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Experimental study of three-dimensional turbulence under a free surface

Timothée Jamin*, Michael Berhanu, and Eric Falcon

  • *Contact author: research@timotheejamin.com
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Phys. Rev. Fluids 10, 034608 – Published 21 March, 2025

DOI: https://doi.org/10.1103/PhysRevFluids.10.034608

Abstract

In many environmental flows, an air-water free surface interacts with a turbulent flow in the water phase. To mimic this situation, we propose an original experimental setup, based on the randomly actuated synthetic jet array forcing used to study turbulence with almost no mean flow. By using a central pump connected to jets, we generate a turbulent flow of tunable intensity, with good isotropy and horizontal homogeneity, up to a maximal turbulent Reynolds number of 8800. The aim here is to characterize how turbulence is modified by the presence of a free surface. We show that the free surface affects turbulence for fluid depths smaller than the integral length. We report that the turbulent fluctuations become strongly anisotropic when approaching the free surface. The vertical velocity fluctuations decrease close to the surface whereas the horizontal ones increase, as reported in previous theoretical predictions and numerical observations. We also observe a strong enhancement of the amplitude of the temporal and spatial power spectra of the horizontal velocity at large scales, showing the strengthening of these velocity fluctuations near the free surface. In addition, these behaviors are studied for various levels of turbulence.

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References (70)

