The Logarithmic Law of the Wall in Flows over Mobile Lattice-Arranged Granular Beds
Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisbon, Portugal
CERIS—Civil Engineering Research and Innovation for Sustainability, 1049-001 Lisbon, Portugal
Author to whom correspondence should be addressed.
Received: 4 April 2019 / Revised: 21 May 2019 / Accepted: 23 May 2019 / Published: 4 June 2019
PDF [7145 KB, uploaded 27 June 2019]
The purpose of the present paper is to provide further insights on the definition of the parameters of the log-law in open-channel flows with rough mobile granular beds. Emphasis is placed in the study of flows over cohesionless granular beds composed of monosized spherical particles in simple lattice arrangements. Potentially influencing factors such as grain size distribution, grain shape and density or cohesion are not addressed in this study. This allows for a preliminary discussion of the amount of complexity needed to obtain the log-law features observed in more realistic open-channel flows. Data collection included instantaneous streamwise and bed-normal flow velocities, acquired with a two-dimensional and two-component (2D2C) Particle Image Velocimetry (PIV) system. The issue of the non uniqueness of the definition of the parameters of the log-law is addressed by testing several hypotheses. In what concerns the von Kármán parameter,
, it is considered as flow-independent or flow-dependent (a fitting parameter). As for the geometric roughness scale,
, it results from a best fit procedure or is computed from a roughness function. In the latter case, the parameter B
is imposed as
or is calculated from the best fit estimate. The analysis of the results reveals that a flow dependent von Kármán parameter, lower than the constant
, should be preferred. Forcing
leads to non-physical values of
and would imply extending the inner layer up about 50% of the flow depth which is physically difficult to explain. Considering a flow dependent von Kármán parameter allows for coherent explanations for the values of the remaining parameters (the geometric roughness scale
, the displacement height
, the roughness height
). In particular, for the same transport rate, the roughness height obtained in a natural sediment bed is much greater than in the case of bed made of monosized glass spheres, underlining the influence of the bed surface complexity (texture and self-organized bed forms, in the water-worked cases) on the definition of the log-law parameters.
This is an open access article distributed under the Creative Commons Attribution License
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
Printed Edition Available!
A printed edition of this Special Issue is available here
Share & Cite This Article
MDPI and ACS Style
Antico, F.; Ricardo, A.M.; Ferreira, R.M.L. The Logarithmic Law of the Wall in Flows over Mobile Lattice-Arranged Granular Beds. Water 2019, 11, 1166.
Antico F, Ricardo AM, Ferreira RML. The Logarithmic Law of the Wall in Flows over Mobile Lattice-Arranged Granular Beds. Water. 2019; 11(6):1166.
Antico, Federica; Ricardo, Ana M.; Ferreira, Rui M.L. 2019. "The Logarithmic Law of the Wall in Flows over Mobile Lattice-Arranged Granular Beds." Water 11, no. 6: 1166.
Show more citation formats
Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.
[Return to top]
For more information on the journal statistics, click here
Multiple requests from the same IP address are counted as one view.