The document discusses methods for estimating shear stress and momentum fluxes in turbulent non-uniform river flows. It presents an existing method ("Noss method") that accounts for contributions from turbulence and secondary currents. Field measurements of velocity distributions were taken in two small rivers in Germany and used to calculate shear stresses. The results show that contributions from secondary currents are generally higher than from turbulent fluctuations. The study recommends using the gravitational method for bulk surveys and the new Noss method for more detailed shear stress distributions in natural river flows.

1. Turbulent and Advective Momentum Fluxes in Streams
C. Noss, T. Salzmann and I. Storchenegger (2010)
Discussed by:
Thomas Berends
Klaas Thomas Jellema
Lieke Melsen
Yihdego Tikue

2. Introduction
Introduction Objective Hypothesis Methodology Measurements Results Conclusion ?
Shear stress central hydraulic parameter
Hydraulic conveyance
Scalar transport coefficients
River bed stability
Shear stress
Bed shear stress Within
(water – riverbed) flow field

3. Introduction
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• Bed resistances, determined by:
• River bed geometry, i.e.. Longitudinal uniformity
• River bed form, e.g. Riffles and dunes
• River bed surface resistances
• Methods for estimating shear stress and momentum
interchange are for uniform flow.
• Not yet investigated through measurements in non-uniform
flow

4. Objective
Introduction Objective Hypothesis Methodology Measurements Results Conclusion ?
• Apply existing methods for estimating shear stress and momentum
interchange on complex flow fields above highly non-uniform river
beds with wide range of irregular distributed morphological structures
• Apply new methods that represent the contribution of turbulence and
secondary currents to the total momentum flux: “Noss method”

5. Hypothesis Noss et al.
Introduction
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Momentum transferred by turbulence and secondary currents can be expected due to
non-uniformity of the investigated small natural rivers
Secondary currents Turbulence

6. Methodology
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• Show selection of methods used to determine shear stress in uniform and non-uniform flow
• Present new method to determine shear stress
• Apply methods to near-natural non-uniform flow rivers

7. Methodology
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Methods for Shear Stress Estimation in uniform flow
• Gravitational method
• Coulomb ‘resistance’ force vs tangent gravitational force  river bed shear
stress = Fgt/river bed surface
• Covariance method
• Reynolds shear stresses
• Does not depend on empirical constant
• Turbulent Kinetic Energy (TKE) method
• Simple linear relationship Reynolds shear stress and TKE
• Constant ratio C
• Simple method to work with
• Logarithmic method
• Requires log-law velocity profile with assumption
of Prandtl’s mixing length theory:

8. Methodology
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Difference uniform and non-uniform flow
Uniform flow: Non-uniform flow:
No variation in velocity in x-y plane Variation in x-y plane, secondary currents

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Methods for Shear Stress Estimation in non-uniform flow
• Gravitational method
• River bed shear stress results from tangent gravitational force and extra
additional forces due to variability of the drag and the gravitational forces
(1D)
• Covariance method
• Secondary currents are present caused by the fact that . ≠0 and must be
considered in total momentum flux within the water column
• Noss et al. method
• Total shear stress is sum of momentum flux by turbulence and secondary
currents , whereby n is a 2D vector of v and w, perpendicular to
u. Transformation from Cartesian to complex system is required to calculated
the sums, products and covariances between 2 vectors u and n.

10. Measurements
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Three‐dimensional velocity distributions and energy slopes at 37 dates at five cross‐sections of two
small rivers in northeast Germany, the Hellbach and the Nebel
Measurements: NORTEK 10 MHz ADV (until October 2006) or by a SONTEK 10 MHz
ADV.
Data is transformed according to Goring and Nikora (2002)

11. Results
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Not applicable because ratio energy slope/riverbed slope is not constant

12. Results
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NOSS
COV
COV
COV
TKE

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TOTAL
(advective)
SEC.CURR
TURBULENCE

14. Conclusion
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• The total shearstress in small natural river flows is neither a precise nor an approximate estimate
by methods assuming a twodimensional boundary layer flow.
• Contributions of secondary currents always higher than the contributions of turbulen fluctuations.
‘’The gravitational method can be
recommended as a survey method for,
e.g., further bulk river
design and postproject evaluation
applications, while the
new method is recommendable for a more
detailed survey of
the shear stress distribution in natural
flows.’’

15. Questions?
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