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Experimental investigation relating free-surface features to subsurface turbulence

Omer M. Babiker1, Jørgen R. Aarnes1, Ali Semati1, Amélie Ferran1, Yi Hui Tee1,2, R. Jason Hearst1, and Simen Å. Ellingsen1,*

  • *Contact author: simen.a.ellingsen@ntnu.no
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Phys. Rev. Fluids 11, 054802 – Published 18 May, 2026

DOI: https://doi.org/10.1103/bmx7-2z3h

Abstract

Turbulent flows beneath a free surface play a central role in the Earth system, yet their coupling to observable surface features remains incompletely understood. Recent studies using direct numerical simulations (DNS) have reported strong correlation between observable surface features and surface divergence as well as velocity statistics directly beneath, but were limited to Reynolds numbers (Re) far below those typical of natural flows, and do not carry the inherent challenges of measurement and flow fidelity that real flows present. We present a laboratory study in which free-surface topology and subsurface turbulent velocity are measured simultaneously in a jet-stirred tank, extending these numerical results to the physical domain. Using a combination of particle-image velocimetry and free-surface profilometry, we access Re up to two orders of magnitude higher than in the DNS. A computer vision method developed for identifying turbulent imprints on the free surface is successfully applied to experimental data, enabling direct comparison with the DNS. The correlation between time series of mean-squared surface divergence and surface features is found to persist as strongly at higher Reynolds numbers, despite the increased disparity of turbulent scales. Beyond the thin viscous layer, all surface-to-bulk correlations scale with the integral length scale across both experimental and numerical cases. The normalized cross-correlation between mean-squared horizontal velocity divergence and surface area covered by structures decreases linearly with depth and remains significant even two integral scales beneath the surface, unlike point-to-point correlations which decay fast, illustrating how correlations are near-instantaneous but spatially nonlocal. These results demonstrate that visible surface features provide considerable quantitative information about energetic flow events even below the surface-influenced layer.

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References (76)

