Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-19T13:05:13.987Z Has data issue: false hasContentIssue false
  • English
  • Français

The effect of waves on subgrid-scale stresses, dissipation and model coefficients in the coastal ocean bottom boundary layer

Published online by Cambridge University Press:  04 July 2007

W. A. M. NIMMO SMITH ,
J. KATZ  and
T. R. OSBORN
W. A. M. NIMMO SMITH
Affiliation:
School of Earth, Ocean & Environmental Sciences, University of Plymouth, Plymouth, Devon, UK
J. KATZ
Affiliation:
Department of Mechanical Engineering, The Johns Hopkins University, Baltimore, Maryland, USA
T. R. OSBORN
Affiliation:
Department of Mechanical Engineering, The Johns Hopkins University, Baltimore, Maryland, USA Department of Earth & Planetary Sciences, The Johns Hopkins University, Baltimore, Maryland, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

Six sets of particle image velocimetry (PIV) data from the bottom boundary layer of the coastal ocean are examined. The data represent periods of high, moderate and weak mean flow relative to the amplitude of wave-induced motion, which correspond to high, moderate and low Reynolds numbers based on the Taylor microscale (Re). The two-dimensional PIV velocity distributions enable spatial filtering to calculate some of the subgrid-scale (SGS) stresses, from which we can estimate the SGS dissipation, and evaluate the performance of typically used SGS stress models. The previously reported mismatch between the SGS and viscous dissipation at moderate and low Reynolds numbers appears to be related to the sparsity of large vortical structures that dominate energy fluxes.

Conditional sampling of SGS stresses and dissipation based on wave phase using Hilbert transforms demonstrate persistent and repeatable direct effects of large-scale but weak straining by the waves on the SGS energy flux at small scales. The SGS energy flux is phase-dependent, peaking when the streamwise-wave-induced velocity is accelerating, and lower when this velocity is decelerating. Combined with strain rate generated by the mean flow, the streamwise wave strain causes negative energy flux (backscatter), whereas the vertical wave strain causes a positive flux. The phase-dependent variations and differences between horizontal and vertical contributions to the cascading process extend to strains that are substantially higher than the wave-induced motion. These trends may explain the measured difference between spatial energy spectra of streamwise velocity fluctuations and spectra of the wall-normal component, i.e. the formation of spectral bumps in the spectra of the streamwise component at the wavenumbers for the transition between inertial and dissipation scales.

All the model coefficients of typical SGS stress models measured here are phase dependent and show similar trends. Thus, the variations of measured SGS dissipation with phase are larger than those predicted by the model variables. In addition, the measured coefficients of the static Smagorinsky SGS stress model decrease with decreasing turbulence levels, and increase with filter size. The dynamic model provides higher correlation coefficients than the Smagorinsky model, but the substantial fluctuations in their values indicate that ensemble averaging is required. The ‘global’ dynamic model coefficients indicate that the use of a scale-dependent dynamic model may be appropriate. The structure function model yields poor correlation coefficients and is found to be over-dissipative under all but the highest turbulence levels. The nonlinear model has higher correlations with measured stresses, as expected, but it also does not reproduce the trends with wave phase.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 583 , 25 July 2007 , pp. 133 - 160
