• Bearman, P. W., 1971: An investigation of the forces on flat plates normal to a turbulent flow. J. Fluid Mech., 46, 177198, https://doi.org/10.1017/S0022112071000478.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Benilov, A. Y., and B. N. Filyushkin, 1970: Application of methods of linear filtration to an analysis of fluctuations in the surface layer of the sea. Izv. Akad. Nauk SSSR, Fiz. Atmos. Okeana, 6, 810819.

    • Search Google Scholar
    • Export Citation
  • Buckles, J., T. J. Hanratty, and R. J. Adrian, 1984: Turbulent flow over large-amplitude wavy surfaces. J. Fluid Mech., 140, 2744, https://doi.org/10.1017/S0022112084000495.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chirayath, V., 2016: Fluid lensing and applications to remote sensing of aquatic environments. Ph.D. dissertation, Stanford University, 177 pp., https://purl.stanford.edu/kw062mg5196.

  • Chirayath, V., and S. A. Earle, 2016: Drones that see through waves—Preliminary results from airborne fluid lensing for centimetre-scale aquatic conservation. Aquat. Conserv., 26, 237250, https://doi.org/10.1002/aqc.2654.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Dean, R. G., and R. A. Dalrymple, 1991: Water Wave Mechanics for Engineers and Scientists. Advanced Series on Ocean Engineering, Vol. 2, World Scientific, 353 pp.

    • Crossref
    • Export Citation
  • Falter, J. L., M. J. Atkinson, and M. A. Merrifield, 2004: Mass-transfer limitation of nutrient uptake by a wave-dominated reef flat community. Limnol. Oceanogr., 49, 18201831, https://doi.org/10.4319/lo.2004.49.5.1820.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Feddersen, F., E. L. Gallagher, R. T. Guza, and S. Elgar, 2003: The drag coefficient, bottom roughness, and wave-breaking in the nearshore. Coastal Eng., 48, 189195, https://doi.org/10.1016/S0378-3839(03)00026-7.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Fringer, O. B., M. Gerritsen, and R. L. Street, 2006: An unstructured-grid, finite-volume, nonhydrostatic, parallel coastal ocean simulator. Ocean Modell., 14, 139173, https://doi.org/10.1016/j.ocemod.2006.03.006.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gong, W., P. Taylor, and A. Dörnbrack, 1996: Turbulent boundary-layer flow over fixed aerodynamically rough two-dimensional sinusoidal waves. J. Fluid Mech., 312, 137, https://doi.org/10.1017/S0022112096001905.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Grant, W. D., and O. S. Madsen, 1979: Combined wave and current interaction with a rough bottom. J. Geophys. Res., 84, 17971808, https://doi.org/10.1029/JC084iC04p01797.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Grant, W. D., and O. S. Madsen, 1982: Movable bed roughness in unsteady oscillatory flow. J. Geophys. Res., 87, 469481, https://doi.org/10.1029/JC087iC01p00469.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hearn, C. J., 1999: Wave-breaking hydrodynamics within coral reef systems and the effect of changing relative sea level. J. Geophys. Res., 104, 30 00730 019, https://doi.org/10.1029/1999JC900262.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hearn, C. J., 2011a: Hydrodynamics of coral reef systems. Encyclopedia of Modern Coral Reefs: Structure, Form and Process, D. Hopley, Ed., Springer, 563–573.

    • Crossref
    • Export Citation
  • Hearn, C. J., 2011b: Perspectives in coral reef hydrodynamics. Coral Reefs, 30, 19, https://doi.org/10.1007/s00338-011-0752-4.

