On a Technique for Measurement of Turbulent Shear Stress in the Presence of Surface Waves

J. H. Trowbridge Woods Hole Oceanographic Institution, Woods Hole, Massachussetts

Search for other papers by J. H. Trowbridge in
Current site
Google Scholar
PubMed
Close
Restricted access

Abstract

Surface waves can produce large biases in estimates of turbulent shear stress obtained from single-sensor measurements of velocity if there is even a small uncertainty in the orientation of either the velocity sensor or the principal axes of the wave-induced velocity field. The wave-induced bias can be diminished substantially by differencing measurements obtained from two velocity sensors separated by a distance larger than the correlation scale of the turbulence but small in comparison to the inverse wavenumber of the surface waves. If the scale separation is sufficiently large, then minus the density times half of the covariance between horizontal and vertical velocity differences is a nearly wave-free estimate of the average of the turbulent shear stresses at the two sensors. A theoretical analysis determines the bias associated with this technique under simplified conditions, in which waves and turbulence are uncorrelated and the waves are weakly nonlinear and narrow-banded in both frequency and direction. Order-of-magnitude estimates indicate that the technique can be used to obtain nearly unbiased estimates of near-bottom turbulent shear stress on continental shelves. A brief set of oceanic measurements demonstrates the success of the technique in practice.

Corresponding author address: J. H. Trowbridge, Dept. of Applied Ocean Physics and Engineering, Woods Hole Oceanographic Institution, MS 12, Woods Hole, MA 02543.

Email: jtrowbridge@whoi.edu

Abstract

Surface waves can produce large biases in estimates of turbulent shear stress obtained from single-sensor measurements of velocity if there is even a small uncertainty in the orientation of either the velocity sensor or the principal axes of the wave-induced velocity field. The wave-induced bias can be diminished substantially by differencing measurements obtained from two velocity sensors separated by a distance larger than the correlation scale of the turbulence but small in comparison to the inverse wavenumber of the surface waves. If the scale separation is sufficiently large, then minus the density times half of the covariance between horizontal and vertical velocity differences is a nearly wave-free estimate of the average of the turbulent shear stresses at the two sensors. A theoretical analysis determines the bias associated with this technique under simplified conditions, in which waves and turbulence are uncorrelated and the waves are weakly nonlinear and narrow-banded in both frequency and direction. Order-of-magnitude estimates indicate that the technique can be used to obtain nearly unbiased estimates of near-bottom turbulent shear stress on continental shelves. A brief set of oceanic measurements demonstrates the success of the technique in practice.

Corresponding author address: J. H. Trowbridge, Dept. of Applied Ocean Physics and Engineering, Woods Hole Oceanographic Institution, MS 12, Woods Hole, MA 02543.

Email: jtrowbridge@whoi.edu

Save
  • Agrawal, Y. C., and D. G. Aubrey, 1992: Velocity observations above a rippled bed using laser Doppler velocimetry. J. Geophys. Res.,97, 20249–20259.

    • Crossref
    • Export Citation
  • Batchelor, G. K., 1967: The Theory of Homogeneous Turbulence. Cambridge University Press, 197 pp.

  • Buchave, P., W. K. George, and J. L. Lumley, 1979: The measurement of turbulence with the laser-Doppler velocimeter. Annu. Rev. Fluid Mech.,11, 505–540.

    • Crossref
    • Export Citation
  • Dean, R. G., and R. A. Dalrymple, 1984: Water Wave Mechanics for Engineers and Scientists. Prentice-Hall, 353 pp.

  • Fredericks, J. J., J. H. Trowbridge, and Y. C. Agrawal, 1994: Observations of near-bottom flow in a wave-dominated nearshore environment. Woods Hole Oceanographic Institution Tech. Rep. WHOI-94-04, 124 pp. [Available from Woods Hole Oceanographic Institution, Woods Hole, MA 02543.].

  • Grant, H. L., 1958: The large eddies of turbulent motion. J. Fluid Mech.,4, 149–90.

    • Crossref
    • Export Citation
  • Grant, W. D., and O. S. Madsen, 1986: The continental shelf bottom boundary layer. Annu. Rev. Fluid Mech.,18, 265–306.

    • Crossref
    • Export Citation
  • Gytre, T., J. E. Nilsen, J. E. Stiansen, and S. Sundby, 1996: Resolving small scale turbulence with acoustic Doppler and acoustic travel time difference current meters from an underwater tower. Proc. Oceans,96, 442–450.

  • Herbers, T. H. C., and R. C. Guza, 1993: Comment on “Velocity observations above a rippled bed using laser Doppler velocimetry” by Y. C. Agrawal and D. G. Aubrey. J. Geophys. Res.,98, 20331–20333.

    • Crossref
    • Export Citation
  • Jeffreys, H., 1974: Cartesian Tensors. Cambridge University Press, 92 pp.

  • Kaimal, J. C., J. C. Wyngaard, and D. A. Haugen, 1968: Deriving power spectra from a three-component sonic anemometer. J. Appl. Meteor.,7, 827–837.

    • Crossref
    • Export Citation
  • Kitaigorodskii, S. A., M. A. Donelan, J. L. Lumley, and E. A. Terray, 1983: Wave-turbulence interaction in the upper ocean. Part II: Statistical characteristics of wave and turbulent components of the random velocity field in a marine surface layer. J. Phys. Oceanogr.,13, 1988–1999.

  • Soulsby, R. L., 1977: Similarity scaling of turbulence spectra in marine and atmospheric boundary layers. J. Phys. Oceanogr.,7, 934–937.

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

    • Crossref
    • Export Citation
  • Trowbridge, J. H., and Y. C. Agrawal, 1995: Glimpses of a wave boundary layer. J. Geophys. Res.,100, 20729–20743.

    • Crossref
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 924 207 15
PDF Downloads 580 135 17