  1. S. A. Thorpe, Dynamical processes of transfer at the sea surface, Prog. Oceanogr. 35, 315 (1995).
  2. F. Veron, W. K. Melville, and L. Lenain, Measurements of ocean surface turbulence and wave–turbulence interactions, J. Phys. Oceanogr. 39, 2310 (2009).
  3. H. Herlina and G. H. Jirka, Experiments on gas transfer at the air-water interface induced by oscillating grid turbulence, J. Fluid Mech. 594, 183 (2008).
  4. E. A. Variano and E. A. Cowen, Turbulent transport of a high-Schmidt-number scalar near an air–water interface, J. Fluid Mech. 731, 259 (2013).
  5. H. Herlina and J. G. Wissink, Simulation of air-water interfacial mass transfer driven by high-intensity isotropic turbulence, J. Fluid Mech. 860, 419 (2019).
  6. M. Brocchini and D. H. Peregrine, The dynamics of strong turbulence at free surfaces. Part 1. Description, J. Fluid Mech. 449, 225 (2001).
  7. Y. Pan and S. Banerjee, A numerical study of free-surface turbulence in channel flow, Phys. Fluids 7, 1649 (1995).
  8. L. Shen and D. K. P. Yue, Large-Eddy simulation of free-surface turbulence, J. Fluid Mech. 440, 75 (2001).
  9. H. Yoshimura and I. Fujita, Investigation of free-surface dynamics in an open-channel flow, J. Hydraul. Res. 58, 1 (2019).
  10. S. Kumar, R. Gupta, and S. Banerjee, An experimental investigation of the characteristics of free-surface turbulence in channel flow, Phys. Fluids 10, 437 (1998).
  11. R. Savelsberg and W. van de Water, Turbulence of a free surface, Phys. Rev. Lett. 100, 034501 (2008).
  12. R. Savelsberg and W. van de Water, Experiments on free-surface turbulence, J. Fluid Mech. 619, 95 (2009).
  13. G. Dolcetti, K. V. Horoshenkov, A. Krynkin, and S. J. Tait, Frequency-wavenumber spectrum of the free surface of shallow turbulent flows over a rough boundary, Phys. Fluids 28, 105105 (2016).
  14. B. Perot and P. Moin, Shear-free turbulent boundary layers. Part 1. Physical insights into near-wall turbulence, J. Fluid Mech. 295, 199 (1995).
  15. I. Calmet and J. Maganaudet, Statistical structure of high-Reynolds-number turbulence close to the free surface of an open-channel flow, J. Fluid Mech. 474, 355 (2003).
  16. G. Campagne, J.-B. Cazalbou, L. Joly, and P. Chassaing, The structure of a statistically steady turbulent boundary layer near a free-slip surface, Phys. Fluids 21, 065111 (2009).
  17. H. Herlina and J. G. Wissink, Direct numerical simulation of turbulent scalar transport across a flat surface, J. Fluid Mech. 744, 217 (2014).
  18. O. Flores, J. J. Riley, and A. Horner-Devine, On the dynamics of turbulence near a free surface, J. Fluid Mech. 821, 248 (2017).
  19. L. Shen, D. K. P. Yue, and G. Triantafyllou, Effect of surfactants on free-surface turbulent flows, J. Fluid Mech. 506, 79 (2004).
  20. J. Bodart, J.-B. Cazalbou, and L. Joly, Direct numerical simulation of unsheared turbulence diffusing towards a free-slip or no-slip surface, J. Turbul. 11, 1 (2010).
  21. J. G. Wissink, H. Herlina, Y. Akar, and M. Uhlmann, Effect of surface contamination on interfacial mass transfer rate, J. Fluid Mech. 830, 5 (2017).
  22. J. C. R. Hunt and J. M. R. Graham, Free-stream turbulence near plane boundaries, J. Fluid Mech. 84, 209 (1978).
  23. M. A. C. Teixeira and S. E. Belcher, Dissipation of shear-free turbulence near boundaries, J. Fluid Mech. 422, 167 (2000).
  24. J. Magnaudet, High-Reynolds-number turbulence in a shear-free boundary layer: Revisiting the Hunt-Graham theory, J. Fluid Mech. 484, 167 (2003).
  25. H. Tennekes and J. L. Lumley, A First Course in Turbulence (MIT Press, Cambridge, MA, 1972).
  26. S. B. Pope, Turbulent Flows, 4th ed. (Cambridge University Press, Cambridge, 2006).
  27. C. C. Chickadel, S. A. Talke, A. R. Horner-Devine, and A. T. Jessup, Infrared-based measurements of velocity, turbulent kinetic energy, and dissipation at the water surface in a tidal river, IEEE Geosci. Remote Sens. Lett. 8, 849 (2011).
  28. S. A. Talke, R. Horner-Devine, C. C. Chickadel, and A. T. Jessup, Turbulent kinetic energy and coherent structures in a tidal river, J. Geophys. Res. Oceans 118, 6965 (2013).
  29. B. H. Brumley and G. H. Jirka, Near-surface turbulence in a grid-stirred tank, J. Fluid Mech. 183, 235 (1987).
  30. S. M. Thompson and J. S. Turner, Mixing across an interface due to turbulence generated by an oscillating grid, J. Fluid Mech. 67, 349 (1975).
  31. S. I. Badulin, S. I. Voropayev, A. V. Kulikov, and A. D. Rozenberg, Effect of turbulence on low-amplitude regular gravity waves, Oceanology 28, 429 (1988).
  32. S. P. McKenna and W. R. McGillis, The role of free-surface turbulence and surfactants in air–water gas transfer, Int. J. Heat Mass Transf. 47, 539 (2004).
  33. L. Chiapponi, S. Longo, and M. Tonelli, Experimental study on oscillating grid turbulence and free surface fluctuation, Exp. Fluids 53, 1515 (2012).
  34. E. A. Variano and E. A. Cowen, A random-jet-stirred turbulence tank, J. Fluid Mech. 604, 1 (2008).
  35. S. P. McKenna, Free-surface turbulence and air-water gas exchange, Ph.D. thesis, Massachusetts Institute of Technology, 2000.
  36. S. Douady, Y. Couder, and M. E. Brachet, Direct observation of the intermittency of intense vorticity filaments in turbulence, Phys. Rev. Lett. 67, 983 (1991).
