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The variation of flow and turbulence across the sediment–water interface

  • J. J. Voermans (a1), M. Ghisalberti (a1) (a2) and G. N. Ivey (a1) (a3)

A basic framework characterising the interaction between aquatic flows and permeable sediment beds is presented here. Through the permeability Reynolds number ( $Re_{K}=\sqrt{K}u_{\ast }/\unicode[STIX]{x1D708}$ , where $K$ is the sediment permeability, $u_{\ast }$ is the shear velocity and $\unicode[STIX]{x1D708}$ is the fluid viscosity), the framework unifies two classical flow typologies, namely impermeable boundary layer flows ( $Re_{K}\ll 1$ ) and highly permeable canopy flows ( $Re_{K}\gg 1$ ). Within this range, the sediment–water interface (SWI) is identified as a transitional region, with $Re_{K}$ in aquatic systems typically $O(0.001{-}10)$ . As the sediments obstruct conventional measurement techniques, experimental observations of interfacial hydrodynamics remain extremely rare. The use of refractive index matching here allows measurement of the mean and turbulent flow across the SWI and thus direct validation of the proposed framework. This study demonstrates a strong relationship between the structure of the mean and turbulent flow at the SWI and $Re_{K}$ . Hydrodynamic characteristics, such as the interfacial turbulent shear stress, velocity, turbulence intensities and turbulence anisotropy tend towards those observed in flows over impermeable boundaries as $Re_{K}\rightarrow 0$ and towards those seen in flows over highly permeable boundaries as $Re_{K}\rightarrow \infty$ . A value of $Re_{K}\approx 1{-}2$ is seen to be an important threshold, above which the turbulent stress starts to dominate the fluid shear stress at the SWI, the penetration depths of turbulence and the mean flow into the sediment bed are comparable and similarity relationships developed for highly permeable boundaries hold. These results are used to provide a new perspective on the development of interfacial transport models at the SWI.

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Adrian, R. J., Meinhart, C. D. & Tomkins, C. D. 2000 Vortex organization in the outer region of the turbulent boundary layer. J. Fluid Mech. 422, 154.
Bai, K., Katz, J. & Meneveau, C. 2015 Turbulent flow structure inside a canopy with complex multi-scale elements. Boundary-Layer Meteorol. 155 (3), 435457.
Battin, T. J., Besemer, K., Bengtsson, M. M., Romani, A. M. & Packmann, A. I. 2016 The ecology and biogeochemistry of stream biofilms. Nat. Rev. Microbiol. 14 (4), 251263.
Bear, J. 1972 Dynamics of Fluids in Porous Media. Courier Dover.
Beavers, G. S. & Joseph, D. D. 1967 Boundary conditions at a naturally permeable wall. J. Fluid Mech. 30 (01), 197207.
Blasco, J., Saenz, V. & Gómez-Parra, A. 2000 Heavy metal fluxes at the sediment–water interface of three coastal ecosystems from south-west of the iberian peninsula. Sci. Total Environ. 247 (2), 189199.
Boudreau, B. P. 2001 Solute transport above the sediment-water interface. In The Benthic Boundary Layer: Transport Processes and Biogeochemistry, pp. 104126. Oxford University Press.
Boulton, A. J., Findlay, S., Marmonier, P., Stanley, E. H. & Valett, H. M. 1998 The functional significance of the hyporheic zone in streams and rivers. Annu. Rev. Ecol. Syst. 29, 5981.
Breugem, W. P., Boersma, B. J. & Uittenbogaard, R. E. 2006 The influence of wall permeability on turbulent channel flow. J. Fluid Mech. 562 (1), 3572.
Chandler, I. D., Guymer, I., Pearson, J. M. & van Egmond, R. 2016 Vertical variation of mixing within porous sediment beds below turbulent flows. Water Resour. Res. 52 (5), 34933509.
Ciceri, G., Maran, C., Martinotti, W. & Queirazza, G. 1992 Geochemical cycling of heavy metals in a marine coastal area: benthic flux determination from pore water profiles and in situ measurements using benthic chambers. Hydrobiologia 235 (1), 501517.
Cowen, E. A. & Monismith, S. G. 1997 A hybrid digital particle tracking velocimetry technique. Exp. Fluids 22 (3), 199211.
Detert, M., Klar, M., Wenka, T. & Jirka, G. H. 2007 Pressure- and velocity-measurements above and within a porous gravel bed at the threshold of stability. Dev. Earth Surf. Processes 11, 85105.
