Abstract
The second log-wake law is a small change of the first log-wake law (or Coles’ log-wake law) for turbulent pipe and symmetric channel flows but makes a big difference in modeling wall-bounded turbulent flows. It has been extended to antisymmetric Couette channel flows theoretically and open channel flows empirically. A recent study of natural river flows indicates that a river velocity distribution is a superposition of a complete antisymmetric channel flow solution due to water surface shear stress and a half symmetric channel flow solution due to gravity. The objective of this research then is to test this hypothesis under the effects of ice cover and wind-induced water surface shear stress with laboratory experiments. To this end, a special experimental device was designed to simulate the effects of gravity, ice cover, and wind-induced shear stress. With this device, 236 vertical distributions of streamwise velocity were measured with a particle image velocimetry (PIV) technique under various simulated conditions of ice cover and water surface shear stress, 75 of which are plotted in this paper. All measured velocity distributions are characterized by a bowl-shaped velocity distribution with a dip phenomenon, a typical boundary layer velocity distribution, or an S-shaped velocity distribution with an inflection. All of these three distribution patterns are well described by the second log-wake law, which also agrees with real-world river flow data. Based on the second log-wake law, an innovative three-point method is proposed for river discharge measurements.
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Acknowledgments
This research was supported by the US Federal Highway Administration Hydraulics R&D Program (Contract DTFH61-349-11-D-00010) through the Genex System to the University of Nebraska-Lincoln. The authors appreciate the constructive comments offered by the three anonymous reviewers, the Associate Editor, and the Editor, which improved this paper significantly during its preparation.
Notation
The following symbols are used in this paper:
- a
- relative position where velocity is measured;
- F
- Froude number;
- g
- gravity acceleration (m/s2);
- h
- flow depth (m);
- K
- weighting factor for three-point method;
- M, N
- interim parameters (m/s);
- p
- model parameter vector;
- Q
- discharge (m3/s);
- q
- unit-width discharge (m2/s);
- R
- Reynolds number;
- Rh
- hydraulic radius (m);
- r2
- coefficient of determination;
- Si
- sine integral function;
- sgn
- sign function;
- u
- streamwise mean velocity (m/s);
- ua, ub
- measured velocities (m/s);
- u+
- dimensionless velocity;
- dimensionless velocity at half flow depth;
- u0.5
- dimensional velocity at half flow depth (m/s);
- u*b
- bed shear velocity (m/s);
- V
- average velocity (m/s);
- Vb
- belt velocity (m/s);
- y
- distance from bed (m);
- β
- ratio of water surface shear stress to bed shear stress;
- γ
- specific weight of water (N/m3);
- Δ
- bed roughness (m);
- η
- dimensionless y normalized by h;
- κ
- von Kármán constant;
- λ
- ratio of water surface shear velocity to bed shear velocity;
- ν
- kinematic water viscosity (m/s2)
- Π
- wake strength due to gravity;
- Πs
- wake strength due to water surface shear stress;
- τ
- shear stress (Pa);
- τb
- bed shear stress (Pa); and
- τs
- water surface shear stress (Pa).
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Published In
Journal of Cold Regions Engineering
Volume 36 • Issue 2 • June 2022
Copyright
© 2022 American Society of Civil Engineers.
History
Received: Mar 21, 2021
Accepted: Jan 29, 2022
Published online: Mar 10, 2022
Published in print: Jun 1, 2022
Discussion open until: Aug 10, 2022
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