  1. S. Banerjee, Upwellings, downdrafts, and whirlpools: Dominant structures in free surface turbulence, Appl. Mech. Rev. 47, S166 (1994).
  2. M. Brocchini and D. H. Peregrine, The dynamics of strong turbulence at free surfaces. Part 1. Description, J. Fluid Mech. 449, 225 (2001).
  3. O. M. Babiker, I. Bjerkebæk, A. Xuan, L. Shen, and S. Å. Ellingsen, Vortex imprints on a free surface as proxy for surface divergence, J. Fluid Mech. 964, R2 (2023).
  4. J. R. Aarnes, O. M. Babiker, A. Xuan, L. Shen, and S. Å. Ellingsen, Vortex structures under dimples and scars in turbulent free-surface flows, J. Fluid Mech. 1007, A38 (2025).
  5. F. Muraro, G. Dolcetti, A. Nichols, S. J. Tait, and K. V. Horoshenkov, Free-surface behaviour of shallow turbulent flows, J. Hydraul. Res. 59, 1 (2021).
  6. M. S. Longuet-Higgins, Surface manifestations of turbulent flow, J. Fluid Mech. 308, 15 (1996).
  7. M. Rashidi, Burst–interface interactions in free surface turbulent flows, Phys. Fluids 9, 3485 (1997).
  8. 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).
  9. 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).
  10. G. Dolcetti and H. García Nava, Wavelet spectral analysis of the free surface of turbulent flows, J. Hydraul. Res. 57, 211 (2019).
  11. T. L. Mandel, S. Gakhar, H. Chung, I. Rosenzweig, and J. R. Koseff, On the surface expression of a canopy-generated shear instability, J. Fluid Mech. 867, 633 (2019).
  12. S. Gakhar, J. R. Koseff, and N. T. Ouellette, On the surface expression of bottom features in free-surface flow, J. Fluid Mech. 900, A41 (2020).
  13. S. Gakhar, J. R. Koseff, and N. T. Ouellette, Extracting free-surface expressions of underwater features, Exp. Fluids 63, 138 (2022).
  14. A. Xuan and L. Shen, Reconstruction of three-dimensional turbulent flow structures using surface measurements for free-surface flows based on a convolutional neural network, J. Fluid Mech. 959, A34 (2023).
  15. K. S. Moen, J. R. Aarnes, S. Å. Ellingsen, and J. N. Kutz, Mapping surface height dynamics to subsurface flow physics in free-surface turbulent flow using a shallow recurrent decoder, arXiv:2510.06202 [physics.flu-dyn]
  16. D. J. Ruth and F. Coletti, Structure and energy transfer in homogeneous turbulence below a free surface, J. Fluid Mech. 1001, A46 (2024).
  17. 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).
  18. E. J. Hopfinger and J. A. Toly, Spatially decaying turbulence and its relation to mixing across density interfaces, J. Fluid Mech. 78, 155 (1976).
  19. B. H. Brumley and G. H. Jirka, Near-surface turbulence in a grid-stirred tank, J. Fluid Mech. 183, 235 (1987).
  20. 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).
  21. 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).
  22. L. Chiapponi, S. Longo, and M. Tonelli, Experimental study on oscillating grid turbulence and free surface fluctuation, Exp. Fluids 53, 1515 (2012).
  23. T. Lacassagne, M. El-Hajem, F. Morge, S. Simoens, and J.-Y. Champagne, Study of gas liquid mass transfer in a grid stirred tank, Oil Gas Sci. Tech. 72, 7 (2017).
  24. E. A. Variano and E. A. Cowen, A random-jet-stirred turbulence tank, J. Fluid Mech. 604, 1 (2008).
  25. W. E. Asher, H. Liang, C. J. Zappa, M. R. Loewen, M. A. Mukto, T. M. Litchendorf, and A. T. Jessup, Statistics of surface divergence and their relation to air–water gas transfer velocity, J. Geophys. Res. 117, C05035 (2012).
  26. 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).
  27. D. Carter, A. Petersen, O. Amili, and F. Coletti, Generating and controlling homogeneous air turbulence using random jet arrays, Exp. Fluids 57, 189 (2016).
  28. T. Jamin, M. Berhanu, and E. Falcon, Experimental study of three-dimensional turbulence under a free surface, Phys. Rev. Fluids 10, 034608 (2025).
  29. Y. Qi, Y. Li, and F. Coletti, Small-scale dynamics and structure of free-surface turbulence, J. Fluid Mech. 1007, A3 (2025).
  30. Y. Li, Y. Wang, Y. Qi, and F. Coletti, Relative dispersion in free-surface turbulence, J. Fluid Mech. 993, R2 (2024).
  31. L. Chatellier, S. Jarny, F. Gibouin, and L. David, A parametric PIV/DIC method for the measurement of free surface flows, Exp. Fluids 54, 1488 (2013).
  32. R. Savelsberg, A. Holten, and W. van de Water, Measurement of the gradient field of a turbulent free surface, Exp. Fluids 41, 629 (2006).
  33. R. Savelsberg and W. van de Water, Experiments on free-surface turbulence, J. Fluid Mech. 619, 95 (2009).
  34. D. Dabiri and M. Gharib, Simultaneous free-surface deformation and near-surface velocity measurements, Exp. Fluids 30, 381 (2001).
  35. D. Dabiri, On the interaction of a vertical shear layer with a free surface, J. Fluid Mech. 480, 217 (2003).
  36. A. Fouras, D. Lo Jacono, G. J. Sheard, and K. Hourigan, Measurement of instantaneous velocity and surface topography in the wake of a cylinder at low Reynolds number, J. Fluids Struct. 24, 1271 (2008).
  37. I. Ng, V. Kumar, G. J. Sheard, K. Hourigan, and A. Fouras, Experimental study of simultaneous measurement of velocity and surface topography: In the wake of a circular cylinder at low Reynolds number, Exp. Fluids 50, 587 (2011).
  38. G. Gomit, L. Chatellier, D. Calluaud, and L. David, Free surface measurement by stereo-refraction, Exp. Fluids 54, 1540 (2013).
  39. T. Steinmann, J. Casas, P. Braud, and L. David, Coupled measurements of interface topography and three-dimensional velocity field of a free surface flow, Exp. Fluids 62, 14 (2021).
  40. G. Gomit, L. Chatellier, and L. David, Free-surface flow measurements by non-intrusive methods: A survey, Exp. Fluids 63, 94 (2022).
  41. A. Semati, A. Shankaran, B. K. Smeltzer, E. Æsøy, R. J. Hearst, and S. Å. Ellingsen, Simultaneous free-surface profilometry and subsurface velocimetry with fringe projection and PIV, Exp. Fluids (to be published) (2026).