Diaz, R. J. 2001 Overview of hypoxia around the world. J. Environ. Qual. 30 (2), 275281.
Ghisalberti, M. 2009 Obstructed shear flows: similarities across systems and scales. J. Fluid Mech. 641, 5161.
Ghisalberti, M. & Nepf, H. M. 2002 Mixing layers and coherent structures in vegetated aquatic flows. J. Geophys. Res. 107 (C2), 3-1–3-11.
Goharzadeh, A., Khalili, A. & Jørgensen, B. B. 2005 Transition layer thickness at a fluid-porous interface. Phys. Fluids 17 (5), 057102.
Goyeau, B., Lhuillier, D., Gobin, D. & Velarde, M. G. 2003 Momentum transport at a fluid-porous interface. Intl J. Heat Mass Transfer 46 (21), 40714081.
Grant, S. B., Stewardson, M. J. & Marusic, I. 2012 Effective diffusivity and mass flux across the sediment-water interface in streams. Water Resour. Res. 48 (5), W05548.
Güss, S. 1998 Oxygen uptake at the sediment-water interface simultaneously measured using a flux chamber method and microelectrodes: must a diffusive boundary layer exist? Estuar. Coast Shelf Sci. 46 (1), 143156.
Häfeli, R., Altheimer, M., Butscher, D. & von Rohr, P. R. 2014 PIV study of flow through porous structure using refractive index matching. Exp. Fluids 55 (5), 113.
Ho, C. M. & Huerre, P. 1984 Perturbed free shear layers. Annu. Rev. Fluid Mech. 16 (1), 365422.
Hondzo, M., Feyaerts, T., Donovan, R. & O’Connor, B. L. 2005 Universal scaling of dissolved oxygen distribution at the sediment-water interface: a power law. Limnol. Oceanogr. 50 (5), 16671676.
Horritt, M. S. & Bates, P. D. 2002 Evaluation of 1D and 2D numerical models for predicting river flood inundation. J. Hydrol. 268 (1), 8799.
Jiménez, J. 2004 Turbulent flows over rough walls. Annu. Rev. Fluid Mech. 36, 173196.
Jorgensen, B. B. & Des Marais, D. J. 1990 The diffusive boundary layer of sediments: oxygen microgradients over a microbial mat. Limnol. Oceanogr. 35, 13431355.
Kim, J., Moin, P. & Moser, R. 1987 Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133166.
Lorke, A., Muller, B., Maerki, M. & Wuest, A. 2003 Breathing sediments: The control of diffusive transport across the sediment-water interface by periodic boundary-layer turbulence. Limnol. Oceanogr. 48 (6), 20772085.
Manes, C., Poggi, D. & Ridolfi, L. 2011a Turbulent boundary layers over permeable walls: scaling and near-wall structure. J. Fluid Mech. 687, 141170.
Manes, C., Pokrajac, D., Nikora, V. I., Ridolfi, L. & Poggi, D. 2011b Turbulent friction in flows over permeable walls. Geophys. Res. Lett. 38 (3), L03402.
Manes, C., Ridolfi, L. & Katul, G. 2012 A phenomenological model to describe turbulent friction in permeable-wall flows. Geophys. Res. Lett. 39 (14), L14403.
Marusic, I., Mathis, R. & Hutchins, N. 2010 Predictive model for wall-bounded turbulent flow. Science 329 (5988), 193196.
Mathis, R., Marusic, I., Cabrit, O., Jones, N. L. & Ivey, G. N. 2014 Modelling bed shear-stress fluctuations in a shallow tidal river. J. Geophys. Res.-Oceans 119, 31853199.
Mignot, E., Barthelemy, E. & Hurther, D. 2009 Double-averaging analysis and local flow characterization of near-bed turbulence in gravel-bed channel flows. J. Fluid Mech. 618, 279303.
Nelson, J. M., Shreve, R. L., McLean, S. R. & Drake, T. G. 1995 Role of near-bed turbulence structure in bed load transport and bed form mechanics. Water Resour. Res. 31 (8), 20712086.
Nepf, H. M. 2012 Flow and transport in regions with aquatic vegetation. Annu. Rev. Fluid Mech. 44, 123142.
Nezu, I. & Nakagawa, H. 1993 Turbulence in Open-Channel Flows. A.A. Balkema.
Nikora, V., Goring, D., McEwan, I. & Griffiths, G. 2001 Spatially averaged open-channel flow over rough bed. J. Hydraul. Engng 127 (2), 123133.
