Using a mechanical approach to quantify flow resistance by submerged, flexible vegetation – A revisit of Kouwen’s approach

• Theoretical analysis is conducted for flexible vegetation in flowing fluids.
• Kouwen and Li flow resistance-vegetation deflection equation is explained by theory.
• Structural flaws are found in the Kouwen and Li empirical equation.
• New parameters to replace vegetation rigidity MEI   and Kouwen parameter MEIτL40.25.

Vegetation-induced flow roughness can result in significant changes in stream hydraulics. This study revisits the well-known empirical equation for submerged flexible vegetation developed by Kouwen and collaborators, which describes the relationships between shear stress, flexural rigidity, and vegetation deflection. Theoretical analysis shows that the theories for the mechanics of large deflection cantilever beams can essentially explain this equation. The results show that for moderate to large deflection (the ratio of deflected height to original height l/L < 0.85 − 0.9) the theoretically derived relationships can be approximated with power-law equations, which have similar exponents to the Kouwen’s equation and agree with its empirical relationships, which indicates the consistency of the underlying physics for the two approaches. Direct comparisons under given vegetation-height conditions also show a general agreement between the empirical and the theoretical equations. For small deflections, the theoretical results exhibit a more intuitive trend, which shows that the shear stress approaches zero at infinitesimal deflection. Additionally, theoretical analysis suggests a different non-dimensional parameter for vegetation mechanical properties and a better structure of the equation, which is expected to improve the estimation of vegetation-induced roughness. Finally, theoretical analysis indicates that even though the structure maintains, the specific relationship between vegetation bending and resistance is dependent on the flow velocity profile. Further development of these approaches need to take flow characteristics into consideration.