Measurements of Form and Frictional Drags over a Rough Topographic Bank

H. W. Wijesekera Naval Research Laboratory, Stennis Space Center, Mississippi

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E. Jarosz Naval Research Laboratory, Stennis Space Center, Mississippi

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W. J. Teague Naval Research Laboratory, Stennis Space Center, Mississippi

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D. W. Wang Naval Research Laboratory, Stennis Space Center, Mississippi

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D. B. Fribance Coastal Carolina University, Conway, South Carolina

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J. N. Moum Oregon State University, Corvallis, Oregon

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S. J. Warner Oregon State University, Corvallis, Oregon

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Abstract

Pressure differences across topography generate a form drag that opposes the flow in the water column, and viscous and pressure forces acting on roughness elements of the topographic surface generate a frictional drag on the bottom. Form drag and bottom roughness lengths were estimated over the East Flower Garden Bank (EFGB) in the Gulf of Mexico by combining an array of bottom pressure measurements and profiles of velocity and turbulent kinetic dissipation rates. The EFGB is a coral bank about 6 km wide and 10 km long located at the shelf edge that rises from 100-m water depth to about 18 m below the sea surface. The average frictional drag coefficient over the entire bank was estimated as 0.006 using roughness lengths that ranged from 0.001 cm for relatively smooth portions of the bank to 1–10 cm for very rough portions over the corals. The measured form drag over the bank showed multiple time-scale variability. Diurnal tides and low-frequency motions with periods ranging from 4 to 17 days generated form drags of about 2000 N m−1 with average drag coefficients ranging between 0.03 and 0.22, which are a factor of 5–35 times larger than the average frictional drag coefficient. Both linear wave and quadratic drag laws have similarities with the observed form drag. The form drag is an important flow retardation mechanism even in the presence of the large frictional drag associated with coral reefs and requires parameterization.

Corresponding author address: Hemantha W. Wijesekera, Naval Research Laboratory, 1009 Balch Blvd., Stennis Space Center, MS 39529. E-mail: hemantha.wijesekera@nrlssc.navy.mil

Abstract

Pressure differences across topography generate a form drag that opposes the flow in the water column, and viscous and pressure forces acting on roughness elements of the topographic surface generate a frictional drag on the bottom. Form drag and bottom roughness lengths were estimated over the East Flower Garden Bank (EFGB) in the Gulf of Mexico by combining an array of bottom pressure measurements and profiles of velocity and turbulent kinetic dissipation rates. The EFGB is a coral bank about 6 km wide and 10 km long located at the shelf edge that rises from 100-m water depth to about 18 m below the sea surface. The average frictional drag coefficient over the entire bank was estimated as 0.006 using roughness lengths that ranged from 0.001 cm for relatively smooth portions of the bank to 1–10 cm for very rough portions over the corals. The measured form drag over the bank showed multiple time-scale variability. Diurnal tides and low-frequency motions with periods ranging from 4 to 17 days generated form drags of about 2000 N m−1 with average drag coefficients ranging between 0.03 and 0.22, which are a factor of 5–35 times larger than the average frictional drag coefficient. Both linear wave and quadratic drag laws have similarities with the observed form drag. The form drag is an important flow retardation mechanism even in the presence of the large frictional drag associated with coral reefs and requires parameterization.

Corresponding author address: Hemantha W. Wijesekera, Naval Research Laboratory, 1009 Balch Blvd., Stennis Space Center, MS 39529. E-mail: hemantha.wijesekera@nrlssc.navy.mil
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  • Baines, P. G., 1979: Observations of stratified flow over two-dimensional obstacles in fluid of finite depth. Tellus, 31, 351371, doi:10.1111/j.2153-3490.1979.tb00914.x.

    • Search Google Scholar
    • Export Citation
  • Baines, P. G., 1995: Topographic Effects in Stratified Flows.Cambridge University Press, 482 pp.

  • Baker, M. A., and C. H. Gibson, 1987: Sampling turbulence in the stratified ocean: Statistical consequences of strong intermittency. J. Phys. Oceanogr., 17, 18171836, doi:10.1175/1520-0485(1987)017<1817:STITSO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Bell, T. H., 1975: Topographically generated internal waves in the open ocean. J. Geophys. Res., 80, 320327, doi:10.1029/JC080i003p00320.

