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Interaction of a deformable free surface with statistically steady homogeneous turbulence

Published online by Cambridge University Press:  10 June 2010

XIN GUO  and
LIAN SHEN
XIN GUO
Affiliation:
Department of Civil Engineering, Johns Hopkins University, Baltimore, MD 21218, USA
LIAN SHEN*
Affiliation:
Department of Civil Engineering, Johns Hopkins University, Baltimore, MD 21218, USA
*
†Email address for correspondence: [email protected]
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Abstract

Direct numerical simulation is performed for the interaction between a deformable free surface and the homogeneous isotropic turbulent flow underneath. The Navier–Stokes equations subject to fully nonlinear free-surface boundary conditions are simulated by using a pseudospectral method in the horizontal directions and a finite-difference method in the vertical direction. Statistically, steady turbulence is generated by using a linear forcing method in the bulk flow below. Through investigation of cases of different Froude and Weber numbers, the present study focuses on the effect of surface deformation of finite amplitude. It is found that the motion of the free surface is characterized by propagating waves and turbulence-generated surface roughness. Statistics of the turbulence field near the free surface are analysed in detail in terms of fluctuations of velocity, fluctuations of velocity gradients and strain rates and the energy budget for horizontal and vertical turbulent motions. Our results illustrate the effects of surface blockage and vanishing shear stress on the anisotropy of the flow field. Using conditional averaging analysis, it is shown that splats and antisplats play an essential role in energy inter-component exchange and vertical transport.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 658 , 10 September 2010 , pp. 33 - 62
Copyright
Copyright © Cambridge University Press 2010

