• Barry, M. E., G. N. Ivey, K. B. Winters, and J. Imberger, 2001: Measurements of diapycnal diffusivities in stratified fluids. J. Fluid Mech., 442, 267291, https://doi.org/10.1017/S0022112001005080.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bluteau, C., N. L. Jones, and G. N. Ivey, 2013: Turbulent mixing efficiency at an energetic ocean site. J. Geophys. Res. Oceans, 118, 46624672, https://doi.org/10.1002/jgrc.20292.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bouffard, D., and L. Boegman, 2013: A diapycnal diffusivity model for stratified environmental flows. Dyn. Atmos. Oceans, 61–62, 1432, https://doi.org/10.1016/j.dynatmoce.2013.02.002.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Cloern, J., 1991: Tidal stirring and phytoplankton bloom dynamics in an estuary. J. Mar. Res., 49, 203221, https://doi.org/10.1357/002224091784968611.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Cross, J., W. Nimmo-Smith, P. Hosegood, and R. Torres, 2014: The dispersal of phytoplankton populations by enhanced turbulent mixing in a shallow coastal sea. J. Mar. Syst., 136, 5564, https://doi.org/10.1016/j.jmarsys.2014.03.009.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Davis, K. A., and S. G. Monismith, 2011: The modification of bottom boundary layer turbulence and mixing by internal waves shoaling on a barrier reef. J. Phys. Oceanogr., 41, 22232241, https://doi.org/10.1175/2011JPO4344.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Deardorff, J., 1980: Stratocumulus-capped mixed layers derived from a three-dimensional model. Bound.-Layer Meteor., 18, 495527, https://doi.org/10.1007/BF00119502.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Dunckley, J. F., J. R. Koseff, J. V. Steinbuck, S. G. Monismith, and A. Genin, 2012: Comparison of mixing efficiency and vertical diffusivity models from temperature microstructure. J. Geophys. Res., 117, C10008, https://doi.org/10.1029/2012JC007967.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ellison, T. H., 1957: Turbulent transport of heat and momentum from an infinite rough plane. J. Fluid Mech., 2, 456466, https://doi.org/10.1017/S0022112057000269.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Endoh, T., Y. Yoshikawa, T. Matsuno, Y. Wakata, K.-J. Lee, and L. Umlauf, 2016: Observational evidence for tidal straining over a sloping continental shelf. Cont. Shelf Res., 117, 1219, https://doi.org/10.1016/j.csr.2016.01.018.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Feddersen, F., J. H. Trowbridge, and A. J. Williams III, 2007: Vertical structure of dissipation in the nearshore. J. Phys. Oceanogr., 37, 17641777, https://doi.org/10.1175/JPO3098.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Furevik, T., and A. Foldvik, 1996: Stability at M2 critical latitude in the Barents Sea. J. Geophys. Res., 101, 88238837, https://doi.org/10.1029/96JC00081.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Garcez Faria, A., E. Thornton, T. Stanton, C. Soares, and T. Lippmann, 1998: Vertical profiles of longshore currents and related bed shear stress and bottom roughness. J. Geophys. Res., 103, 32173232, https://doi.org/10.1029/97JC02265.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gregg, M. C., E. A. D’Asaro, J. J. Riley, and E. Kunze, 2018: Mixing efficiency in the ocean. Annu. Rev. Mar. Sci., 10, 443473, https://doi.org/10.1146/annurev-marine-121916-063643.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Heinze, R., D. Mironov, and S. Raasch, 2015: Second-moment budgets in cloud topped boundary layers: A large-eddy simulation study. J. Adv. Model. Earth Syst., 7, 510536, https://doi.org/10.1002/2014MS000376.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hibiya, T., M. Nagasawa, and Y. Niwa, 2006: Global mapping of diapycnal diffusivity in the deep ocean based on the results of expendable current profiler (XCP) surveys. Geophys. Res. Lett., 33, L03611, https://doi.org/10.1029/2005GL025218.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hibiya, T., M. Nagasawa, and Y. Niwa, 2007: Latitudinal dependence of diapycnal diffusivity in the thermocline observed using a microstructure profiler. Geophys. Res. Lett., 34, L24602, https://doi.org/10.1029/2007GL032323.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ivey, G. N., and J. Imberger, 1991: On the nature of turbulence in a stratified fluid. Part I: The energetics of mixing. J. Phys. Oceanogr., 21, 650658, https://doi.org/10.1175/1520-0485(1991)021<0650:OTNOTI>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Jackett, D., T. McDougall, R. Feistel, D. Wright, and S. Griffies, 2006: Algorithms for density, potential temperature, conservative temperature, and the freezing temperature of seawater. J. Atmos. Oceanic Technol., 23, 17091728, https://doi.org/10.1175/JTECH1946.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kitamura, Y., A. Hori, and T. Yagi, 2013: Flux Richardson number and turbulent Prandtl number in a developing stable boundary layer. J. Meteor. Soc. Japan, 91, 655666, https://doi.org/10.2151/jmsj.2013-507.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Leibovich, S., and S. Lele, 1985: The influence of the horizontal component of Earth’s angular velocity on the instability of the Ekman layer. J. Fluid Mech., 150, 4187, https://doi.org/10.1017/S0022112085000039.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lozovatsky, I. D., and H. J. S. Fernando, 2013: Mixing efficiency in natural flows. Philos. Trans. Roy. Soc. London, 371A, 1982, https://doi.org/10.1098/rsta.2012.0213.