  37. S. Fauve, C. Laroche, and B. Castaing, Pressure fluctuations in swirling turbulent flows, J. Phys. II 3, 271 (1993).
  38. F. Ravelet, A. Chiffaudel, and F. Daviaud, Supercritical transition to turbulence in an inertially driven von Kármán closed flow, J. Fluid Mech. 601, 339 (2008).
  39. A. Cazaubiel, J.-B. Gorce, J.-C. Bacri, M. Berhanu, C. Laroche, and E. Falcon, Three-dimensional turbulence generated homogeneously by magnetic particles, Phys. Rev. Fluids 6, L112601 (2021).
  40. J.-B. Gorce and E. Falcon, Statistical equilibrium of large scales in three-dimensional hydrodynamic turbulence, Phys. Rev. Lett. 129, 054501 (2022).
  41. P. Gutiérrez and S. Aumaître, Surface waves propagating on a turbulent flow, Phys. Fluids 28, 025107 (2016).
  42. E. A. Variano, E. Bodenschatz, and E. A. Cowen, A random synthetic jet array driven turbulence tank, Exp. Fluids 37, 613 (2004).
  43. A. Ghazi Nezami, M. Byron, and B. A. Johnson, Laboratory generation of zero-mean-flow homogeneous isotropic turbulence: Non-grid approaches, Flow 3, E42 (2023).
  44. W. Hwang and J. K. Eaton, Creating homogeneous and isotropic turbulence without a mean flow, Exp. Fluids 36, 444 (2004).
  45. G. Bellani and E. A. Variano, Homogeneity and isotropy in a laboratory turbulent flow, Exp. Fluids 55, 1646 (2014).
  46. D. Carter, A. Petersen, O. Amili, and F. Coletti, Generating and controlling homogeneous air turbulence using random jet arrays, Exp. Fluids 57, 189 (2016).
  47. B. A. Johnson and E. A. Cowen, Turbulent boundary layers absent mean shear, J. Fluid Mech. 835, 217 (2018).
  48. L. B. Esteban, J. S. Shrimpton, and B. Ganapathisubramani, Laboratory experiments on the temporal decay of homogeneous anisotropic turbulence, J. Fluid Mech. 862, 127 (2019).
  49. A. Pérez-Alvarado, L. Mydlarski, and S. Gaskin, Effect of the driving algorithm on the turbulence generated by a random jet array, Exp. Fluids 57, 20 (2016).
  50. J. George, F. Minel, and M. Grisenti, Physical and hydrodynamical parameters controlling gas-liquid mass transfer, Int. J. Heat Mass Transf. 37, 1569 (1994).
  51. F. Minel and J. George, Hydrodynamics in a jet-agitated vessel close to the gas-liquid surface, in Air-Water Gas Transfer, edited by B. Jähne and E. C. Monahan (AEON Verlag & Studio, Hanau, 1995), pp. 665–673.
  52. C. Guo and L. Shen, Interaction of a deformable free surface with statistically steady homogeneous turbulence, J. Fluid Mech. 658, 33 (2010).
  53. S. Delbos, V. Weitbrecht, T. Bleninger, P. Grand, E. Chassaing, D. Lincot, O. Kerrec, and G. Jirka, Homogeneous turbulence at an electrodeposition surface induced by randomly firing jet arrays, Exp. Fluids 46, 1105 (2009).
  54. T. Jamin, Interactions between free-surface waves and hydrodynamic flows, Ph.D. thesis, Université Paris Diderot, 2016.
  55. W. Thielicke and E. Stamhuis, Pivlab – towards user-friendly, affordable and accurate digital particle image velocimetry in matlab, J. Open Res. Software 2, e30 (2014).
  56. H. Tennekes, Eulerian and lagrangian time microscales in isotropic turbulence, J. Fluid Mech. 67, 561 (1975).
  57. U. Frisch, Turbulence: The Legacy of A. N. Kolmogorov (Cambridge University Press, Cambridge, 1995).
  58. C. Bailly and G. Comte-Bellot, Turbulence (Springer, Switzerland, 2015).
  59. K. R. Sreenivasan, On the universality of the kolmogorov constant, Phys. Fluids 7, 2778 (1995).
  60. D. Carter and F. Coletti, Scale-to-scale anisotropy in homogeneous turbulence, J. Fluid Mech. 827, 250 (2017).
  61. A. Sanchis and A. Jensen, Dynamic masking of PIV images using the Radon transform in free surface flows, Exp. Fluids 51, 871 (2011).
  62. T. Jamin, L. Gordillo, G. Ruiz-Chavarría, M. Berhanu, and E. Falcon, Experiments on generation of surface waves by an underwater moving bottom, Proc. R. Soc. A 471, 20150069 (2015).
  63. J. C. R. Hunt, Turbulence structure in thermal convection and shear-free boundary layers, J. Fluid Mech. 138, 161 (1984).
  64. J. Lucassen, Longitudinal capillary waves. Part 1.-Theory, Trans. Faraday Soc. 64, 2221 (1968).
  65. W. G. Van Dorn, Boundary dissipation of oscillatory waves, J. Fluid Mech. 24, 769 (1966).
  66. J. W. Miles, Surface-wave damping in closed basins, Proc. R. Soc. Lond. A 297, 459 (1967).
  67. D. M. Henderson and J. W. Miles, Single-mode faraday waves in small cylinders, J. Fluid Mech. 213, 95 (1990).
  68. J. L. Hammack and D. M. Henderson, Resonant interactions among surface water waves, Annu. Rev. Fluid Mech. 25, 55 (1993).
  69. N. M. Frew, E. J. Bock, U. Schimpf, T. Hara, H. Haußecker, J. B. Edson, W. R. McGillis, R. K. Nelson, S. P. McKenna, B. M. Uz, and B. Jähne, Air–sea gas transfer: Its dependence on wind stress, small–scale roughness, and surface films, J. Geophys. Res. 109, C08S17 (2004).
  70. E. L. G. Kit, E. J. Strang, and H. J. S. Fernando, Measurement of turbulence near shear-free density interfaces, J. Fluid Mech. 334, 293 (1997).

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Phys. Rev. Fluids 10, 034608– Published 21 March, 2025
  • Received 22 January 2024
  • Accepted 5 December 2024
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