    • Search Google Scholar
    • Export Citation
  • Blumberg, A. F., and G. L. Mellor, 1987: A description of a three-dimensional coastal ocean circulation model. The Three Dimensional Coastal Ocean Models, N. S. Heaps, Ed., Coastal and Estuarine Sciences Series, Vol. 4, Amer. Geophys. Union, 1–16.

  • Bougeault, P., B. Benech, B. Carissimo, J. Pelon, and E. Richard, 1990: Momentum budget over the Pyrenees: The PYREX experiment. Bull. Amer. Meteor. Soc., 71, 806818, doi:10.1175/1520-0477(1990)071<0806:MBOTPT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Bright, T. J., G. P. Kraemer, G. A. Minnery, and S. T. Viada, 1984: Hermatypes of the Flower Garden Banks, northwestern Gulf of Mexico: A comparison to other western Atlantic reefs. J. Mar. Sci., 34, 491476.

    • Search Google Scholar
    • Export Citation
  • Clark, T. L., and M. J. Miller, 1991: Pressure drag and momentum fluxes due to the Alps. II: Representation in large-scale models. Quart. J. Roy. Meteor. Soc., 117, 527552, doi:10.1002/qj.49711749906.

    • Search Google Scholar
    • Export Citation
  • Deacon, E. L., 1953: Vertical profiles of mean wind in the surface layers of the atmosphere. Geophysical Memoirs, No. 91, H. M. Stationery Office, 63 pp.

  • Dewey, R. K., and W. R. Crawford, 1988: Bottom stress estimates from vertical dissipation rate profiles on the continental shelf. J. Phys. Oceanogr., 18, 11671177, doi:10.1175/1520-0485(1988)018<1167:BSEFVD>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Donohue, K., P. Hamilton, K. Leaman, R. Leben, M. Prater, D. R. Watts, and E. Waddell, 2006: Exploratory study of deepwater currents in the Gulf of Mexico. Volume II: Technical report. U.S. Department of the Interior Mineral Management Service, OCS Study MMS 2006-074, 408 pp.

  • Donohue, K., P. Hamilton, R. R. Leben, D. R. Watts, and E. Waddell, 2008: Survey of deepwater currents in the northwestern Gulf of Mexico. Volume II: Technical report. U.S. Department of the Interior, Minerals Management Service, OCS Study MMS 2008-031, 364 pp.

  • Doyle, J. D., and Q. F. Jiang, 2006: Observations and numerical simulations of mountain waves in the presence of directional wind shear. Quart. J. Roy. Meteor. Soc., 132, 18771905, doi:10.1256/qj.05.140.

    • Search Google Scholar
    • Export Citation
  • Durran, D. R., 1986: Another look at downslope wind storms. Part I: The development of analogs to supercritical flow in an infinitely deep, continuously stratified fluid. J. Atmos. Sci., 43, 25272543, doi:10.1175/1520-0469(1986)043<2527:ALADWP>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Durran, D. R., 1990: Mountain waves and downslope winds. Atmospheric Processes over Complex Terrain, Meteor. Monogr., No. 45, Amer. Meteor. Soc., 59–81.

  • Edwards, K. A., P. MacCready, J. N. Moum, G. Pawlak, J. Klymak, and A. Perlin, 2004: Form drag and mixing due to tidal flow past a sharp point. J. Phys. Oceanogr., 34, 12971312, doi:10.1175/1520-0485(2004)034<1297:FDAMDT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Firing, E., J. Ranada, and P. Caldwell, cited 1995: CODAS ADCP processing. [Available online at http://currents.soest.hawaii.edu/docs/doc/codas_doc/.]

  • Garrett, C., and E. Kunze, 2007: Internal tide generation in the deep ocean. Annu. Rev. Fluid Mech., 39, 5787, doi:10.1146/annurev.fluid.39.050905.110227.

    • Search Google Scholar
    • Export Citation
  • Gill, A. E., 1982: Atmosphere–Ocean Dynamics.Academic Press, 662 pp.

