Edge flow in inhomogeneous canopy

Edge flow in inhomogeneous canopy Louis-Etienne Boudreault, Barry Gardiner, Andreas Bechmann, Ebba Dellwik To cite this version: Louis-Etienne Boudreault, Barry Gardiner, Andreas Bechmann, Ebba Dellwik. Edge flow in inhomogeneous canopy. Mathematical Modelling of Wind Damage Risk to Forests, Oct 2015, Arcachon, France. ฀hal-02740297฀ HAL Id: hal-02740297 https://hal.inrae.fr/hal-02740297 Submitted on 2 Jun 2020 HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. ❊❞❣❡ ✢♦✇ ✐♥ ✐♥❤♦♠♦❣❡♥❡♦✉s ❝❛♥♦♣② ▲♦✉✐s✲➱t✐❡♥♥❡ ❇♦✉❞r❡❛✉❧t ❙②❧✈❛✐♥ ❉✉♣♦♥t ❆♥❞r❡❛s ❇❡❝❤♠❛♥♥ ❊❜❜❛ ❉❡❧❧✇✐❦ ▲♦✉✐s✲➱t✐❡♥♥❡ ❇♦✉❞r❡❛✉❧t ❊❞❣❡ ✢♦✇ ✐♥ ✐♥❤♦♠♦❣❡♥❡♦✉s ❝❛♥♦♣② ✷✽ ♦❝t♦❜❡r ✷✵✶✺ ▼♦t✐✈❛t✐♦♥ ◮ ◮ ▼♦st ♦❢ ❦♥♦✇❧❡❞❣❡ ♦♥ ❢♦r❡st ❡❞❣❡ ✢♦✇s ✿ ♥✉♠❡r✐❝❛❧ ❛♥❞ ✇✐♥❞✲t✉♥♥❡❧ ❡①♣❡r✐♠❡♥ts ✇❤❡r❡ ❝❛♥♦♣② ❤♦r✐③♦♥t❛❧❧② ❤♦♠♦❣❡♥❡♦✉s ❉✐✛❡r❡♥❝❡s ✐♥ ✐♥❤♦♠♦❣❡♥❡♦✉s ❝❛♥♦♣② ❄ ✭✸❉ tr❡❡✲s❝❛❧❡ ❤❡t❡r♦❣❡♥❡✐t✐❡s✮ ✶✲✶✵♠ ▲♦✉✐s✲➱t✐❡♥♥❡ ❇♦✉❞r❡❛✉❧t ❊❞❣❡ ✢♦✇ ✐♥ ✐♥❤♦♠♦❣❡♥❡♦✉s ❝❛♥♦♣② ✷✽ ♦❝t♦❜❡r ✷✵✶✺ ❊❞❣❡ s✐t❡ ❍❡❧✐❝♦♣t❡r✲❜❛s❡❞ ❤✐❣❤ r❡s♦❧✉t✐♦♥ s❝❛♥s ✭> ✶✵ r❡t✉r♥s/♠✷ ✮ ✭❉❡❧❧✇✐❦ → ▲❊❙ ✐♥♣✉t ❡t ❛❧✳✱ ✭❇♦✉❞r❡❛✉❧t ✷✵✶✹✱ ❡t ❛❧✳✱ ◗❏❘▼❙✮ ✷✵✶✺✱ ❆❋▼✮ ❋♦r❡st ❣r✐❞ ✿ ∆① , ② = ✷ ♠ ∆③ = ✶ ♠ ▲♦✉✐s✲➱t✐❡♥♥❡ ❇♦✉❞r❡❛✉❧t ❊❞❣❡ ✢♦✇ ✐♥ ✐♥❤♦♠♦❣❡♥❡♦✉s ❝❛♥♦♣② ✷✽ ♦❝t♦❜❡r ✷✵✶✺ ▼♦❞❡❧ ❞❡t❛✐❧s ◆❡✉tr❛❧ ✢♦✇ ❉♦♠❛✐♥ ▲❊❙ ♠♦❞❡❧ 20h 10h ◆❙^ − ❡q♥s . ◮ ❙♣❛t✐❛❧❧②✲✜❧t❡r❡❞ ◮ ✶✳✺✲♦r❞❡r ❙●❙ ♠♦❞❡❧ 