in curvilinear coordinate systems. J. Comput. Phys. 14, 105–125.Google Scholar
Wallace, J. M. 2016 Quadrant analysis in turbulence reserach: history and evolution. Annu. Rev. Fluid Mech. 48, 131–158.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., Meneveau, C. & Shen, L. 2014a Effect of downwind swells on offshore wind energy harvesting – a large-eddy simulation study. J. Renew. Energy 70, 11–23.CrossRefGoogle Scholar
Yang, D., Meneveau, C. & Shen, L. 2014b Large-eddy simulation of offshore wind farm. Phys. Fluids 26, 025101.Google Scholar
Yang, D. & Shen, L. 2009 Characteristics of coherent vortical structures in turbulent flows over progressive surface waves. Phys. Fluids 21, 125106.CrossRefGoogle 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
Yang, D. & Shen, L. 2011a Simulation of viscous flows with undulatory boundaries. Part I: basic solver. J. Comput. Phys. 230, 5488–5509.Google Scholar
Yang, D. & Shen, L. 2011b Simulation of viscous flows with undulatory boundaries. Part II: coupling with other solvers for two-fluid computations. J. Comput. Phys. 230, 5510–5531.CrossRefGoogle Scholar
Yang, J. & Balaras, E. 2006 An embedded-boundary formulation for large-eddy simulation of turbulent flows interacting with moving boundaries. J. Comput. Phys. 215, 12–40.Google Scholar
Zang, Y., Street, R. L. & Koseff, J. R. 1994 A non-staggered grid, fractional step method for time-dependent incompressible Navier–Stokes equations in curvilinear coordinates. J. Comput. Phys. 114, 18–33.Google Scholar
Zedler, E. A. & Street, R. L. 2001 Large-eddy simulation of sediment transport: currents over ripples. ASCE J. Hydraul. Engng 127, 444–452.CrossRefGoogle Scholar