  • Hench, J. L., and J. H. Rosman, 2013: Observations of spatial flow patterns at the coral colony scale on a shallow reef flat. J. Geophys. Res. Oceans, 118, 11421156, https://doi.org/10.1002/jgrc.20105.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Henn, D. S., and R. I. Sykes, 1999: Large-eddy simulation of flow over wavy surfaces. J. Fluid Mech., 383, 75112, https://doi.org/10.1017/S0022112098003723.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Jaramillo, S., and G. Pawlak, 2011: AUV-based bed roughness mapping over a tropical reef. Coral Reefs, 30, 1123, https://doi.org/10.1007/s00338-011-0731-9.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Jimenez, J., 2004: Turbulent flows over rough walls. Annu. Rev. Fluid Mech., 36, 173196, https://doi.org/10.1146/annurev.fluid.36.050802.122103.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Jonsson, I. G., and N. A. Carlsen, 1976: Experimental and theoretical investigations in an oscillatory turbulent boundary layer. J. Hydraul. Res., 14, 4560, https://doi.org/10.1080/00221687609499687.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Koweek, D. A., R. B. Dunbar, S. G. Monismith, D. A. Mucciarone, C. B. Woodson, and L. Samuel, 2015: High-resolution physical and biogeochemical variability from a shallow back reef on Ofu, American Samoa: An end-member perspective. Coral Reefs, 34, 979991, https://doi.org/10.1007/s00338-015-1308-9.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kundu, P. K., and I. M. Cohen, 2008: Fluid Mechanics. 4th ed. Academic Press, 872 pp.

  • Lentz, S. J., J. H. Churchill, K. A. Davis, J. T. Farrar, J. Pineda, and V. Starczak, 2016: The characteristics and dynamics of wave-driven flow across a platform coral reef in the Red Sea. J. Geophys. Res. Oceans, 121, 13601376, https://doi.org/10.1002/2015JC011141.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lentz, S. J., K. A. Davis, J. H. Churchill, and T. M. DeCarlo, 2017: Coral reef drag coefficients—Water depth dependence. J. Phys. Oceanogr., 47, 10611075, https://doi.org/10.1175/JPO-D-16-0248.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lettau, H., 1969: Note on aerodynamic roughness-parameter estimation on the basis of roughness-element description. J. Appl. Meteor., 8, 828832, https://doi.org/10.1175/1520-0450(1969)008<0828:NOARPE>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lowe, R. J., J. R. Koseff, and S. G. Monismith, 2005: Oscillatory flow through submerged canopies: 1. Velocity structure. J. Geophys. Res., 110, C10016, https://doi.org/10.1029/2004JC002788.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lübcke, H., S. Schmidt, T. Rung, and F. Thiele, 2001: Comparison of LES and RANS in bluff-body flows. J. Wind Eng. Ind. Aerodyn., 89, 14711485, https://doi.org/10.1016/S0167-6105(01)00134-9.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • McDonald, C. B., J. R. Koseff, and S. G. Monismith, 2006: Effects of the depth to coral height ratio on drag coefficients for unidirectional flow over coral. Limnol. Oceanogr., 51, 12941301, https://doi.org/10.4319/lo.2006.51.3.1294.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Mei, C., M. Stiassnie, and D. Yue, 2005: Theory and Applications of Ocean Surface Waves. Advanced Series on Ocean Engineering, Vol. 23, World Scientific, 1071 pp.

  • Monismith, S. G., 2007: Hydrodynamics of coral reefs. Annu. Rev. Fluid Mech., 39, 3755, https://doi.org/10.1146/annurev.fluid.38.050304.092125.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Monismith, S. G., L. M. M. Herdman, S. Ahmerkamp, and J. L. Hench, 2013: Wave transformation and wave-driven flow across a steep coral reef. J. Phys. Oceanogr., 43, 13561379, https://doi.org/10.1175/JPO-D-12-0164.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Nelson, K. S., and O. B. Fringer, 2017: Reducing spin-up time for simulations of turbulent channel flow. Phys. Fluids, 29, 105101, https://doi.org/10.1063/1.4993489.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Nielsen, P., 1992: Coastal Bottom Boundary Layers and Sediment Transport. World Scientific, 323 pp.

    • Crossref
    • Export Citation
  • Nikuradse, J., 1933: Strömungsgesetze in Rauhen Rohren. Verein Deutscher Ingenieure Forschungsheft 361, 22 pp.

  • Nunes, V., and G. Pawlak, 2008: Observations of bed roughness of a coral reef. J. Coastal Res., 24, 3950, https://doi.org/10.2112/05-0616.1.