40h W in d ✭❉❡❛r❞♦✛✱ ✶✾✽✵✮ ◮ M2 ▼♦❞✐✜❡❞ ❢♦r ❝❛♥♦♣② ✢♦✇ ✭❉✉♣♦♥t ✫ ❇r✉♥❡t✱ ✷✵✵✽✱ ✷✵✵✾ ❀ ❉✉♣♦♥t ❡t ❛❧✳✱ ✷✵✶✶✮ M1 ▲❊❙ r❡s♦❧✉t✐♦♥ ✿ ◮ ❙♦❧✈❡❞ ✇✐t❤ ❆❘P❙ ❝♦❞❡ ✭❳✉❡ ❡t ❛❧✳✱ ✶✾✾✺ ❀ ✷✵✵✵ ❀ ✷✵✵✶✮ ✶♠ ✷♠ ▲♦✉✐s✲➱t✐❡♥♥❡ ❇♦✉❞r❡❛✉❧t ✷♠ ❊❞❣❡ ✢♦✇ ✐♥ ✐♥❤♦♠♦❣❡♥❡♦✉s ❝❛♥♦♣② ✷✽ ♦❝t♦❜❡r ✷✵✶✺ z (m) ❈❛s❡ ❞❡s❝r✐♣t✐♦♥ 100 80 60 40 20 0 a y (m2 m 3 ) z (m) 0.25 0.10 0.05 -3 -2 -1 0 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 100 80 60 40 20 0 0.50 ❍❡t❡r♦❣❡♥❡♦✉s ❡❞❣❡✲❝❛s❡ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 h/ 0.01 hy PAI y PAI/ 3 2 1 0 1 2 a y (m2 m 3 ) 3 4 5 6 7 8 9 10 11 12 13 14 15 ❍♦♠♦❣❡♥❡♦✉s ❡❞❣❡✲❝❛s❡ 0.50 0.25 0.10 0.05 -3 -2 -1 0 1 2 ▲♦✉✐s✲➱t✐❡♥♥❡ ❇♦✉❞r❡❛✉❧t 3 4 5 6 7 x/h 8 9 10 11 12 13 14 15 ❊❞❣❡ ✢♦✇ ✐♥ ✐♥❤♦♠♦❣❡♥❡♦✉s ❝❛♥♦♣② 0.01 ✷✽ ♦❝t♦❜❡r ✷✵✶✺ ❋❧♦✇ ❛✈❡r❛❣✐♥❣ ❢r❛♠❡✇♦r❦ ◮ ❚✐♠❡ ✰ s♣❛t✐❛❧ ❛✈❡r❛❣✐♥❣ ✿ φ′✐ = φ✐ − φ̄✐ φ̄′′✐ = φ̄✐ − hφ̄✐ i ◮ (hφ̄✐ i② ♦r hφ̄✐ i①② ) ■♥❤♦♠♦❣❡♥❡♦✉s ❝❛♥♦♣② ✿ ❞✐s♣❡rs✐✈❡ ✢✉①❡s ✐♠♣♦rt❛♥t ❄ ∂h¯ ✉✐ i ∂h¯ ✉ i ✶ ∂h¯♣ i ∂h❚✐❥t♦t i = −h¯ ✉❥ i ✐ − − − h❋❉t♦t i ∂t ∂ ①❥ ρ ∂ ①✐ ∂ ①❥ ❙❡❝♦♥❞✲♦r❞❡r ♠♦♠❡♥ts ✿ h❚✐❥t♦t i = h✉✐′ ✉❥′ i + h✉¯✐ ′′ ✉¯❥ ′′ i | {z } | {z } t✉r❜✉❧❡♥t ❞✐s♣❡rs✐✈❡ ❚❤✐r❞✲♦r❞❡r ♠♦♠❡♥ts ✭s❦❡✇♥❡ss✮ ✿ h❚✐✐✐t♦t i = h✉✐′ ✉✐′ ✉✐′ i + ✸h✉✐ ✉✐ ′′ ✉¯✐ ′′ i − ✻h✉¯✐ ih✉¯✐ ′′ ✉¯✐ ′′ i + ✷h✉¯✐ ′′ ✉¯✐ ′′ ✉¯✐ ′′ i {z } | {z } | t✉r❜✉❧❡♥t ▲♦✉✐s✲➱t✐❡♥♥❡ ❇♦✉❞r❡❛✉❧t ❞✐s♣❡rs✐✈❡ ❊❞❣❡ ✢♦✇ ✐♥ ✐♥❤♦♠♦❣❡♥❡♦✉s ❝❛♥♦♣② ✷✽ ♦❝t♦❜❡r ✷✵✶✺ ❍❛❧❢✲❝❛♥♦♣② ❤❡✐❣❤t ✈✐❡✇ ❍❡t❡r♦❣❡♥❡♦✉s ❡❞❣❡✲❝❛s❡ 20 PAI 20 u/ uref 10 y/h 15 8 0.40 15 0.35 0.30 6 10 xy 0.45 0.25 10 4 0.20 0.15 5 2 0.10 5 0.05 0 0 -5 0 5 x/h ▲♦✉✐s✲➱t✐❡♥♥❡ ❇♦✉❞r❡❛✉❧t 10 15 0.00 0 -5 0 5 10 15 x/h ❊❞❣❡ ✢♦✇ ✐♥ ✐♥❤♦♠♦❣❡♥❡♦✉s ❝❛♥♦♣② ✷✽ ♦❝t♦❜❡r ✷✵✶✺ ❚✇♦✲❞✐♠❡♥s✐♦♥❛❧ ✈✐❡✇ ✿ str❡❛♠✇✐s❡ ✈❡❧♦❝✐t② z (m) ❍❡t❡r♦❣❡♥❡♦✉s 100 80 60 40 20 0 u y/ uref xy -3 -2 -1 0 z (m) ❍♦♠♦❣❡♥❡♦✉s 100 80 60 40 20 0 u y/ uref 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 xy -3 -2 -1 0 1 2 ▲♦✉✐s✲➱t✐❡♥♥❡ ❇♦✉❞r❡❛✉❧t 3 4 5 6 7 x/h 8 9 10 11 12 13 14 15 ❊❞❣❡ ✢♦✇ ✐♥ ✐♥❤♦♠♦❣❡♥❡♦✉s ❝❛♥♦♣② 1.1 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 1.1 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 ✷✽ ♦❝t♦❜❡r ✷✵✶✺ ❚✇♦✲❞✐♠❡♥s✐♦♥❛❧ ✈✐❡✇ ✿ t✉r❜✉❧❡♥t ❦✐♥❡t✐❝ ❡♥❡r❣② z (m) ❍❡t❡r♦❣❡♥❡♦✉s 100 80 60 40 20 0 Etot y/ u2 ,ref xy -3 -2 -1 0 1 z (m) ❍♦♠♦❣❡♥❡♦✉s 100 80 60 40 20 0 Etot y/ u2 ,ref -3 -2 -1 0 2 3 4 5 6 7 8 9 10 11 12 13 14 15 xy 1 2 ▲♦✉✐s✲➱t✐❡♥♥❡ ❇♦✉❞r❡❛✉❧t 3 4 5 6 7 x/h 8 9 10 11 12 13 14 15 ❊❞❣❡ ✢♦✇ ✐♥ ✐♥❤♦♠♦❣❡♥❡♦✉s ❝❛♥♦♣② 4.2 3.9 3.6 3.3 3.0 2.7 2.4 2.1 1.8 1.5 1.2 0.9 0.6 0.3 0.0 4.2 3.9 3.6 3.3 3.0 2.7 2.4 2.1 1.8 1.5 1.2 0.9 0.6 0.3 0.0 ✷✽ ♦❝t♦❜❡r ✷✵✶✺ z (m) ❚✇♦✲❞✐♠❡♥s✐♦♥❛❧ ✈✐❡✇ ✿ t✉r❜✉❧❡♥t ✢✉① ❍❡t❡r♦❣❡♥❡♦✉s 100 80 60 40 20 0 2 Ttot uw y/ u ,ref xy -3 -2 -1 0 1 z (m) ❍♦♠♦❣❡♥❡♦✉s 100 80 60 40 20 0 2 Ttot uw y/ u ,ref -3 -2 -1 0 2 3 4 5 6 7 8 9 10 11 12 13 14 15 xy 1 2 ▲♦✉✐s✲➱t✐❡♥♥❡ ❇♦✉❞r❡❛✉❧t 3 4 5 6 7 x/h 8 9 10 11 12 13 14 15 ❊❞❣❡ ✢♦✇ ✐♥ ✐♥❤♦♠♦❣❡♥❡♦✉s ❝❛♥♦♣② 0.4 0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 0.4 0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 ✷✽ ♦❝t♦❜❡r ✷✵✶✺ ❚✇♦✲❞✐♠❡♥s✐♦♥❛❧ ✈✐❡✇ ✿ ❝♦rr❡❧❛t✐♦♥ ❝♦❡✣❝✐❡♥t z (m) ❍❡t❡r♦❣❡♥❡♦✉s 100 80 60 40 20 0 rtot uw -3 -2 -1 0 z (m) ❍♦♠♦❣❡♥❡♦✉s 100 80 60 40 20 0 rtot uw 0.5 0.4 0.3 0.2 0.1 0.0 0.1 0.2 0.3 y 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0.5 0.4 0.3 0.2 0.1 0.0 0.1 0.2 0.3 y -3 -2 -1 0 1 2 ▲♦✉✐s✲➱t✐❡♥♥❡ ❇♦✉❞r❡❛✉❧t 3 4 5 6 7 x/h 8 9 10 11 12 13 14 15 ❊❞❣❡ ✢♦✇ ✐♥ ✐♥❤♦♠♦❣❡♥❡♦✉s ❝❛♥♦♣② ✷✽ ♦❝t♦❜❡r ✷✵✶✺ ❚✇♦✲❞✐♠❡♥s✐♦♥❛❧ ✈✐❡✇ ✿ s❦❡✇♥❡ss ♦❢ str❡❛♠✇✐s❡ ✈❡❧♦❝✐t② z (m) ❍❡t❡r♦❣❡♥❡♦✉s 100 80 60 40 20 0 Sktot u -3 -2 -1 0 z (m) ❍♦♠♦❣❡♥❡♦✉s 100 80 60 40 20 0 Sktot u 1.8 1.5 1.2 0.9 0.6 0.3 0.0 0.3 y 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1.8 1.5 1.2 0.9 0.6 0.3 0.0 0.3 y -3 -2 -1 0 1 2 ▲♦✉✐s✲➱t✐❡♥♥❡ ❇♦✉❞r❡❛✉❧t 3 4 5 6 7 x/h 8 9 10 11 12 13 14 15 ❊❞❣❡ ✢♦✇ ✐♥ ✐♥❤♦♠♦❣❡♥❡♦✉s ❝❛♥♦♣② ✷✽ ♦❝t♦❜❡r ✷✵✶✺ ❚✇♦✲❞✐♠❡♥s✐♦♥❛❧ ✈✐❡✇ ✿ s❦❡✇♥❡ss ♦❢ ✈❡rt✐❝❛❧ ✈❡❧♦❝✐t② z (m) ❍❡t❡r♦❣❡♥❡♦✉s 100 80 60 40 20 0 Sktot w z (m) 0.0 0.3 0.6 0.9 1.2 1.5 -3 -2 -1 0 ❍♦♠♦❣❡♥❡♦✉s 100 80 60 40 20 0 0.3 y Sktot w 