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Beyond the Constant Stress Assumption: A Mechanistic Derivation of the Log-Law for Open Channel Flow
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DOI：10.3390/w18161976.png)
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Abstract
En 中文
The logarithmic law of the wall is a foundational element in turbulence modeling. Its classical derivation, rooted in Prandtl’s mixing-length theory, is predicated on the existence of a constant shear stress layer. This paper demonstrates that this foundational assumption is not strictly satisfied for two-dimensional, uniform open-channel flows, where the Reynolds shear stress profile exhibits a distinct peak near the bed and never forms a true constant stress zone. We present a novel mechanistic derivation that circumvents this inconsistency. By reframing the bed shear stress as the time-averaged momentum flux from discrete, wall-coherent eddy impacts, we recover the log law through a mechanistic framework. Our model starts from the physical definition of the Reynolds stress at the bed, employs kinematic scaling for the velocity fluctuations, and incorporates the geometric constraint of eddy size. This approach does not require a constant stress layer and provides a more physically defensible explanation for the emergence and robustness of the log-law, directly linking it to the underlying structure of wall turbulence. The derivation resolves the long-standing paradox between the theory’s assumption and the empirical reality in open channel flows.
Keywords:
log-law
open-channel flow
constant stress layer
wall turbulence
Reynolds shear stress
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W
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3
Papers:
3.1W
Citations:
7.4W
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