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References

REFERENCES

Borue, V., Orszag, S. A. & Staroselsky, I. 1995 Interaction of surface waves with turbulence: direct numerical simulations of turbulent open-channel flow. J. Fluid Mech. 286, 1–23.CrossRefGoogle Scholar
Brocchini, M. 2002 Free surface boundary conditions at a bubbly/weakly splashing air–water interface. Phys. Fluids 14, 1834–1840.CrossRefGoogle Scholar
Brocchini, M. & Peregrine, D. H. 2001 The dynamics of strong turbulence at free surfaces. Part 2. Free-surface boundary conditions. J. Fluid Mech. 449, 255–290.CrossRefGoogle Scholar
Brumley, B. H. & Jirka, G. H. 1987 Near-surface turbulence in a grid-stirred tank. J. Fluid Mech. 183, 235–263.CrossRefGoogle Scholar
Calmet, I. & Magnaudet, J. 2003 Statistical structure of high-Reynolds-number turbulence close to the free surface of an open-channel flow. J. Fluid Mech. 474, 355–378.CrossRefGoogle Scholar
Dabiri, D. & Gharib, M. 2001 Simultaneous free-surface deformation and near-surface velocity measurements. Exp. Fluids 30, 381–390.CrossRefGoogle Scholar
Dimas, A. A. & Triantafyllou, G. S. 1994 Nonlinear interaction of shear flow with a free surface. J. Fluid Mech. 260, 211–246.CrossRefGoogle Scholar
Dommermuth, D. G. 1994 The initialization of vortical free-surface flows. J. Fluids Engng 116, 95–102.CrossRefGoogle Scholar
Dopazo, C., Lozano, A. & Barreras, F. 2000 Vorticity constraints on a fluid/fluid interface. Phys. Fluids 12, 1928–1931.CrossRefGoogle Scholar
Guo, X. 2010 Simulation-based study of turbulence interacting with a deformable free surface. Master's thesis, Johns Hopkins University, Baltimore, MD.Google Scholar
Guo, X. & Shen, L. 2009 On the generation and maintenance of waves and turbulence in simulations of free-surface turbulence. J. Comput. Phys. 228, 7313–7332.CrossRefGoogle Scholar
Handler, R. A., Swean, T. F. Jr., Leighton, R. I. & Swearingen, J. D. 1993 Length scales and the energy balance for turbulence near a free surface. AIAA J. 31, 1998–2007.CrossRefGoogle Scholar
Harlow, F. H. & Welch, J. E. 1965 Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface. Phys. Fluids 8, 2182–2189.CrossRefGoogle Scholar
Herlina, & Jirka, G. H. 2008 Experiments on gas transfer at the air–water interface induced by oscillating grid turbulence. J. Fluid Mech. 594, 183–208.CrossRefGoogle Scholar
Hinze, J. O. 1959 Turbulence. McGraw-Hill.Google Scholar
Hodges, B. R. & Street, R. L. 1999 On simulation of turbulent nonlinear free-surface flows. J. Comput. Phys. 151, 425–457.CrossRefGoogle Scholar
Hong, W.-L. & Walker, D. T. 2000 Reynolds-averaged equations for free-surface flows with application to high-Froude-number jet spreading. J. Fluid Mech. 417, 183–209.CrossRefGoogle Scholar
Hunt, J. C. R. 1984 Turbulence structure in thermal convection and shear-free boundary layers. J. Fluid Mech. 138, 161–184.CrossRefGoogle Scholar
Hunt, J. C. R. & Graham, J. M. R. 1978 Free-stream turbulence near plane boundaries. J. Fluid Mech. 84, 209–235.CrossRefGoogle Scholar
Jeong, J., Hussain, F., Schoppa, W. & Kim, J. 1997 Coherent structures near the wall in a turbulent channel flow. J. Fluid Mech. 332, 185–214.CrossRefGoogle Scholar
Kang, M., Fedkiw, R. P. & Liu, X.-D. 2000 A boundary condition capturing method for multiphase incompressible flow. J. Sci. Comput. 15, 323–360.CrossRefGoogle Scholar
Kim, J. 1983 On the structure of wall-bounded turbulent flows. Phys. Fluids 26, 2088–2097.CrossRefGoogle Scholar
Kim, J. & Moin, P. 1985 Application of a fractional-step method to incompressible Navier–Stokes equations. J. Comput. Phys. 59, 308–323.CrossRefGoogle Scholar
Kitaigorodskii, S. A. & Lumley, J. L. 1983 Wave–turbulence interactions in the upper ocean. Part I. The energy balance of the interacting fields of surface wind waves and wind-induced three-dimensional turbulence. J. Phys. Oceanogr. 13, 1977–1987.2.0.CO;2>CrossRefGoogle Scholar
Komori, S., Nagaosa, R., Murakami, Y., Chiba, S., Ishii, K. & Kuwahara, K. 1993 Direct numerical simulation of three-dimensional open-channel flow with zero-shear gas–liquid interface. Phys. Fluids A 5, 115–125.CrossRefGoogle Scholar
Kumar, S., Gupta, R. & Banerjee, S. 1998 An experimental investigation of the characteristics of free-surface turbulence in channel flow. Phys. Fluids 10, 437–456.CrossRefGoogle Scholar
Lam, K. & Banerjee, S. 1988 Investigation of turbulent flow bounded by a wall and a free surface. In Fundamentals of Gas–Liquid Flows (ed. Michaelides, E. E. & Sharma, M. P.), pp. 29–38. ASME.Google Scholar
Leighton, R. I., Swean, T. F. Jr., Handler, R. A. & Swearingen, J. D. 1991 Interaction of vorticity with a free surface in turbulent open channel flow. Paper 91–0236. AIAA.CrossRefGoogle Scholar
Longuet-Higgins, M. S. 1998 Vorticity and curvature at a free surface. J. Fluid Mech. 356, 149–153.CrossRefGoogle Scholar