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0.3 y 0.0 0.3 0.6 0.9 1.2 1.5 -3 -2 -1 0 1 2 ▲♦✉✐s✲➱t✐❡♥♥❡ ❇♦✉❞r❡❛✉❧t 3 4 5 6 7 x/h 8 9 10 11 12 13 14 15 ❊❞❣❡ ✢♦✇ ✐♥ ✐♥❤♦♠♦❣❡♥❡♦✉s ❝❛♥♦♣② ✷✽ ♦❝t♦❜❡r ✷✵✶✺ z (m) ❚✇♦✲❞✐♠❡♥s✐♦♥❛❧ ✈✐❡✇ ✿ r❛t✐♦ ♦❢ ❞✐s♣❡rs✐✈❡ t♦ t♦t❛❧ ✢✉① h✉¯✐ ′′ ✉¯❥ ′′ i② h✉¯✐ ′′ ✉¯❥ ′′ i② +h✉ ′ ✉ ′ i② ✉✲✈❛r✐❛♥❝❡ uu -3 -2 -1 0 1 2 3 ❥ z (m) ✐ z (m) ξ✐❥ = 100 80 60 40 20 0 100 80 60 40 20 0 100 80 60 40 20 0 4 5 6 7 8 9 10 11 12 13 14 15 ✇✲✈❛r✐❛♥❝❡ ww -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 ✉✇✲❝♦✈❛r✐❛♥❝❡ uw -3 -2 -1 0 1 ▲♦✉✐s✲➱t✐❡♥♥❡ ❇♦✉❞r❡❛✉❧t 2 3 4 5 6 7 x/h 8 9 10 11 12 13 14 15 ❊❞❣❡ ✢♦✇ ✐♥ ✐♥❤♦♠♦❣❡♥❡♦✉s ❝❛♥♦♣② 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 ✷✽ ♦❝t♦❜❡r ✷✵✶✺ z (m) z (m) ❚✇♦✲❞✐♠❡♥s✐♦♥❛❧ ✈✐❡✇ ✿ r❛t✐♦ ♦❢ ❞✐s♣❡rs✐✈❡ t♦ t♦t❛❧ ✢✉① 100 80 60 40 20 0 100 80 60 40 20 0 ✉ ✸ ✲♠♦♠❡♥t uuu -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 ✇ ✸ ✲♠♦♠❡♥t www -3 -2 -1 0 1 2 ▲♦✉✐s✲➱t✐❡♥♥❡ ❇♦✉❞r❡❛✉❧t 3 4 5 6 7 x/h 8 9 10 11 12 13 14 15 ❊❞❣❡ ✢♦✇ ✐♥ ✐♥❤♦♠♦❣❡♥❡♦✉s ❝❛♥♦♣② 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 ✷✽ ♦❝t♦❜❡r ✷✵✶✺ ✶❉ ✉✲✈❡❧♦❝✐t②✴❚❑❊ ✉✲✈❡❧♦❝✐t② 100 Homogeneous Heterogeneous 80 z (m) t✉r❜✉❧❡♥t ❦✐♥❡t✐❝ ❡♥❡r❣② 100 80 60 60 40 40 20 0 20 ❘❡❧❛t✐✈❡ ❞✐✛❡r❡♥❝❡ ❛t ❝❛♥♦♣② ❤❡✐❣❤t ✿ ✸✺% 0 2 4 u xy/ u 6 8 ✶✽% 10 0 0 1 ,ref xy ▲♦✉✐s✲➱t✐❡♥♥❡ ❇♦✉❞r❡❛✉❧t 2 E ❊❞❣❡ ✢♦✇ ✐♥ ✐♥❤♦♠♦❣❡♥❡♦✉s ❝❛♥♦♣② tot 3 xy/ u 4 5 2 ,ref xy ✷✽ ♦❝t♦❜❡r ✷✵✶✺ ✶❉ ✉✲❜✉❞❣❡t t♦t❛❧ ❜✉❞❣❡t 100 Homogeneous Heterogeneous 80 ❞r❛❣ t❡r♠ ❜✉❞❣❡t 100 80 ■♥t❡❣r❛t❡❞ ❞r❛❣ ✿ ✸.