Turbulent and advective momentum fluxes in natural streams

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

Introduction

Shear stress central hydraulic parameter Hydraulic conveyance

Scalar transport coefficients River bed stability

Shear stress

Bed shear stress (water – riverbed)

Within flow field

Introduction Objective Hypothesis Methodology Measurements Results Conclusion ?

• Bed resistances, determined by: • River bed geometry, i.e.. Longitudinal uniformity • River bed form, e.g. Riffles and dunes • River bed surface resistances

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• Methods for estimating shear stress and momentum interchange are for uniform flow.

• Not yet investigated through measurements in non-uniform flow


• 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”

Objective


Momentum transferred by turbulence and secondary currents can be expected due to non-uniformity of the investigated small natural rivers

Hypothesis Noss et al. Introduction Objective Hypothesis Methodology Measurements Results Conclusion ?

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Secondary currents Turbulence

• 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

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:

Methodology

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Difference uniform and non-uniform flow

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Uniform flow: No variation in velocity in x-y plane

Non-uniform flow: Variation in x-y plane, secondary currents

Methods for Shear Stress Estimation in non-uniform flow

Methodology

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• 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.


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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)

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Not applicable because ratio energy slope/riverbed slope is not constant

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CO

V

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NO

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TKE

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TUR

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Conclusion

• 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.’’

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Education

Turbulent and advective momentum fluxes in natural streams