Nikora, V., Koll, K., McEwan, I., McLean, S. & Dittrich, A. 2004 Velocity distribution in the roughness layer of rough-bed flows. J. Hydraul. Engng 130 (10), 10361042.
Nikora, V., McEwan, I., McLean, S., Coleman, S., Pokrajac, D. & Walters, R. 2007 Double-averaging concept for rough-bed open-channel and overland flows: theoretical background. J. Hydraul. Engng 133 (8), 873883.
Nokes, R. 2016 Streams. System Theory and Design. University of Canterbury, version 2.05.
O’Connor, B. L. & Harvey, J. W. 2008 Scaling hyporheic exchange and its influence on biogeochemical reactions in aquatic ecosystems. Water Resour. Res. 44 (12), W12423.
Packman, A. I., Salehin, M. & Zaramella, M. 2004 Hyporheic exchange with gravel beds: basic hydrodynamic interactions and bedform-induced advective flows. J. Hydraul. Engng 130 (7), 647656.
Perot, B. & Moin, P. 1995 Shear-free turbulent boundary layers. Part 1. Physical insights into near-wall turbulence. J. Fluid Mech. 295, 199227.
Poggi, D., Porporato, A., Ridolfi, L., Albertson, J. D. & Katul, G. G. 2004 The effect of vegetation density on canopy sub-layer turbulence. Boundary-Layer Meteorol. 111 (3), 565587.
Pokrajac, D, Finnigan, J. J., Manes, C., McEwan, I. K. & Nikora, V. I. 2006 On the definition of the shear velocity in rough bed open channel flows. In Proc. Intl. Conference on Flucial Hydraulics River Flow 2006, Lisbon, vol. 1, pp. 8998. CRC Press.
Prinos, P., Sofialidis, D. & Keramaris, E. 2003 Turbulent flow over and within a porous bed. J. Hydraul. Engng 129 (9), 720733.
Rabalais, N. N., Smith, L. E., Harper, D. E. & Justic, D. 2001 Effects of seasonal hypoxia on continental shelf benthos. In Coastal Hypoxia: Consequences for Living Resources and Ecosystems (ed. Rabalais, N. N. & Turner, R. E.), American Geophysical Union.
Raupach, M. R., Finnigan, J. J. & Brunei, Y. 1996 Coherent eddies and turbulence in vegetation canopies: the mixing-layer analogy. Boundary-Layer Meteorol. 78 (3–4), 351382.
Rosgen, D. L. 1994 A classification of natural rivers. Catena 22 (3), 169199.
Roy, H., Huettel, M. & Jorgensen, B. B. 2004 Transmission of oxygen concentration fluctuations through the diffusive boundary layer overlying aquatic sediments. Limnol. Oceanogr. 49 (3), 686692.
Ruff, J. F. & Gelhar, L. W. 1972 Turbulent shear flow in porous boundary. J. Engng Mech. 98, 975991.
Saffman, P. G. 1971 On the boundary condition at the surface of a porous medium. Stud. Appl. Maths 50 (2), 93101.
Schlichting, H. 1979 Boundary-Layer Theory. McGraw-Hill.
Smalley, R., Leonardi, S., Antonia, R., Djenidi, L. & Orlandi, P. 2002 Reynolds stress anisotropy of turbulent rough wall layers. Exp. Fluids 33 (1), 3137.
Suga, K., Matsumura, Y., Ashitaka, Y., Tominaga, S. & Kaneda, M. 2010 Effects of wall permeability on turbulence. Intl J. Heat Fluid Flow 31 (6), 974984.
Suga, K., Mori, M. & Kaneda, M. 2011 Vortex structure of turbulence over permeable walls. Intl J. Heat Fluid Flow 32 (3), 586595.
Tennekes, H. & Lumley, J. L. 1972 A First Course in Turbulence. MIT Press.
Tilton, N. & Cortelezzi, L. 2008 Linear stability analysis of pressure-driven flows in channels with porous walls. J. Fluid Mech. 604, 411445.
Uzol, O., Chow, Y. C., Katz, J. & Meneveau, C. 2002 Unobstructed particle image velocimetry measurements within an axial turbo-pump using liquid and blades with matched refractive indices. Exp. Fluids 33 (6), 909919.
White, B. L. & Nepf, H. M. 2007 Shear instability and coherent structures in shallow flow adjacent to a porous layer. J. Fluid Mech. 593, 132.
Wilson, A. M., Huettel, M. & Klein, S. 2008 Grain size and depositional environment as predictors of permeability in coastal marine sands. Estuar. Coast Shelf Sci. 80 (1), 193199.
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