Copyright
Copyright © Cambridge University Press 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Bertuccioli, L., Roth, G. I., Katz, J. & Osborn, T. R. 1999 A submersible particle image velocimetry system for turbulence measurements in the bottom boundary layer. J. Atmos. Oceanic Technol. 16, 1635–1646.2.0.CO;2>CrossRefGoogle Scholar
Borue, V. & Orszag, S. A. 1998 Local energy flux and subgrid-scale statistics in three-dimensional turbulence. J. Fluid Mech. 366, 1–31.CrossRefGoogle Scholar
Champagne, F. H., Friehe, C. A., LaRue, J. C. Rue, J. C. & Wyngaard, J. C. 1977 Flux measurements, flux estimation techniques and fine scale turbulence measurements in the surface layer over land. J. Atmos. Sci. 34, 515–530.2.0.CO;2>CrossRefGoogle Scholar
Chen, J., Katz, J. & Meneveau, C. 2005 Implication of mismatch between stress and strain-rate in turbulence subjected to rapid straining and destraining on dynamic LES models. Trans. ASME: J. Fluids Engng 127, 840–850.Google Scholar
Chen, J., Meneveau, C. & Katz, J. 2006 Scale interactions of turbulence subjected to a straining–relaxation–detstraining cycle. J. Fluid Mech. 562, 123–150.CrossRefGoogle Scholar
Deardorff, J. W. 1980 Stratocumulus-capped mixed layers derived from a three-dimensional model. Boundary Layer Met. 18, 495–527.CrossRefGoogle Scholar
Denbo, D. W. & Skyllingstad, E. D. 1996 An ocean large-eddy simulation model with application to deep convection in the Greenland Sea. J. Geophys. Res. 101 (C1), 1095–1110.CrossRefGoogle Scholar
Doron, P., Bertuccioli, L., Katz, J. & Osborn, T. R. 2001 Turbulence characteristics and dissipation estimates in the coastal ocean bottom boundary layer from PIV data. J. Phys. Oceanogr. 31, 2108–2134.2.0.CO;2>CrossRefGoogle Scholar
Falkovich, G. 1994 Bottleneck phenomenon in developed turbulence. Phys. Fluids 6, 1411–1414.CrossRefGoogle Scholar
Friedman, P. D. & Katz, J. 2002 Mean rise-rate of droplets in isotropic turbulence. Phys. Fluids 6, 1411–1414.Google Scholar
Germano, M., Piomelli, U., Moin, P. & Cabot, W. H. 1991 A dynamic subgrid-scale eddy viscosity model. Phys. Fluids A 3, 1760.CrossRefGoogle Scholar
Green, T., Medwin, H. & Paquin, J. E. 1972 Measurements of surface wave decay due to underwater turbulence. Nature 237, 115–117.Google Scholar
Horiuti, K. 1993 A proper velocity scale for modelling subgrid-scale eddy viscosities in large-eddy simulation. Phys. Fluids A 5, 146–157.CrossRefGoogle Scholar
Hristov, T., Friehe, C. & Miller, S. 1998 Wave-coherent fields in air flow over ocean waves: identification of cooperative behavior buried in turbulence. Phys. Rev. Lett. 81, 5245–5248.CrossRefGoogle Scholar
Huang, N. E., Shen, Z., Long, S. R., Wu, M. C., Shih, H. H., Zheng, Q., Yen, N., Tung, C. C. & Liu, H. H. 1998 The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proc. R. Soc. Lond. A 454, 903–995.CrossRefGoogle Scholar
Kitaigorodskii, S. A., Donelan, M. A., Lumley, J. L. & Terray, E. A. 1983 Wave-turbulence interactions in the upper ocea. Part II: Statistical characteristics of wave and turbulent components of the random velocity field in the marine surface layer. J. Phys. Oceanogr. 13, 1988–1999.2.0.CO;2>CrossRefGoogle Scholar
Kitaigorodskii, S. A. & Lumley, J. L. 1983 Wave-turbulence interactions in the upper ocean. Part I: The energy balance on the interacting fields of surface wind waves and wind-induced three-dimensional turbulence. J. Phys. Oceanogr. 13, 1977–1987.2.0.CO;2>CrossRefGoogle Scholar
Leonard, A. 1974 Energy cascade in large-eddy simulations of turbulent fluid flows. Adv. Geophys. 18, 237–248.CrossRefGoogle Scholar
Lesieur, M. & Metais, O. 1996 New trends in large-eddy simulations of turbulence. Annu. Rev. Fluid Mech. 28, 45–82.CrossRefGoogle Scholar