✻% ❧♦✇❡r z (m) 60 60 Ftot D 40 Ftot D u w z 20 0 uw z xy ❙✐♥❦ xy Ftot D 20 ❙♦✉r❝❡ 0 Tempo. terms + Disp. terms Tempo. terms xy 2.0 1.5 1.0 0.5 0.0 0.5 1.0 1.5 2.0 2 (h/ u ,ref xy) * u xy/ t ▲♦✉✐s✲➱t✐❡♥♥❡ ❇♦✉❞r❡❛✉❧t 40 xy = Disp. terms xy ❙✐♥❦ 15 10 ❊❞❣❡ ✢♦✇ ✐♥ ✐♥❤♦♠♦❣❡♥❡♦✉s ❝❛♥♦♣② ❙♦✉r❝❡ 5 2 (h/ u ,ref 0 xy) * 5 u xy/ 10 15 t ✷✽ ♦❝t♦❜❡r ✷✵✶✺ ❈♦♥❧✉s✐♦♥ ■♠♣❛❝ts ♦❢ tr❡❡✲s❝❛❧❡ ❤❡t❡r♦❣❡♥❡✐t✐❡s ✐♥ ❡❞❣❡ ✢♦✇ ❛♥❛❧②s❡❞ ■♥s✐❞❡ t❤❡ ❝❛♥♦♣② ✿ ✶✳ ✷✳ ✸✳ ✹✳ ✺✳ ✻✳ ❋❛st❡r ✢♦✇ ♣❡♥❡tr❛t✐♦♥ ❍✐❣❤❡r ❚❑❊ ▲♦✇❡r ❡✣❝✐❡♥❝② ❍✐❣❤❡r s❦❡✇♥❡ss ✭❣✉sts✮ ▲♦✇❡r ❞r❛❣ ■♠♣♦rt❛♥t ❞✐s♣❡rs✐✈❡ ✢✉①❡s ❛t t❤❡ ❡❞❣❡ ✭✶✵✲✽✵✪ ♦❢ t♦t❛❧ ✢✉①✮✱ ✉♣ t♦ ✺✵✪ ❛t ❝❛♥♦♣② t♦♣ ❢♦r ✉✲✈❛r✐❛♥❝❡ ❆❜♦✈❡ t❤❡ ❝❛♥♦♣② ✿ ✶✳ ❙❧✐❣❤t❧② ❤✐❣❤❡r ✇✐♥❞ s♣❡❡❞ ✴ s❛♠❡ ❧❡✈❡❧ ♦❢ ❚❑❊ ▲♦✉✐s✲➱t✐❡♥♥❡ ❇♦✉❞r❡❛✉❧t ❊❞❣❡ ✢♦✇ ✐♥ ✐♥❤♦♠♦❣❡♥❡♦✉s ❝❛♥♦♣② ✷✽ ♦❝t♦❜❡r ✷✵✶✺ ❈♦♥s❡q✉❡♥❝❡s ✿ ✶✳ ■♠♣♦rt❛♥t t♦ ♣✐❝t✉r❡ ✇❡❧❧ t❤❡ ❡❞❣❡ ✈❡rt✐❝❛❧ ❢♦❧✐❛❣❡ ❞✐str✐❜✉t✐♦♥ ✐♥ ♥✉♠❡r✐❝❛❧ s✐♠✉❧❛t✐♦♥ ♦❢ ❤♦♠♦❣❡♥❡♦✉s ❝❛♥♦♣② ✷✳ ❯♥❞❡r❡st✐♠❛t✐♦♥ ♦❢ ❣✉st ♦❝❝✉r❡♥❝❡ ✐♥ ❤♦♠♦❣❡♥❡♦✉s ❝❛♥♦♣② ✭s❦❡✇♥❡ss ❧♦❝❛❧✮ ✸✳ ▲♦✇❡r ❧♦❛❞s ♦♥ tr❡❡s ✴ ❤✐❣❤❡r ♣r♦❞✉❝t✐♦♥ ❢♦r ✇✐♥❞ t✉r❜✐♥❡s ❚❤❛♥❦ ②♦✉ ❢♦r ②♦✉r ❛tt❡♥t✐♦♥ ✦ ▲♦✉✐s✲➱t✐❡♥♥❡ ❇♦✉❞r❡❛✉❧t ❊❞❣❡ ✢♦✇ ✐♥ ✐♥❤♦♠♦❣❡♥❡♦✉s ❝❛♥♦♣② ✷✽ ♦❝t♦❜❡r ✷✵✶✺