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Examination of outer-layer similarity in wall turbulence over obstructed surfaces
Fluid Dynamics · Submitted 26 May 2023
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Our results suggest a modified outer-layer similarity, where the K\'arm\'an constant, $\kappa$, is not 0.39, but turbulence is otherwise smooth-wall-like.
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The abstract, sentence by sentence
Turbulent flows over canopies of rigid filaments with different densities, $\lambda_f$, are studied using direct simulations at Reynolds numbers $Re_\tau\approx550-1000$. The canopies have heights $h^+\approx110-220$, and are an instance of obstructing substrate. We show that conventional methods used to determine the zero-plane displacement can be at odds with proper outer-layer similarity and may not be applicable for flows at moderate $Re_\tau$. Instead, we determine $\Delta y$ and the length and velocity scales that recover outer-layer similarity by minimising the difference between the smooth-wall and canopy diagnostic function everywhere above the roughness sublayer, not just in the logarithmic layer. We also investigate if the zero-plane displacement and the friction velocity can be set independently, but find that outer-layer similarity is more consistently recovered when they are coupled. Our results suggest a modified outer-layer similarity, where the K\'arm\'an constant, $\kappa$, is not 0.39, but turbulence is otherwise smooth-wall-like. When the canopy is dense, the flow above the tips is essentially smooth-wall-like, with smooth-wall-like $\kappa\approx0.39$ and origin essentially at the tip plane. For intermediate densities, the overlying flow perceives a deeper zero-plane displacement, in agreement with previous studies, but exhibits a lower K\'arm\'an constant, $\kappa\approx0.34-0.36$. For sparse canopies, $\kappa$ tends back to its smooth-wall value, and the zero-plane-displacement height is at the canopy bed. For all canopies studied, the decrease in $\kappa$ never exceeds 15%, which is significantly less than that obtained in some previous works using conventional methods to assess outer-layer similarity.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Turbulent flows over canopies of rigid filaments with different densities, $\lambda_f$, are studied using direct simulations at Reynolds numbers $Re_\tau\approx550-1000$. | method 0.62 | 0.94 | 0.02 | asserted 0.94 |
| s1 | The canopies have heights $h^+\approx110-220$, and are an instance of obstructing substrate. | method 0.65 | 0.65 | 0.02 | asserted 1.00 |
| s2 | We show that conventional methods used to determine the zero-plane displacement can be at odds with proper outer-layer similarity and may not be applicable for flows at moderate $Re_\tau$. | result 0.55 | 0.58 | 0.22 | hedged possibility 0.60 |
| s3 | Instead, we determine $\Delta y$ and the length and velocity scales that recover outer-layer similarity by minimising the difference between the smooth-wall and canopy diagnostic function everywhere above the roughness sublayer, not just in the logarithmic layer. | method 0.98 | 0.97 | 0.14 | asserted 1.00 |
| s4 | We also investigate if the zero-plane displacement and the friction velocity can be set independently, but find that outer-layer similarity is more consistently recovered when they are coupled. | result 0.88 | 0.97 | 0.09 | asserted 0.99 |
| s5 | Our results suggest a modified outer-layer similarity, where the K\'arm\'an constant, $\kappa$, is not 0.39, but turbulence is otherwise smooth-wall-like. | interpretation 0.57 | 0.90 | 0.62 | hedged possibility 0.99 |
| s6 | When the canopy is dense, the flow above the tips is essentially smooth-wall-like, with smooth-wall-like $\kappa\approx0.39$ and origin essentially at the tip plane. | result 0.99 | 0.91 | 0.12 | asserted 1.00 |
| s7 | For intermediate densities, the overlying flow perceives a deeper zero-plane displacement, in agreement with previous studies, but exhibits a lower K\'arm\'an constant, $\kappa\approx0.34-0.36$. | result 1.00 | 0.84 | 0.14 | asserted 0.97 |
| s8 | For sparse canopies, $\kappa$ tends back to its smooth-wall value, and the zero-plane-displacement height is at the canopy bed. | result 1.00 | 0.89 | 0.09 | asserted 0.54 |
| s9 | For all canopies studied, the decrease in $\kappa$ never exceeds 15%, which is significantly less than that obtained in some previous works using conventional methods to assess outer-layer similarity. | result 0.96 | 0.88 | 0.21 | asserted 1.00 |
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Original abstract
Turbulent flows over canopies of rigid filaments with different densities, $\lambda_f$, are studied using direct simulations at Reynolds numbers $Re_\tau\approx550-1000$. The canopies have heights $h^+\approx110-220$, and are an instance of obstructing substrate. We show that conventional methods used to determine the zero-plane displacement can be at odds with proper outer-layer similarity and may not be applicable for flows at moderate $Re_\tau$. Instead, we determine $\Delta y$ and the length and velocity scales that recover outer-layer similarity by minimising the difference between the smooth-wall and canopy diagnostic function everywhere above the roughness sublayer, not just in the logarithmic layer. We also investigate if the zero-plane displacement and the friction velocity can be set independently, but find that outer-layer similarity is more consistently recovered when they are coupled. Our results suggest a modified outer-layer similarity, where the K\'arm\'an constant, $\kappa$, is not 0.39, but turbulence is otherwise smooth-wall-like. When the canopy is dense, the flow above the tips is essentially smooth-wall-like, with smooth-wall-like $\kappa\approx0.39$ and origin essentially at the tip plane. For intermediate densities, the overlying flow perceives a deeper zero-plane displacement, in agreement with previous studies, but exhibits a lower K\'arm\'an constant, $\kappa\approx0.34-0.36$. For sparse canopies, $\kappa$ tends back to its smooth-wall value, and the zero-plane-displacement height is at the canopy bed. For all canopies studied, the decrease in $\kappa$ never exceeds 15%, which is significantly less than that obtained in some previous works using conventional methods to assess outer-layer similarity.
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