Test the predicted effects of spacing, permeability, and forcing on layer thickness

Test whether the roughness-controlled layer thickens linearly with element spacing, whether bed permeability activates a canopy mechanism that extends the layer to two to five element heights, and whether forcing strength and element shape affect the layer thickness only logarithmically.

Background

The paper proposes that element spacing, bed permeability, and wake strength control the thickness of the roughness-controlled layer through different mechanisms. The kinematic decay length is proportional to element spacing; permeability could introduce distributed drag and a canopy instability; and forcing strength or element shape enters through the crest-level dispersive-velocity amplitude in a logarithmic relation.

These predictions are not established by the eleven densely packed, immobile marble-bed cases analyzed in the paper. The authors identify sparser, permeable, and mobile beds as the natural configurations for testing whether the predicted margin between the roughness-controlled layer and the logarithmic layer persists.

References

The margin is expected to be controlled by the bed rather than by the forcing: the layer should thicken linearly with the element spacing; permeability would activate the canopy mechanism and could push the layer to two to five element heights, comparable to $\delta_w$ itself; the forcing and the element shape enter only logarithmically. These expectations remain to be tested, and sparser, permeable, and mobile beds, where the margin narrows, are the natural next step.

— Roughness-controlled layer in oscillatory turbulent boundary layers over densely packed uniform roughness  (2608.17543 - Liu et al., 18 Aug 2026) in Conclusions, final paragraph of Section 6