  • Grant, W. D., and O. S. Madsen, 1982: Movable bed roughness in unsteady oscillatory flow. J. Geophys. Res., 87, 469481, doi:10.1029/JC087iC01p00469.

    • Search Google Scholar
    • Export Citation
  • Gregg, M. C., 1987: Diapycnal mixing in the thermocline: A review. J. Geophys. Res., 92, 52495286, doi:10.1029/JC092iC05p05249.

  • Grubisic, V., and Coauthors, 2008: The terrain-induced rotor experiment: A field campaign overview including observational highlights. Bull. Amer. Meteor. Soc.,89, 1513–1533, doi:10.1175/2008BAMS2487.1.

  • Hafner, T. A., and R. B. Smith, 1985: Pressure drag on the European Alps in relation to synoptic events. J. Atmos. Sci., 42, 562575, doi:10.1175/1520-0469(1985)042<0562:PDOTEA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Hodur, R. M., 1997: The Naval Research Laboratory’s Coupled Ocean/Atmosphere Mesoscale Prediction System (COAMPS). Mon. Wea. Rev., 125, 14141430, doi:10.1175/1520-0493(1997)125<1414:TNRLSC>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Hunt, J. C. R., and W. H. Snyder, 1980: Experiments on stably and neutrally stratified flow over a model three-dimensional hill. J. Fluid Mech., 96, 671704, doi:10.1017/S0022112080002303.

    • Search Google Scholar
    • Export Citation
  • Jayne, S. R., and L. C. St. Laurent, 2001: Parameterizing tidal dissipation over rough topography. Geophys. Res. Lett., 28, 811814, doi:10.1029/2000GL012044.

    • Search Google Scholar
    • Export Citation
  • Khatiwala, S., 2003: Generation of internal tides in an ocean of finite depth: Analytical and numerical calculations. Deep-Sea Res. I, 50, 321, doi:10.1016/S0967-0637(02)00132-2.

    • Search Google Scholar
    • Export Citation
  • Kim, Y.-J., and A. Arakawa, 1995: Improvement of orographic gravity parameterization using a mesoscale gravity wave model. J. Atmos. Sci., 52, 18751902, doi:10.1175/1520-0469(1995)052<1875:IOOGWP>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Kim, Y.-J., S. D. Eckermann, and H.-Y. Chun, 2003: An overview of the past, present and future of gravity-wave drag parameterization for numerical climate and weather prediction models: Survey article. Atmos.–Ocean, 41, 6598, doi:10.3137/ao.410105.

    • Search Google Scholar
    • Export Citation
  • Lamb, K. G., 1994: Numerical experiments of internal wave generation by strong tidal flow across a finite amplitude bank edge. J. Geophys. Res., 99, 843864, doi:10.1029/93JC02514.

    • Search Google Scholar
    • Export Citation
  • Legg, S., and K. M. H. Huijts, 2006: Preliminary simulations of internal waves and mixing generated by finite amplitude tidal flow over isolated topography. Deep-Sea Res. II, 53, 140156, doi:10.1016/j.dsr2.2005.09.014.

    • Search Google Scholar
    • Export Citation
  • Long, R. R., 1955: Some aspects of the flow of stratified fluids. Tellus, 7, 341357, doi:10.1111/j.2153-3490.1955.tb01171.x.

  • Lott, F., and M. J. Miller, 1997: A new subgrid-scale orographic drag parameterization: Its formulation and testing. Quart. J. Roy. Meteor. Soc., 123, 101127, doi:10.1002/qj.49712353704.

    • Search Google Scholar
    • Export Citation
  • McCabe, R., P. MacCready, and G. Pawlak, 2006: Form drag due to flow separation at a headland. J. Phys. Oceanogr., 36, 21362152, doi:10.1175/JPO2966.1.

    • Search Google Scholar
    • Export Citation
  • Minnery, G. A., 1990: Crustose coralline algae from the Flower Garden Banks, northwestern Gulf of Mexico; Controls on distribution and growth morphology. J. Sediment. Res., 60, 9921007, doi:10.1306/D4267663-2B26-11D7-8648000102C1865D.

