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Turbulence production in flow over a wavy wall

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Abstract

Measurements of the spatial and time variation of two components of the velocity have been made over a sinusoidal solid wavy boundary with a height to length ratio of 2a/λ = 0.10 and with a dimensionless wave number of α+ = (2π/λ)(v/u ) = 0.02. For these conditions, both intermittent and time-mean flow reversals are observed near the troughs of the waves. Statistical quantities that are determined are the mean streamwise and normal velocities, the root-meansquare of the fluctuations of the streamwise and normal velocities, and the Reynolds shear stresses. Turbulence production is calculated from these measurements.

The flow is characterized by an outer flow and by an inner flow extending to a distance of about α−1 from the mean level of the surface. Turbulence production in the inner region is fundamentally different from flow over a flat surface in that it is mainly associated with a shear layer that separates from the back of the wave. Flow close to the surface is best described by an interaction between the shear layer and the wall, which produces a retarded zone and a boundary-layer with large wall shear stresses.

Measurements of the outer flow compare favorably with measurements over a flat wall if velocities are made dimensionless by a friction velocity defined with a shear stress obtained by extrapolating measurements of the Reynolds stress to the mean levels of the surface (rather than from the drag on the wall).

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Abbreviations

a :

wave amplitude

e :

natural logarithm constant

h :

channel half height

k :

sand roughness length scale

p :

pressure

U, V :

streamwise, normal velocity components

u, v :

streamwise, normal velocity fluctuations

x, y :

streamwise, normal Cartesian coordinates

α :

wave number (2π/λ)

λ :

wave length

κ :

von Karmon's constant

ν :

kinematic viscosity

ρ :

fluid density

τ :

shear stress

b :

bulk quantity

fl :

flat channel quantity

0 :

reference quantity

t :

total drag

w :

wave wall quantity

⋆:

friction velocity (u )

+:

quantity made dimensionless with u and v

Over bar:

time averaged quantity

〈〉:

wave-averaged quantity defined such that \(\left\langle \phi \right\rangle = {1 \mathord{\left/ {\vphantom {1 \lambda }} \right. \kern-\nulldelimiterspace} \lambda }\int_0^\lambda {\phi {\text{d}}x} \)

Reference

  • Brooke JW; Hanratty TJ (1993) Origin of turbulence-producing eddies in a channel flow. Phys Fluids 5:1011

    Google Scholar 

  • Buckles JJ; Adrian RJ; Hanratty TJ (1984) Turbulent flow over a large-amplitude wavy surface. J Fluid Mech 27:140

    Google Scholar 

  • Clauser FH (1954) Turbulent boundary layers in adverse pressure gradients. J Aeronaut Sci 21:91

    Google Scholar 

  • Cohen LS; Hanratty TJ (1968) Effect of waves at a gas-liquid interface on a turbulent air flow. J Fluid Mech 31:467

    Google Scholar 

  • Frederick KA; Hanratty TJ (1988) Velocity measurements for a turbulent nonseparated flow over solid waves. Exp Fluids 6:477

    Google Scholar 

  • Gill LE; Hewitt GF; Lacey PMC (1964) Sampling probe studies of the gas core in annular two-phase flow; Part 2. Studies of the effect of phase flow rates on phase velocity and velocity distribution. Chem Eng Sci 19:665

    Google Scholar 

  • Hanratty TJ; Campbell JA (1994) Measurement of wall shear stress. Fluid Dynamics Measurements, Second Edition, Hemisphere Publishing

  • Hudson JD (1993) The effect of a wavy boundary on a turbulent flow. PhD Thesis, Univ. of Illinois, Urbana

    Google Scholar 

  • Kline SJ; Robinson SK (1989) Turbulent boundary layer structure: Progress, status, and challenges. Proceedings of the 2nd IUTAM Symposium on Structure of Turbulence and Drag Reduction (Fed. Institute of Technology, Zurich, Switzerland)

    Google Scholar 

  • Kuzan JD; Hanratty TJ; Adrian RJ (1989) Turbulent flows with incipient separation over solid waves. J Fluid Mech 7:88

    Google Scholar 

  • McLean JW (1983) Computation of turbulent flow over a moving wavy boundary. Phys Fluids 26:2065

    Google Scholar 

  • Niederschulte MA (1988) Turbulent flow through a rectangular channel. PhD Thesis, Univ. of Illinois, Urbana

    Google Scholar 

  • Niederschulte MA; Adrian RJ; Hanratty TJ (1990) Measurements of turbulent flow in a channel at low Reynolds numbers. Exp Fluids 9:222

    Google Scholar 

  • Schliching H (1979) Boundary-layer theory. McGraw-Hill Series in Mechanical Eng., Seventh Edition:615

  • Zilker DP; Hanratty TJ (1979) Influence of the amplitude of a solid wavy wall on a turbulent flow. Part 2. Separated flows. J Fluid Mech 90:257

    Google Scholar 

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This work is being supported by the National Science Foundation under NSF CTS 92-00936.

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Hudson, J.D., Dykhno, L. & Hanratty, T.J. Turbulence production in flow over a wavy wall. Experiments in Fluids 20, 257–265 (1996). https://doi.org/10.1007/BF00192670

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