    • Search Google Scholar
    • Export Citation
  • Maronga, B., and Coauthors, 2015: The parallelized large-eddy simulation model (PALM) version 4.0 for atmospheric and oceanic flows: Model formulation, recent developments, and future perspectives. Geosci. Model Dev., 8, 25152551, https://doi.org/10.5194/gmd-8-2515-2015.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Mater, B., and S. Venayagamoorthy, 2014a: The quest for an unambiguous parameterization of mixing efficiency in stably stratified geophysical flows. Geophys. Res. Lett., 41, 46464653, https://doi.org/10.1002/2014GL060571.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Mater, B., and S. Venayagamoorthy, 2014b: A unifying framework for parameterizing stably stratified shear-flow turbulence. Phys. Fluids, 26, 036601, https://doi.org/10.1063/1.4868142.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Mellor, G., and T. Yamada, 1982: Development of a turbulence closure model for geophysical fluid problem. Rev. Geophys. Space Phys., 20, 851875, https://doi.org/10.1029/RG020i004p00851.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Monismith, S., J. Koseff, and B. White, 2018: Mixing efficiency in the presence of stratification: When is it constant? Geophys. Res. Lett., 45, 56275634, https://doi.org/10.1029/2018GL077229.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Moum, J. N., 1996: Efficiency of mixing in the main thermocline. J. Geophys. Res., 101, 12 05712 069, https://doi.org/10.1029/96JC00508.

  • Moum, J. N., and T. R. Osborn, 1986: Mixing in the main thermocline. J. Phys. Oceanogr., 16, 12501259, https://doi.org/10.1175/1520-0485(1986)016<1250:MITMT>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Munk, W., 1966: Abyssal recipes. Deep-Sea Res. Oceanogr. Abstr., 13, 707730, https://doi.org/10.1016/0011-7471(66)90602-4.