Li, M., Sanford, L. & Chao, S. Y. 2005 Effects of time dependence in unstratified tidal boundary layers: results from large eddy simulations. Estuarine, Coastal Shelf Sci. 62, 193–204.CrossRefGoogle Scholar
Lilly, D. K. 1967 The representation of small-scale turbulence in numerical simulations. In Proc. IBM Scientific Computing Symposium on Environmental Sciences, pp. 195–209. IBM form no. 320-1951, White Plains, New York.Google Scholar
Lilly, D. K. 1992 A proposed modification of the Germano subgrid-scale closure method. Phys. Fluids A 4, 633–635.CrossRefGoogle Scholar
Liu, S., Katz, J. & Meneveau, C. 1999 Evolution and modeling of subgrid scales during rapid straining of turbulence. J. Fluid Mech. 387, 281–320.CrossRefGoogle Scholar
Liu, S., Meneveau, C. & Katz, J. 1994 On the properties of similarity subgrid-scale models as deduced from measurements in a turbulent jet. J. Fluid Mech. 275, 83–119.CrossRefGoogle Scholar
Liu, S., Meneveau, C. & Katz, J. 1995 Experimental study of similarity subgrid-scale models of turbulence in the far-field of a jet. Appl. Sci. Res. 54, 177–190.CrossRefGoogle Scholar
Luznik, L. 2006 Turbulence characteristics of a tidally driven bottom boundary layer of the coastal ocean. PhD thesis, The Johns Hopkins University.Google Scholar
Luznik, L., Gurka, R., NimmoSmith, W. A. M. Smith, W. A. M., Zhu, W., Katz, J. & Osborn, T. R. 2007 a Distribution of energy spectra, Reynolds stresses, turbulence production and dissipation in a tidally driven bottom boundary layer. J. Phys. Oceanogr. (in press).Google Scholar
Luznik, L., NimmoSmith, W. A. M. Smith, W. A. M., Osborn, T. R., & Katz, J. 2007 Turbulence and waves in the bottom boundary layer of the coastal ocean. J. Phys. Oceanogr. (submitted).Google Scholar
Mason, P. J. 1989 Large-eddy simulation of the convective atmospheric boundary layer. J. Atmos. Sci. 46, 1492–1516.2.0.CO;2>CrossRefGoogle Scholar
Meneveau, C. & Katz, J. 1999 Dynamic testing of subgrid models in large eddy simulation based on the Germano identity. Phys. Fluids 11, 245–247.CrossRefGoogle Scholar
Meneveau, C. & Katz, J. 2000 Scale-invariance and turbulence models for large-eddy simulation. Annu. Rev. Fluid Mech. 32, 1–32.CrossRefGoogle Scholar
Metais, O. & Lesieur, M. 1992 Spectral large-eddy simulation of isotropic and stably stratified turbulence. J. Fluid Mech. 239, 157–194.CrossRefGoogle Scholar
Min, H. S. & Noh, Y. 2004 Influence of the surface heating on Langmuir circulation. J. Phys. Oceanogr. 34, 2630–2641.CrossRefGoogle Scholar
Moin, P. & Kim, J. 1982 Numerical investigation of turbulent channel flow. J. Fluid Mech. 118, 341–377.CrossRefGoogle Scholar
Nepf, H. M., Cowen, E. A., Kimmel, S. J. & Monismith, S. G. 1995 Longitudinal vortices beneath breaking waves. J. Geophys. Res. 100, 16211–16221.CrossRefGoogle Scholar
NimmoSmith, W. A. M. Smith, W. A. M., Atsavapranee, P., Katz, J. & Osborn, T. R. 2002 PIV measurements in the bottom boundary layer of the coastal ocean. Exps. Fluids 33, 962–971.CrossRefGoogle Scholar
Nimmo Smith, W. A. M., Katz, J. & Osborn, T. R. 2005 On the structure of turbulence in the bottom boundary layer of the coastal ocean. J. Phys. Oceanogr. 35, 72–93 (referred to herein as NS05).CrossRefGoogle Scholar
Nimmo Smith, W. A. M., Osborn, T. R. & Katz, J. 2004 PIV measurements in the bottom boundary layer of the coastal ocean. In PIV and Water Waves (ed. Grue, J., Liu, P. L.-F. & Pedersen, G. K.). Advances in Coastal and Ocean Engineering, vol. 9, chap. 2, pp. 51–79. World Scientific.CrossRefGoogle Scholar
Noh, Y., Min, H. S. & Raasch, S. 2004 Large eddy simulation of the ocean mixed layer: the effects of wave breaking and Langmuir circulation. J. Phys. Oceanogr. 34, 720–735.2.0.CO;2>CrossRefGoogle Scholar