  • Perry, A., W. H. Schoflield, and P. N. Joubbert, 1969: Rough wall turbulent boundary layers. J. Fluid Mech., 37, 383413, https://doi.org/10.1017/S0022112069000619.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Reidenbach, M. A., S. G. Monismith, J. R. Koseff, G. Yahel, and A. Genin, 2006: Boundary layer turbulence and flow structure over a fringing coral reef. Limnol. Oceanogr., 51, 19561968, https://doi.org/10.4319/lo.2006.51.5.1956.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Rodi, W., 1997: Comparison of LES and RANS calculations of the flow around bluff bodies. J. Wind Eng. Ind. Aerodyn., 69–71, 5575, https://doi.org/10.1016/S0167-6105(97)00147-5.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Rogers, J. S., S. G. Monismith, R. B. Dunbar, and D. Koweek, 2015: Field observations of wave-driven circulation over spur and groove formations on a coral reef. J. Geophys. Res. Oceans, 120, 145160, https://doi.org/10.1002/2014JC010464.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Rogers, J. S., S. G. Monismith, D. A. Koweek, W. I. Torres, and R. B. Dunbar, 2016: Thermodynamics and hydrodynamics in an atoll reef system and their influence on coral cover. Limnol. Oceanogr., 61, 21912206, https://doi.org/10.1002/lno.10365.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Rogers, J. S., S. G. Monismith, O. B. Fringer, D. A. Koweek, and R. B. Dunbar, 2017: A coupled wave-hydrodynamic model of an atoll with high friction: Mechanisms for flow, connectivity, and ecological implications. Ocean Modell., 110, 6682, https://doi.org/10.1016/j.ocemod.2016.12.012.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Roshko, A., 1961: Experiments on the flow past a circular cylinder at very high Reynolds number. J. Fluid Mech., 10, 345356, https://doi.org/10.1017/S0022112061000950.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Rosman, J. H., and J. L. Hench, 2011: A framework for understanding drag parameterizations for coral reefs. J. Geophys. Res., 116, C08025, https://doi.org/10.1029/2010JC006892.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Salvetti, M. V., R. Damiani, and F. Beux, 2001: Three-dimensional coarse large-eddy simulations of the flow above two-dimensional sinusoidal waves. Int. J. Numer. Methods Fluids, 35, 617642, https://doi.org/10.1002/1097-0363(20010330)35:6<617::AID-FLD104>3.0.CO;2-M.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Schlichting, H., 1979: Boundary-Layer Theory. 7th ed. McGraw-Hill, 817 pp.

  • 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, 15 46715 472, https://doi.org/10.1029/JC093iC12p15467.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Suosaari, E. P., and Coauthors, 2016: New multi-scale perspectives on the stromatolites of Shark Bay, Western Australia. Nat. Sci. Rep., 6, 20557, https://doi.org/10.1038/srep20557.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Swart, D. H., 1977: Predictive equations regarding coastal transports. Coastal Eng., 104, 11491158, https://doi.org/10.1061/9780872620834.066.

    • Search Google Scholar
    • Export Citation
  • Symonds, G., K. P. Black, and I. R. Young, 1995: Wave-driven flow over shallow reefs. J. Geophys. Res., 100, 26392648, https://doi.org/10.1029/94JC02736.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Thomas, F. I. M., and M. J. Atkinson, 1997: Ammonium uptake by coral reefs: Effects of water velocity and surface roughness on mass transfer. Limnol. Oceanogr., 42, 8188, https://doi.org/10.4319/lo.1997.42.1.0081.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Vetter, O., J. M. Becker, M. A. Merrifield, C. Pequignet, J. Aucan, S. J. Boc, and C. E. Pollock, 2010: Wave setup over a Pacific island fringing reef. J. Geophys. Res., 115, C12066, https://doi.org/10.1029/2010JC006455.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Warner, J. C., C. R. Sherwood, H. G. Arango, and R. P. Signell, 2005: Performance of four turbulence closure models implemented using a generic length scale method. Ocean Modell., 8, 81113, https://doi.org/10.1016/j.ocemod.2003.12.003.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wooding, R. A., E. F. Bradley, and J. K. Marshall, 1973: Drag due to regular arrays of roughness elements of varying geometry. Bound.-Layer Meteor., 5, 285308, https://doi.org/10.1007/BF00155238.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zilker, D. P., and T. J. Hanratty, 1979: Influence of the amplitude of a solid wavy wall on a turbulent flow. Part 2. Separated flows. J. Fluid Mech., 90, 257271, https://doi.org/10.1017/S0022112079002196.