Lugt, H. J. 1987 Local flow properties at a viscous free surface. Phys. Fluids 30, 3647–3652.CrossRefGoogle Scholar
Lundgren, T. 2003 Linearly forced isotropic turbulence. Tech. Rep. 461. Center for Turbulence Research, Stanford, CA.Google Scholar
Lundgren, T. & Koumoutsakos, P. 1999 On the generation of vorticity at a free surface. J. Fluid Mech. 382, 351–366.CrossRefGoogle Scholar
Magnaudet, J. 2003 High-Reynolds-number turbulence in a shear-free boundary layer: revisiting the Hunt–Graham theory. J. Fluid Mech. 484, 167–196.CrossRefGoogle Scholar
McKenna, S. P. & McGillis, W. R. 2004 The role of free-surface turbulence and surfactants in air–water gas transfer. Intl J. Heat Mass Transfer 47, 539–553.CrossRefGoogle Scholar
Nagaosa, R. 1999 Direct numerical simulation of vortex structures and turbulent scalar transfer across a free surface in a fully developed turbulence. Phys. Fluids 11, 1581–1595.CrossRefGoogle Scholar
Nagaosa, R. & Handler, R. A. 2003 Statistical analysis of coherent vortices near a free surface in a fully developed turbulence. Phys. Fluids 15, 375–394.CrossRefGoogle Scholar
Nielsen, P. & Skovgaard, O. 1990 The effect of using non-orthogonal boundary-fitted grids for solving the shallow water equations. Intl J. Numer. Methods Fluids 11, 177–188.CrossRefGoogle Scholar
Olmez, H. S. & Milgram, J. H. 1992 An experimental study of attenuation of short water waves by turbulence. J. Fluid Mech. 239, 133–156.CrossRefGoogle Scholar
Pan, Y. & Banerjee, S. 1995 A numerical study of free-surface turbulence in channel flow. Phys. Fluids 7, 1649–1664.CrossRefGoogle Scholar
Perot, B. & Moin, P. 1995 Shear-free turbulent boundary layers. Part 1. Phyiscal insights into near-wall turbulence. J. Fluid Mech. 295, 199–227.CrossRefGoogle Scholar
Phillips, O. M. 1958 The equilibrium range in the spectrum of wind-generated waves. J. Fluid Mech. 4, 426–434.CrossRefGoogle Scholar
Rashidi, M. 1997 Burst-interface interactions in free surface turbulent flows. Phys. Fluids 9, 3485–3501.CrossRefGoogle Scholar
Rosales, C. & Meneveau, C. 2005 Linear forcing in numerical simulations of isotropic turbulence: physical space implementations and convergence properties. Phys. Fluids 17, 095106.CrossRefGoogle Scholar
Sankaranarayanan, S. & Spaulding, M. L. 2003 A study of the effects of grid non-orthogonality on the solution of shallow water equations in boundary-fitted coordinate systems. J. Comput. Phys. 184, 299–320.CrossRefGoogle Scholar
Sarpkaya, T. 1996 Vorticity, free surface, and surfactants. Annu. Rev. Fluid. Mech. 28, 83–128.CrossRefGoogle Scholar
Savelsberg, R. & van de Water, W. 2009 Experiments on free-surface turbulence. J. Fluid Mech. 619, 95–125.CrossRefGoogle Scholar
Shen, L., Triantafyllou, G. S. & Yue, D. K. P. 2000 Turbulent diffusion near a free surface. J. Fluid Mech. 407, 145–166.CrossRefGoogle Scholar
Shen, L., Yue, D. K. P. & Triantafyllou, G. S. 2004 Effect of surfactants on free-surface turbulent flows. J. Fluid Mech. 506, 79–115.CrossRefGoogle Scholar
Shen, L., Zhang, X., Yue, D. K. P. & Triantafyllou, G. S. 1999 The surface layer for free-surface turbulent flows. J. Fluid Mech. 386, 167–212.CrossRefGoogle Scholar
Smolentsev, S. & Miraghaie, R. 2005 Study of a free surface in open-channel water flows in the regime from ‘weak’ to ‘strong’ turbulence. Intl J. Multiph. Flow 31, 921–939.CrossRefGoogle Scholar
Sullivan, P. P. & Patton, E. G. 2008 A highly parallel algorithm for turbulence simulations in planetary boundary layers: Results with meshes up to 10243. In Eighteenth Conference on Boundary Layer and Turbulence, Stockholm, Sweden, p. 11B.5.Google Scholar
Teixeira, M. A. C. & Belcher, S. E. 2000 Dissipation of shear-free turbulence near boundaries. J. Fluid Mech. 422, 167–191.CrossRefGoogle Scholar
Teixeira, M. A. C. & Belcher, S. E. 2002 On the distortion of turbulence by a progressive surface wave. J. Fluid Mech. 458, 229–267.CrossRefGoogle Scholar
Teixeira, M. A. C. & Belcher, S. E. 2006 On the initiation of surface waves by turbulent shear flow. Dyn. Atmos. Oceans 41, 1–27.CrossRefGoogle Scholar
Tennekes, H. & Lumley, J. L. 1972. A First Course in Turbulence. The MIT press.CrossRefGoogle Scholar
Tryggvason, G. 1988 Deformation of a free surface as a result of vortical flows. Phys. Fluids 31, 955–957.CrossRefGoogle Scholar
Tsai, W.-T. 1998 A numerical study of the evolution and structure of a turbulent shear layer under a free surface. J. Fluid Mech. 354, 239–276.CrossRefGoogle Scholar
Variano, E. A. & Cowen, E. A. 2008 A random-jet-stirred turbulence tank. J. Fluid Mech. 604, 1–32.CrossRefGoogle Scholar
Walker, D. T., Leighton, R. I. & Garza-Rios, L. O. 1996 Shear-free turbulence near a flat free surface. J. Fluid Mech. 320, 19–51.CrossRefGoogle Scholar
Watanabe, Y., Saeki, H. & Hosking, R. J. 2005 Three-dimensional vortex structures under breaking waves. J. Fluid Mech. 545, 291–328.CrossRefGoogle Scholar