Ölmez, H. S. & Milgram, J. H. 1992 An experimental study of attenuation of short water waves by turbulence. J. Fluid Mech. 239, 133–156.CrossRefGoogle Scholar
Phillips, O. M. 1959 The scattering of gravity waves by turbulence. J. Fluid Mech. 5, 177–192.CrossRefGoogle Scholar
Piomelli, U. 1999 Large-eddy simulation: achievements and challenges. Prog. Aerospace Sci. 35, 335–362.CrossRefGoogle Scholar
Piomelli, U., Cabot, W. H., Moin, P. & Lee, S. 1991 Subgrid-scale backscatter in turbulent and transition flows. Phys. Fluids A 3, 1766–1771.CrossRefGoogle Scholar
Piomelli, U., Moin, P. & Ferziger, J. H. 1988 Model consistency in large eddy simulation of turbulent channel flows. Phys. Fluids 31, 1884–1891.CrossRefGoogle Scholar
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
Porte-Agel, F., Meneveau, C. & Parlange, M. B. 2000 A scale-dependent dynamic model for large-eddy simulation: application to a neutral atmospheric boundary layer. J. Fluid Mech. 415, 261–284.CrossRefGoogle Scholar
Raupach, M. R., Antonia, R. A. & Rajagopalan, S. 1991 Rough-wall turbulent boundary layers. Appl. Mech. Rev. 44, 1–25.CrossRefGoogle Scholar
Roth, G. I. & Katz, J. 2001 Five techniques for increasing the speed and accuracy of PIV interrogation. Meas. Sci. Technol. 12, 238–245.CrossRefGoogle Scholar
Roth, G. I., Mascenik, D. T. & Katz, J. 1999 Measurements of the flow structure and turbulence within a ship bow wave. Phys. Fluids 11, 3512–3523.CrossRefGoogle Scholar
Saddoughi, S. G. & Veeravalli, S. V. 1994 Local isotropy in turbulent boundary layers at high Reynolds number. J. Fluid Mech. 268, 333–372.CrossRefGoogle Scholar
Scotti, A., Meneveau, C. & Lilly, D. K. 1993 Generalized Smagorinsky model for anisotropic grids. Phys. Fluids A 5, 2306–2308.CrossRefGoogle Scholar
Shaw, R. H. & Schumann, U. 1992 Large-eddy simulation of turbulent flow above and within a forest. Boundary Layer Met. 61, 47–64.CrossRefGoogle Scholar
Skyllingstad, E. D., Smyth, W. D., Moum, J. N. & Wijesekera, H. 1999 Upper-ocean turbulence during a westerly wind burst: a comparison of large-eddy simulation results and microstructure measurements. J. Phys. Oceanogr. 29, 5–28.2.0.CO;2>CrossRefGoogle Scholar
Skyllingstad, E. D. & Wijesekera, H. W. 2004 Large-eddy simulation of flow over two-dimensional obstacles: high drag states and mixing. J. Phys. Oceanogr. 34, 94–112.2.0.CO;2>CrossRefGoogle Scholar
Smagorinsky, J. 1963 General circulation experiments with the primitive equations. Mon. Weath. Rev. 91, 99–164.2.3.CO;2>CrossRefGoogle Scholar
Snodgrass, F. E., Groves, G. W., Hasselmann, K. F., Miller, G. R., Munk, W. H. & Powers, W. H. 1966 Propagation of ocean swell across the pacific. Phil. Trans. R. Soc. Lond. A 259, 431–497.Google Scholar
Tao, B., Katz, J. & Meneveau, C. 2002 Statistical geometry of subgrid-scale stresses determined from holographic particle image velocimetry measurements. J. Fluid Mech. 457, 35–78.CrossRefGoogle Scholar
Teixeira, M. A. C. & Belcher, S. E. 2002 On the distortion of turbulence by a progressive surface wave. J. Fluid Mech. 458, 229–267.CrossRefGoogle Scholar
Terray, E. A., Donelan, M. A., Agrawal, Y. C., Drennan, W. M., Kahma, K. K., Williams, A. J., Hwang, P. A. & Kitaigorodskii, S. A. 1996 Estimates of kinetic energy dissipation under breaking waves. J. Phys. Oceanogr. 26, 792–807.2.0.CO;2>CrossRefGoogle Scholar
Thais, L. & Magnaudet, J. 1996 Turbulent structure beneath surface gravity waves sheared by the wind. J. Fluid Mech. 328, 313–344.CrossRefGoogle Scholar
Townsend, A. A. 1961 Equilibrium layers and wall turbulence. J. Fluid Mech. 11, 97–120.CrossRefGoogle Scholar
Trowbridge, J. H. 1998 On a technique for measurement of turbulent shear stress in the presence of surface waves. J. Atmos. Oceanic Technol. 15, 290–298.2.0.CO;2>CrossRefGoogle Scholar