  • Munk, W., and C. Wunsch, 1998: Abyssal recipes II: Energetics of tidal and wind mixing. Deep-Sea Res., 45, 19772010, https://doi.org/10.1016/S0967-0637(98)00070-3.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Nagasawa, M., T. Hibiya, Y. Niwa, M. Watanabe, Y. Isoda, S. Takagi, and Y. Kamei, 2002: Distribution of fine-scale shear in the deep waters of the North Pacific obtained using expendable current profilers. J. Geophys. Res., 107, 3221, https://doi.org/10.1029/2002JC001376.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Oakey, N. S., 1982: Determination of the rate of dissipation of turbulent energy from simultaneous temperature and velocity shear microstructure measurements. J. Phys. Oceanogr., 12, 256271, https://doi.org/10.1175/1520-0485(1982)012<0256:DOTROD>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Osborn, T., 1980: Estimates of the local rate of vertical diffusion from dissipation measurements. J. Phys. Oceanogr., 10, 8389, https://doi.org/10.1175/1520-0485(1980)010<0083:EOTLRO>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Peters, H., 1999: Spatial and temporal variability of turbulent mixing in an estuary. J. Mar. Res., 57, 805845, https://doi.org/10.1357/002224099321514060.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Raasch, S., and M. Schröter, 2001: PALM—A large-eddy simulation model performing on massively parallel computers. Meteor. Z., 10, 363373, https://doi.org/10.1127/0941-2948/2001/0010-0363.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Rehmann, C. R., 2004: Scaling for the mixing efficiency of stratified grid turbulence. J. Hydraul. Res., 42, 3542, https://doi.org/10.1080/00221686.2004.9641181.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Rehmann, C. R., and J. R. Koseff, 2004: Mean potential energy change in stratified grid turbulence. Dyn. Atmos. Oceans, 37, 271294, https://doi.org/10.1016/j.dynatmoce.2003.09.001.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Reidenbach, M., S. Monismith, J. 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
  • Rippeth, T. P., N. R. Fisher, and J. H. Simpson, 2001: The cycle of turbulent dissipation in the presence of tidal straining. J. Phys. Oceanogr., 31, 24582471, https://doi.org/10.1175/1520-0485(2001)031<2458:TCOTDI>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Rippeth, T. P., J. Simpson, E. Williams, and M. Inall, 2003: Measurement of the rates of production and dissipation of turbulent kinetic energy in an energetic tidal flow: Red Wharf Bay revisited. J. Phys. Oceanogr., 33, 18891901, https://doi.org/10.1175/1520-0485(2003)033<1889:MOTROP>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Rohr, J. J., E. C. Itsweire, and C. W. Van Atta, 1984: Mixing efficiency in stably-stratified decaying turbulence. Geophys. Astrophys. Fluid Dyn., 29, 221236, https://doi.org/10.1080/03091928408248190.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Scotti, A., and B. White, 2016: The mixing efficiency of stratified turbulent boundary layers. J. Phys. Oceanogr., 46, 31813191, https://doi.org/10.1175/JPO-D-16-0095.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Shaw, W. J., J. H. Trowbridge, and A. J. Williams III, 2001: Budgets of turbulent kinetic energy and scalar variance in the continental shelf bottom boundary layer. J. Geophys. Res., 106, 95519564, https://doi.org/10.1029/2000JC000240.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Shih, L. H., J. R. Koseff, G. N. Ivey, and J. H. Ferziger, 2005: Parameterization of turbulent fluxes and scales using homogeneous sheared stably stratified turbulence simulations. J. Fluid Mech., 525, 193214, https://doi.org/10.1017/S0022112004002587.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Simpson, J., W. Crawford, T. Rippeth, and A. Campbell, 1996: The vertical structure of turbulent dissipation in shelf seas. J. Phys. Oceanogr., 26, 15791590, https://doi.org/10.1175/1520-0485(1996)026<1579:TVSOTD>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Stretch, D. D., J. W. Rottman, S. K. Venayagamoorthy, K. K. Nomura, and C. R. Rehmann, 2010: Mixing efficiency in decaying stably stratified turbulence. Dyn. Atmos. Oceans, 49, 2536, https://doi.org/10.1016/j.dynatmoce.2008.11.002.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tilzer, M., and C. Goldman, 1978: Importance of mixing, thermal stratification and light adaptation for phytoplankton productivity in Lake Tahoe (California-Nevada). Ecology, 59, 810821, https://doi.org/10.2307/1938785.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tsutsumi, E., and T. Matsuno, 2012: Observations of turbulence under weakly and highly stratified conditions in the Ariake Sea. J. Oceanogr., 68, 369386, https://doi.org/10.1007/s10872-012-0103-2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Venayagamoorthy, S., and J. Koseff, 2016: On the flux Richardson number in stably stratified turbulence. J. Fluid Mech., 798, R1, https://doi.org/10.1017/jfm.2016.340.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wakata, Y., 2010: Numerical simulation of ocean bottom boundary layer. Theor. Appl. Mech. Japan, 58, 145151.