    • Crossref
    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 26 26 26
PDF Downloads 25 25 25

Connecting Flow over Complex Terrain to Hydrodynamic Roughness on a Coral Reef

View More View Less
  • 1 Environmental Fluid Mechanics Laboratory, Department of Civil and Environmental Engineering, Stanford University, Stanford, California
  • | 2 NASA Ames Laboratory for Advanced Sensing, Moffett Field, California
  • | 3 College of Engineering, University of Georgia, Athens, Georgia
  • | 4 Department of Aeronautics and Astronautics, Stanford University, Stanford, California
  • | 5 Environmental Fluid Mechanics Laboratory, Department of Civil and Environmental Engineering, Stanford University, Stanford, California
Restricted access

Abstract

Flow over complex terrain causes stress on the bottom leading to drag, turbulence, and formation of a boundary layer. But despite the importance of the hydrodynamic roughness scale z0 in predicting flows and mixing, little is known about its connection to complex terrain. To address this gap, we conducted extensive field observations of flows and finescale measurements of bathymetry using fluid-lensing techniques over a shallow coral reef on Ofu, American Samoa. We developed a validated centimeter-scale nonhydrostatic hydrodynamic model of the reef, and the results for drag compare well with the observations. The total drag is caused by pressure differences creating form drag and is only a function of relative depth and spatially averaged streamwise slope, consistent with scaling for kδ-type roughness, where k is the roughness height and δ is the boundary layer thickness. We approximate the complex reef surface as a superposition of wavy bedforms and present a simple method for predicting z0 from the spatial root-mean-square of depth and streamwise slope of the bathymetric surface and a linear coefficient a1, similar to results from other studies on wavy bedforms. While the local velocity profiles vary widely, the horizontal average is consistent with a log-layer approximation. The model grid resolution required to accurately compute the form drag is O(10–50) times the dominant horizontal hydrodynamic scale, which is determined by a peak in the spectra of the streamwise slope. The approach taken in this study is likely applicable to other complex terrains and could be explored for other settings.

Supplemental information related to this paper is available at the Journals Online website: https://doi.org/10.1175/JPO-D-18-0013.s1.

© 2018 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Justin Rogers, jsrogers@stanford.edu

Abstract

Flow over complex terrain causes stress on the bottom leading to drag, turbulence, and formation of a boundary layer. But despite the importance of the hydrodynamic roughness scale z0 in predicting flows and mixing, little is known about its connection to complex terrain. To address this gap, we conducted extensive field observations of flows and finescale measurements of bathymetry using fluid-lensing techniques over a shallow coral reef on Ofu, American Samoa. We developed a validated centimeter-scale nonhydrostatic hydrodynamic model of the reef, and the results for drag compare well with the observations. The total drag is caused by pressure differences creating form drag and is only a function of relative depth and spatially averaged streamwise slope, consistent with scaling for kδ-type roughness, where k is the roughness height and δ is the boundary layer thickness. We approximate the complex reef surface as a superposition of wavy bedforms and present a simple method for predicting z0 from the spatial root-mean-square of depth and streamwise slope of the bathymetric surface and a linear coefficient a1, similar to results from other studies on wavy bedforms. While the local velocity profiles vary widely, the horizontal average is consistent with a log-layer approximation. The model grid resolution required to accurately compute the form drag is O(10–50) times the dominant horizontal hydrodynamic scale, which is determined by a peak in the spectra of the streamwise slope. The approach taken in this study is likely applicable to other complex terrains and could be explored for other settings.

Supplemental information related to this paper is available at the Journals Online website: https://doi.org/10.1175/JPO-D-18-0013.s1.

© 2018 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Justin Rogers, jsrogers@stanford.edu

Supplementary Materials

    • Supplemental Materials (PDF 943.58 KB)
Save