    • Search Google Scholar
    • Export Citation
  • Moum, J. N., and J. D. Nash, 2000: Topographically induced drag and mixing at a small bank on the continental shelf. J. Phys. Oceanogr., 30, 20492054, doi:10.1175/1520-0485(2000)030<2049:TIDAMA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Moum, J. N., and W. D. Smyth, 2006: The pressure disturbance of a nonlinear internal wave train. J. Fluid Mech., 558, 153177, doi:10.1017/S0022112006000036.

    • Search Google Scholar
    • Export Citation
  • Moum, J. N., and J. D. Nash, 2008: Seafloor pressure measurements of nonlinear internal waves. J. Phys. Oceanogr., 38, 481491, doi:10.1175/2007JPO3736.1.

    • Search Google Scholar
    • Export Citation
  • Nakamura, T., T. Awaji, T. Hatayama, K. Akitomo, and T. Takizawa, 2000: The generation of large-amplitude unsteady lee waves by subinertial K1 tidal flow: A possible mixing mechanism in the Kuril Straits. J. Phys. Oceanogr., 30, 16011621, doi:10.1175/1520-0485(2000)030<1601:TGOLAU>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Nash, J. D., and J. N. Moum, 2001: Internal hydraulic flows on the continental shelf: High drag states over a small bank. J. Geophys. Res., 106, 45934612, doi:10.1029/1999JC000183.

    • Search Google Scholar
    • Export Citation
  • Nikuradse, J., 1950: Stromungsgesetz in rauhren rohren (Laws of flow in rough pipes). NACA Tech. Memo. 1292, 63 pp. [Available online at http://www.hach.ulg.ac.be/cms/en/system/files/Nikuardse%2520trad%2520NASA.pdf.]

  • Nikurashin, M., and R. Ferrari, 2011: Global energy conversion rate from geostrophic flows into internal lee waves in the deep ocean. Geophys. Res. Lett., 38, L08610, doi:10.1029/2011GL046576.

    • Search Google Scholar
    • Export Citation
  • Oke, P. R., J. S. Allen, R. N. Miller, G. D. Egbert, and P. M. Kosro, 2002: Assimilation of surface velocity data into a primitive equation coastal ocean model. J. Geophys. Res., 107, 31223147, doi:10.1029/2000JC000511.

    • Search Google Scholar
    • Export Citation
  • Olafsson, H., and P. Bougeault, 1996: Nonlinear flows past an elliptic mountain ridge. J. Atmos. Sci., 53, 24652489, doi:10.1175/1520-0469(1996)053<2465:NFPAEM>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Pawlak, G., P. MacCready, K. A. Edwards, and R. McCabe, 2003: Observations on the evolution of tidal vorticity at a stratified deep water headland. Geophys. Res. Lett., 30, 2234, doi:10.1029/2003GL018092.

    • Search Google Scholar
    • Export Citation
  • Perkins, H., F. De Strobel, and L. Gauldesi, 2000: The Barny Sentinel trawl-resistant ADCP bottom mount: Design, testing, and application. IEEE J. Oceanic Eng., 25, 430436, doi:10.1109/48.895350.

    • Search Google Scholar
    • Export Citation
  • Polzin, K. L., J. M. Toole, J. R. Ledwell, and R. W. Schmitt, 1997: Spatial variability of turbulent mixing in the abyssal ocean. Science, 276, 9396, doi:10.1126/science.276.5309.93.

    • Search Google Scholar
    • Export Citation
  • Pratt, L. J., 1986: Hydraulic control of sill flow with bottom friction. J. Phys. Oceanogr., 16, 19701980, doi:10.1175/1520-0485(1986)016<1970:HCOSFW>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Queney, P., 1948: The problem of air flow over mountains: A summary of theoretical studies. Bull. Amer. Meteor. Soc., 29, 1626.

  • 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, doi:10.4319/lo.2006.51.5.1956.

    • 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, doi:10.1029/2010JC006892.

    • Search Google Scholar
    • Export Citation
  • Schlichting, H., 1962: Boundary Layer Theory.6th ed. McGraw-Hill, 817 pp.

  • Seim, K. S., I. Fer, and H. Avlesen, 2012: Stratified flow over complex topography: A model study of the bottom drag and associated mixing. Cont. Shelf Res., 34, 4152, doi:10.1016/j.csr.2011.11.016.

