Simulating the Effect of Wind-Driven Shear Stress on Turbulent Open-Channel Flow
Shoko Sugimoto1, Ko Shirakawa1, Yuji Sugihara1 ( 1Kyushu University , Japan ) , Michio Sanjou2 , Takaaki Okamoto2 ( 2Kyoto University , Japan )Backgorund and Objectives

Results and Discussion

Direct Numerical Simulation

Thoughseveralexperimental The basic equations consist of the continuity equation for incompressible
DNS, 𝑅𝑒𝜏 = 150
1k-ε model, 𝑅𝑒𝜏 = 150
23 Scaling relation for surface divergence based
approaches have been attempted so far, fluid, the Navier-Stokes equation and the advection-diffusion equation for
on Taylor micro scale (DNS, 𝑅𝑒𝜏 = 150)
there are no clear findings or a passive scalar as follows: The subscript ∗ denotes the dimensionless ηηconclusions about the response of open quantity.
channel turbulence to wind-driven shear
stress. This problem may be redefined
as an examination of the effect of wind
Increasingstress on mass transport in river flow.
In this study, we investigate the effect of
the surface shear stress on open-channel
flow turbulence through numericalUk-ε Modelsimulations. We discuss the crossU
Response of averaged streamwise velocity distributions to 𝝉𝒔correlation coefficients between thesurface scalar flux and the turbulence
Streamwise velocity fluctuation on water surface , Surface divergence , Scalar flux on water surface
characteristics close to the water surface∗
1.
In
thecaseof𝝉to identify turbulent motions controlling𝒔 = 𝟎, the scalar flux
increases intensively in the positive
the air-water scalar transport.
surface divergence areas.
(DNS, 𝑅𝑒𝜏 = 150)
2. Effects of surface shear stress•••

2 = ρ𝑢 2
ρ𝑔ℎ 𝑠𝑖𝑛 𝜃 + ρ𝑢𝜏𝑠𝜏𝑏2
ρ𝑔ℎ 𝑠𝑖𝑛 𝜃𝑢𝜏𝑠∗=1−=1−
𝜏𝑠22ρ𝑢𝜏𝑏𝑢𝜏𝑏2𝑢𝜏𝑠∗𝜏𝑠 ≡ 2 < 1𝑢𝜏𝑏

Turbulence dynamics governing thescalar transport seems to change fromthe surface divergence to the otherphysical mechanism.

The gravitational and the surface shear
forces are balanced with the bottom
shear force.

Cross-Correlation Coefficients

The degree of the agreement is found tobe low between the surface divergenceand the scalar flux.
The relation of the surface divergencewith the scalar flux is changed incomparison with the analytical solution.
The streched structures can be seen in thenear the water surface under the actionof positive shear stress.

Cross correlation for streamwise direction , Cross correlation for spanwise direction

Analytical Solution for Scalar Transport Velocity

Cross correlation for surface divergence

Cross correlation for streamwise• The case of 𝜏𝑠∗ =0 is symmetric with direction 𝐶𝑥 𝑟𝑥 (DNS, 𝑅𝑒𝜏 = 150)
𝐶𝑥
Surface divergence β∗
respect to the origin of 𝑟𝑥 = 0 ,whereas for the other values of 𝜏𝑠∗ , it
becomes asymmetric.
• When the positive shear stress,𝐶𝑥 𝑟𝑥 increases relatively in theregion of 𝑟𝑥 > 0. Conversely, in thecases of 𝜏𝑠∗ = −0.1 and − 0.2, the𝑟𝑥𝐶∗𝑥
downward overshoot of 𝐶𝑥 𝑟𝑥 isSpanwise vorticity ωzobserved in the region of 𝑟𝑥 > 0.

Cross correlation for 𝝎∗𝒛• From the streamwise correlation
with 𝜔𝑧∗ shown in the figure, it isseen that the relation of 𝐶𝑥(𝑟𝑥) with𝜏𝑠∗ becomes complicated especiallyin the case of the negative shear
stress.

𝑟𝑥

Cross correlation for spanwise
The cross-correlation coefficients direction𝐶z 𝑟z (DNS, 𝑅𝑒𝜏 = 150)

Cross correlation for surface divergence•𝐶𝑧 𝑟𝑧 shows symmetric shapeswith respect to 𝑟𝑧 = 0 regardless ofthe sign and magnitude of 𝜏𝑠∗ .
• The maximum values of the crosscorrelation coefficients 𝐶𝑥 𝑟𝑥 and𝐶𝑧 𝑟𝑧 take 0.75 approximately
when 𝜏𝑠∗ = 0, supporting that thesurface divergence is an important
physical quantity for describing thescalar flux at the water surface.
Cross correlation for 𝝎∗𝒛• The correlation drawn in the figure
shows symmetrical variation withrespect to 𝑟𝑧 = 0, but the behavior
is not monotonous in the case ofnegative shear stress.

Conclusion✓ In this study, we have investigated the response of open-channel turbulence to wind-driven surface shear stress by using the numerical methods of DNS and the standard k‐ε model.
✓ It has been seen that the vertical distributions of the streamwise velocity and the Reynolds stress vary depending on the positive or negative sign of the surface shear stress.
✓ The numerical results from DNS have provided that under the condition of negative shear stress, the streamwise velocity around the half-water depth is increased than that in the case of no shear stress.
✓ The surface divergence calculated from DNS has been confirmed to be universally scaled with the Taylor microscale regardless of the positive or negative sign of the shear stress.
✓ It has been concluded from the cross-correlation coefficients that the scalar flux considerably increases when vortex structure is arranged so as to induce a strong upward flow toward the water surface.

𝐶𝑧

Surface divergence β∗𝐶𝑧Spanwise vorticity ω∗z𝑟𝑧𝑟𝑧

References
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