The manifestation of fluid-transmitted bed shear stress in a smooth annular flume: a comparison of methods

Abstract

The most commonly used methods of calculating mean, fluid-transmitted bed shear stresses within a benthic boundary layer have been investigated. The work was carried out in an annular flume 2 m in diameter and 0.40 m deep—the Lab Carousel. This flume is a laboratory equivalent to the Sea Carousel (an in situ flume). A well developed boundary layer 0.02 m thick was confirmed for a range of flows measured using a Laser Doppler Velocimeter (LDV) within the Lab Carousel. There was a good relationship found between flow speed in the Lab Carousel and Sea Carousel, which corresponded well with a direct measurement method (particle tracking) using neutrally buoyant particles. The purpose of this investigation was to compare the accuracies and relative differences of eight ways of determining bed shear stress under smooth bed conditions: five using velocity as a proxy; and three considered direct. The proxy methods investigated were; (1) the Law of the Wall; (2) the Quadratic Stress Law; (3) the Turbulent Kinetic Energy (TKE) method; (4) Prandtl’s seventh power law; (5) and the Reynolds stress calculation. Three ‘direct’ measurements of bed shear stress were: (6) hot film probes; (7) inverting Newton’s second law to define frictional drag through flow deceleration; and (8) numerical simulation. All the methods gave sensible results with the expected trends of increasing stress under increasing flow velocity. The best correlation of the proxy methods was found between Prandtl’s seventh power law and flow deceleration; the other methods over predicting the stress by up to a factor of 10. There was a good coherence between the estimates of stress using an Acoustic Doppler Velocimeter (ADV) and the LDV at 0.15 m above the bed. The use of Sternberg’s constant drag coefficient (CD100 = 3 × 10?3) in stress calculations yielded the greatest over prediction. The hot film probes showed radial differences in stress, which were in general greatest in the middle and lowest near the outer wall. All the methods appear to converge at low current velocities. The TKE and flow deceleration methods showed similar results over a bed roughened with 0.011 m diameter uniform gravel, suggesting that they may be valid for naturally roughened beds.

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ORCID for Charlotte E.L. Thompson: orcid.org/0000-0003-1105-6838

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