    • Search Google Scholar
    • Export Citation
  • Skyllingstad, E. D., and H. W. Wijesekera, 2004: Large-eddy simulation of flow over two-dimensional obstacles: High drag states and mixing. J. Phys. Oceanogr., 34, 94112, doi:10.1175/1520-0485(2004)034<0094:LSOFOT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Smith, R. B., 1978: A measurement of mountain drag. J. Atmos. Sci., 35, 16441654, doi:10.1175/1520-0469(1978)035<1644:AMOMD>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Smith, R. B., 1979: The influence of the earth’s rotation on mountain wave drag. J. Atmos. Sci., 36, 177180, doi:10.1175/1520-0469(1979)036<0177:TIOTER>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Smith, R. B., 1980: Linear theory of stratified hydrostatic flow past an isolated mountain. Tellus, 32, 348364, doi:10.1111/j.2153-3490.1980.tb00962.x.

    • Search Google Scholar
    • Export Citation
  • Smith, R. B., 1989: Hydrostatic airflow over mountains. Advances in Geophysics, Vol. 31, Academic Press, 1–41, doi:10.1016/S0065-2687(08)60052-7.

  • Stull, R. B., 1988: An Introduction to Boundary Layer Meteorology.Kluwer Academic Publishers, 666 pp.

  • Teague, W. J., H. W. Wijesekera, E. Jarosz, D. B. Fribance, A. Lugo-Fernández, and Z. R. Hallock, 2013: Current and hydrographic conditions at the East Flower Garden Bank in 2011. Cont. Shelf Res., 63, 43–58, doi:10.1016/j.csr.2013.04.039.

    • Search Google Scholar
    • Export Citation
  • Tennekes, H., and J. L. Lumley, 1972: A First Course in Turbulence.MIT Press, 300 pp.

  • Vosper, S. B., I. P. Castro, W. H. Snyder, and S. D. Mobbs, 1999: Experimental studies of strongly stratified flow past three-dimensional orography. J. Fluid Mech., 390, 223249, doi:10.1017/S0022112099005133.

    • Search Google Scholar
    • Export Citation
  • Warner, S. J., 2012: Using bottom pressure to quantify tidal form drag on a sloping headland. Ph.D. thesis, University of Washington, 131 pp.

  • Warner, S. J., and P. MacCready, 2009: Dissecting the pressure field in tidal flow past a headland: When is form drag “real”? J. Phys. Oceanogr., 39, 29712984, doi:10.1175/2009JPO4173.1.

    • Search Google Scholar
    • Export Citation
  • Warner, S. J., P. MacCready, J. N. Moum, and J. D. Nash, 2013: Measurement of tidal form drag using seafloor pressure sensors. J. Phys. Oceanogr., 43, 11501172, doi:10.1175/JPO-D-12-0163.1.

    • Search Google Scholar
    • Export Citation
  • Wijesekera, H. W., D. W. Wang, W. J. Teague, and E. Jarosz, 2010: High sea-floor stress induced by extreme hurricane waves. Geophys. Res. Lett., 37, L11604, doi:10.1029/2010GL043124.

    • Search Google Scholar
    • Export Citation
  • Wijesekera, H. W., D. W. Wang, W. J. Teague, E. Jarosz, W. E. Rogers, D. B. Fribance, and J. N. Moum, 2013: Surface wave effects on high-frequency currents over a shelf edge bank. J. Phys. Oceanogr., 43, 16271647, doi:10.1175/JPO-D-12-0197.1.

    • Search Google Scholar
    • Export Citation
  • Wolk, F., H. Yamazaki, L. Seuront, and R. G. Lueck, 2002: A new free-fall profiler for measuring biophysical microstructure. J. Atmos. Oceanic Technol., 19, 780793, doi:10.1175/1520-0426(2002)019<0780:ANFFPF>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Wood, N., A. R. Brown, and F. E. Hewer, 2001: Parameterizing the effects of orography on the boundary layer: An alternative to effective roughness lengths. Quart. J. Roy. Meteor. Soc., 127, 759777, doi:10.1002/qj.49712757303.

    • Search Google Scholar
    • Export Citation
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