  • Wakata, Y., 2013: Some properties of tidal currents estimated from analytical and LES simulation studies. J. Oceanogr., 69, 737751, https://doi.org/10.1007/s10872-013-0204-6.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wakata, Y., T. Endoh, and Y. Yoshikawa, 2017: LES study of near-seabed tide-induced turbulence in the East China Sea. Cont. Shelf Res., 145, 2131, https://doi.org/10.1016/j.csr.2017.06.020.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Walter, R., M. E. Squibb, C. Woodson, J. Koseff, and S. Monismith, 2014: Stratified turbulence in the nearshore coastal ocean: Dynamics and evolution in the presence of internal bores. J. Geophys. Res. Oceans, 119, 87098730, https://doi.org/10.1002/2014JC010396.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Yamada, T., 1975: The critical Richardson number and the ratio of the eddy transport. J. Atmos. Sci., 32, 926933, https://doi.org/10.1175/1520-0469(1975)032<0926:TCRNAT>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zhou, Q., J. R. Taylor, and C. Caulfield, 2017: Self-similar mixing in stratified plane Couette flow for varying Prandtl number. J. Fluid Mech., 820, 86120, https://doi.org/10.1017/jfm.2017.200.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zilitinkevich, S. S., T. Elperin, N. Kleeorin, I. Rogachevskii, I. Esau, T. Mauritsen, and M. W. Miles, 2008: Turbulence energetics in stably stratified geophysical flows: Strong and weak mixing regimes. Quart. J. Roy. Meteor. Soc., 134, 793799, https://doi.org/10.1002/qj.264.

    • Crossref
    • Search Google Scholar
    • Export Citation
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LES Study of Vertical Eddy Diffusivity Estimation in Bottom Boundary Layers

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  • 1 Research Institute for Applied Mechanics, Kyushu University, Kasuga, Fukuoka, Japan
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Abstract

Osborn’s method is commonly used to obtain diffusion coefficient K from the turbulent dissipation rate ε. This method is the relational expression . The dissipation flux coefficient is often set to a constant value of 0.2, but this study of LES revealed that varies greatly vertically in the bottom boundary layer because of the influence of the seabed. Consequently, the eddy diffusion coefficient is overestimated in the lower part of the bottom boundary, but it is slightly underestimated in the upper part. Therefore, Osborn’s method with constant cannot give the correct diffusivity. Furthermore, even if treating as a function of flux Richardson number , as defined originally by Osborn, the estimation is underestimated by the advection effect because of the influence of spatial nonuniformity. Energy budget analysis revealed that this defect can be improved using the extended flux Richardson number, which can be estimated by multiplying using a constant correction factor. Furthermore, we proposed two alternative estimation methods. For the first method, which estimates the relation between and the gradient Richardson number , can be expressed with instead of with a correction factor. We can estimate the reasonable diffusivity if we have current data supplementary to obtain . For the second method, can be expressed as a similarity function of the height above the bottom normalized by the Ozmidov scale. This method can provide an acceptable estimate of diffusivity without current data for several circumstances.

© 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: Yoshinobu Wakata, wakata@riam.kyushu-u.ac.jp

Abstract

Osborn’s method is commonly used to obtain diffusion coefficient K from the turbulent dissipation rate ε. This method is the relational expression . The dissipation flux coefficient is often set to a constant value of 0.2, but this study of LES revealed that varies greatly vertically in the bottom boundary layer because of the influence of the seabed. Consequently, the eddy diffusion coefficient is overestimated in the lower part of the bottom boundary, but it is slightly underestimated in the upper part. Therefore, Osborn’s method with constant cannot give the correct diffusivity. Furthermore, even if treating as a function of flux Richardson number , as defined originally by Osborn, the estimation is underestimated by the advection effect because of the influence of spatial nonuniformity. Energy budget analysis revealed that this defect can be improved using the extended flux Richardson number, which can be estimated by multiplying using a constant correction factor. Furthermore, we proposed two alternative estimation methods. For the first method, which estimates the relation between and the gradient Richardson number , can be expressed with instead of with a correction factor. We can estimate the reasonable diffusivity if we have current data supplementary to obtain . For the second method, can be expressed as a similarity function of the height above the bottom normalized by the Ozmidov scale. This method can provide an acceptable estimate of diffusivity without current data for several circumstances.

© 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: Yoshinobu Wakata, wakata@riam.kyushu-u.ac.jp
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