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Boundary layer structure of oscillatory open-channel shallow flows over smooth and rough beds

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Abstract

The boundary layer structure of oscillatory shallow open channel flows has been studied in a wide flume. Fluorescence solution was released at a porous rough bed through a diffuser covered by gravel of 0.5 cm grain size. A planar laser-induced fluorescence (PLIF) system was used to visualise the dye plumes in both vertical and horizontal planes for a qualitative understanding of the roles of large-scale flow structures in mass transport. A variety of tests were conducted for a range of oscillatory periods (30–240 s), water depths (3–16 cm) and velocity amplitudes (0.027–0.325 m/s), which cover a wide range of oscillatory flows with Reynolds numbers Re a varied from 0.3 × 104 (laminar) to 2.1 × 106 (fully turbulent). For quantitative investigation, a novel technique, namely combined laser-induced fluorescence (LIF) and 2D laser Doppler velocimetry (LDV) (LIF/LDV), was developed and used to measure the velocity and solute concentration simultaneously in a vertical plane over 50 cycles. From the dye plumes revealed by the PLIF in transitional flows, there are different patterns of flow structure and solute transport with three representative stages of acceleration, deceleration and flow reversal. In the acceleration stage, turbulence was suppressed with dye layers adhering to the surface with little vertical mass transport. In the deceleration stage, flame-like turbulent structures occurred when turbulence generation was prominent. This was investigated quantitatively by recording the percentage occurrence of the adhered smooth layers per cycle. For those smooth bed cases with Re a  < 1.8 × 105, the adhered smooth dye layers type of boundary layer occupied 100% of the oscillation period. Over a sufficiently high Re a , a rough bed can generate fully turbulent oscillatory flows without the appearance of adhering dye layers. Between these two extremes, a transitional flow regime occurs in a wide range of flow conditions: Re a  > 2.7 × 104 over the rough bed and Re a  > 8.3 × 106 over a smooth bed.

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Abbreviations

a :

amplitude of free stream motion

D g :

median diameter of gravel

H :

water depth

K s :

Nikuradse’s roughness height

K +s :

roughness Reynolds number

Re a :

Reynolds number based on a

Re δ :

Reynolds number based on Stokes thickness

Re h :

Reynolds number based on water depth

t :

real time

T :

wave period

u x , u y :

measured velocities in x and y direction from LDV

U 0 :

amplitude of free stream velocity

U, V:

ensemble averaged velocity in x and y directions

u′, v′:

random turbulence velocities in x and y directions

\({ - \overline{{{u}{'}{v}{'}}} }\) :

Reynolds stress

\({ \tilde{U},\,\tilde{V}}\) :

wave phase-averaged velocities in x and y directions

U fm :

maximum friction velocity

x :

co-ordinate along the main flow direction in horizontal plane

y :

co-ordinate in vertical direction from the bottom of flume

δ:

laminar boundary or Stokes thickness

δb :

oscillatory boundary layer thickness

ω:

wave angle frequency

ν:

kinematic viscosity

ν t :

eddy viscosity

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Acknowledgement

This study is supported by a grant (GR/L/34570) from the UK Engineering and Physical Science Research Council (EPSRC). The three-dimensional LDV was made available from the EPSRC Instrument Pool. F.E. Tang was supported by a UK Overseas Research Studentship.

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Authors and Affiliations

  1. Department of Engineering, University of Liverpool, Liverpool, UK

    Daoyi Chen

  2. School of Informatics, University of Edinburgh, Edinburgh, UK

    Chaoquan Chen

  3. Curtin University of Technology Sarawak Campus, CDT 250 98009 Miri, Sarawak, Malaysia

    Fu-Ee Tang

  4. School of Mechanical, Aerospace and Civil Engineering, University of Manchester, Manchester, UK

    Peter Stansby

  5. Department of Engineering, University of Liverpool, Liverpool, UK

    Ming Li

Authors
  1. Daoyi Chen
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  2. Chaoquan Chen
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  3. Fu-Ee Tang
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  4. Peter Stansby
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  5. Ming Li
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Correspondence to Daoyi Chen.

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Chen, D., Chen, C., Tang, FE. et al. Boundary layer structure of oscillatory open-channel shallow flows over smooth and rough beds. Exp Fluids 42, 719–736 (2007). https://doi.org/10.1007/s00348-007-0280-8

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  • DOI: https://doi.org/10.1007/s00348-007-0280-8

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