  42. R. A. Antonia, L. Djenidi, L. Danaila, and S. L. Tang, Small scale turbulence and the finite Reynolds number effect, Phys. Fluids 29, 020715 (2017).
  43. K. R. Sreenivasan, An update on the energy dissipation rate in isotropic turbulence, Phys. Fluids 10, 528 (1998).
  44. M. Sinhuber, E. Bodenschatz, and G. P. Bewley, Decay of turbulence at high Reynolds numbers, Phys. Rev. Lett. 114, 034501 (2015).
  45. R. J. Adrian, C. D. Meinhart, and C. D. Tomkins, Vortex organization in the outer region of the turbulent boundary layer, J. Fluid Mech. 422, 1 (2000).
  46. A. Lozano-Durán and J. Jiménez, Time-resolved evolution of coherent structures in turbulent channels: Characterization of eddies and cascades, J. Fluid Mech. 759, 432 (2014).
  47. Herlina and J. G. Wissink, Simulation of air–water interfacial mass transfer driven by high-intensity isotropic turbulence, J. Fluid Mech. 860, 419 (2019).
  48. G. Bellani, M. A. Nole, and E. A. Variano, Turbulence modulation by large ellipsoidal particles: Concentration effects, Acta Mech. 224, 2291 (2013).
  49. L. B. Esteban, J. S. Shrimpton, and B. Ganapathisubramani, Laboratory experiments on the temporal decay of homogeneous anisotropic turbulence, J. Fluid Mech. 862, 99 (2019).
  50. A. G. Nezami, M. Byron, and B. A. Johnson, Laboratory generation of zero-mean-flow homogeneous isotropic turbulence: Non-grid approaches, Flow 3, E42 (2023).
  51. X. Guo and L. Shen, Interaction of a deformable free surface with statistically steady homogeneous turbulence, J. Fluid Mech. 658, 33 (2010).
  52. J. Westerweel and F. Scarano, Universal outlier detection for PIV data, Exp. Fluids 39, 1096 (2005).
  53. B. Wieneke, PIV uncertainty quantification from correlation statistics, Meas. Sci. Technol. 26, 074002 (2015).
  54. P. J. Cobelli, A. Maurel, V. Pagneux, and P. Petitjeans, Global measurement of water waves by Fourier transform profilometry, Exp. Fluids 46, 1037 (2009).
  55. A. Xuan and L. Shen, A conservative scheme for simulation of free-surface turbulent and wave flows, J. Comput. Phys. 378, 18 (2019).
  56. C. Rosales and C. Meneveau, Linear forcing in numerical simulations of isotropic turbulence: Physical space implementations and convergence properties, Phys. Fluids 17, 095106 (2005).
  57. H. Tennekes and J. L. Lumley, A First Course in Turbulence (MIT Press, Cambridge, MA, 1972).
  58. J. C. R. Hunt and J. M. R. Graham, Free-stream turbulence near plane boundaries, J. Fluid Mech. 84, 209 (1978).
  59. J. C. R. Hunt, Turbulence structure in thermal convection and shear-free boundary layers, J. Fluid Mech. 138, 161 (1984).
  60. L. Shen, X. Zhang, D. K. P. Yue, and G. S. Triantafyllou, The surface layer for free-surface turbulent flows, J. Fluid Mech. 386, 167 (1999).
  61. I. Calmet and J. Magnaudet, Statistical structure of high-Reynolds-number turbulence close to the free surface of an open-channel flow, J. Fluid Mech. 474, 355 (2003).
  62. J. Magnaudet, High-Reynolds-number turbulence in a shear-free boundary layer: Revisiting the Hunt–Graham theory, J. Fluid Mech. 484, 167 (2003).
  63. A. Fuchs, S. Kharche, A. Patil, J. Friedrich, M. Wächter, and J. Peinke, An open source package to perform basic and advanced statistical analysis of turbulence data and other complex systems, Phys. Fluids 34, 101801 (2022).
  64. D. E. Turney and S. Banerjee, Air–water gas transfer and near-surface motions, J. Fluid Mech. 733, 588 (2013).
  65. M. McCready, E. Vassiliadou, and T. Hanratty, Computer simulation of turbulent mass transfer at a mobile interface, AIChE J. 32, 1108 (1986).
  66. D. E. Turney, W. C. Smith, and S. Banerjee, A measure of near‐surface fluid motions that predicts air–water gas transfer in a wide range of conditions, Geophys. Res. Lett. 32, L04607 (2005).
  67. R. Nagaosa, Direct numerical simulation of vortex structures and turbulent scalar transfer across a free surface in a fully developed turbulence, Phys. Fluids 11, 1581 (1999).
  68. J. R. Aarnes, O. M. Babiker, A. Xuan, L. Shen, and S. Å. Ellingsen, Replication data for: “Vortex structures under dimples and scars in turbulent free-surface flows” (PART 1/4), DataverseNO, V1 (2025), https://doi.org/10.18710/XQ81WH.
  69. O. M. Babiker, J. R. Aarnes, A. Semati, A. Ferran, Y. H. Tee, R. J. Hearst, and S. Å. Ellingsen, Replication data for: Experimental investigation relating free-surface features to sub-surface turbulence, DataverseNO, V1 (2025), https://doi.org/10.18710/TSIZCQ.
  70. C. Poelma, J. Westerweel, and G. Ooms, Turbulence statistics from optical whole-field measurements in particle-laden turbulence, Exp. Fluids 40, 663 (2006).
  71. P. Lavoie, G. Avallone, F. De Gregorio, G. P. Romano, and R. A. Antonia, Spatial resolution of PIV for the measurement of turbulence, Exp. Fluids 43, 39 (2007).
  72. R. J. Hearst and P. Lavoie, Decay of turbulence generated by a square-fractal-element grid, J. Fluid Mech. 741, 567 (2014).
  73. J. C. Vassilicos, Dissipation in turbulent flows, Annu. Rev. Fluid Mech. 47, 95 (2015).
  74. A. N. Kolmogorov, The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers, Dokl. Akad. Nauk SSSR 434, 9 (1991).
  75. D. O. Mora, E. Muñiz Pladellorens, P. Riera Turró, M. Lagauzere, and M. Obligado, Energy cascades in active-grid-generated turbulent flows, Phys. Rev. Fluids 4, 104601 (2019).
  76. Herlina and J. G. Wissink, Direct numerical simulation of turbulent scalar transport across a flat surface, J. Fluid Mech. 744, 217 (2014).

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Phys. Rev. Fluids 11, 054802– Published 18 May, 2026
  • Received 6 January 2026
  • Accepted 10 April 2026
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