{"id":{"repo_id":"cambridge","oai_identifier":"oai:www.repository.cam.ac.uk:1810/386833"},"canonical_url":"https://search.dev.ndltd.org/etd/cambridge/oai:www.repository.cam.ac.uk:1810/386833","repository":{"repo_id":"cambridge","name":"Cambridge University","base_url":"https://api.repository.cam.ac.uk/server/oai/request"},"display":{"title":"Flow regimes in canopy turbulence","abstract":"This thesis investigates turbulent flow regimes over canopies using direct numerical simulations. The term `canopy' refers to a group of substantial roughness elements protruding into the flow, which generally results in two distinct regions of interest: the near-canopy region, where the flow is directly influenced by the canopy, and the outer layer, where the flow sufficiently far above the canopy is minimally disturbed. The first part of the thesis aims to identify and characterise the canopy density regime, which has a direct impact on the flow within and immediately above the canopy. In the sparse regime, turbulence penetrates relatively unhindered into the canopy, whereas in the dense regime, this penetration is limited. It is shown that the common measure of canopy density based on frontal density λ_f does not accurately predict the density regime for practical canopies with anisotropic layouts, which suggests that λ_f does not necessarily encapsulate the key physics governing canopy density. Instead, we focus directly on whether the overlying turbulence penetrates or not to determine if a canopy behaves as dense or sparse. We propose metrics that measure turbulence penetration by focusing on individual turbulent eddies, particularly structures of intense Reynolds shear stress u'v'. These metrics indicate whether such eddies penetrate within the canopy or are precluded from doing so. We use these metrics to analyse a series of isotropic and anisotropic canopies across a range of frontal densities λ_f≈0.01-2.04, heights h^+≈44-266 and Reynolds numbers Re_τ≈180-2000. Our findings suggest that the penetration of overlying eddies and whether a canopy behaves as dense or sparse essentially depend on the spanwise gap between canopy elements and how that compares to the typical spanwise width of the overlying eddies, which scale in inner units at low Re_τ. At higher Re_τ, these eddies are expected to scale in outer units. In essence, a canopy is sparse if the characteristic turbulent eddies near the canopy-tip plane fit between the elements, while a canopy is dense if these eddies are too large compared to the spanwise gap, where turbulence penetration is precluded. In the second part of the thesis, we assess outer-layer similarity in flows over canopies from sparse to dense, with λ_f≈0.01-2.04, at moderate-to-high Reynolds numbers Re_τ≈550-2000. The canopies have heights h^+≈110-220, and are used as an instance of obstructing substrate for the assessment of outer-layer similarity. 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_τ. Instead, we determine the zero-plane displacement 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. In addition, we explore the possibility of the zero-plane displacement and the friction velocity being set independently, but find that outer-layer similarity is more consistently recovered when they are coupled. We observe that although the Kármán constant κ may not have smooth-wall-like values, the flow statistics are smooth-wall-like in the logarithmic layer (and above) if the surface effect is limited within the near-wall region. This suggests a modified outer-layer similarity, where κ 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 κ≈0.39 and origin essentially at the tip plane. For canopies with intermediate density, the overlying flow perceives a deeper zero-plane displacement into the canopy, which is consistent with observations reported by previous studies, but exhibits a lower Kármán constant, κ≈0.34-0.36. For sparse canopies, κ 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 κ never exceeds 15%, which is significantly less than that obtained in some previous works using conventional methods to assess outer-layer similarity.","abstract_html":"This thesis investigates turbulent flow regimes over canopies using direct numerical simulations. The term `canopy' refers to a group of substantial roughness elements protruding into the flow, which generally results in two distinct regions of interest: the near-canopy region, where the flow is directly influenced by the canopy, and the outer layer, where the flow sufficiently far above the canopy is minimally disturbed. The first part of the thesis aims to identify and characterise the canopy density regime, which has a direct impact on the flow within and immediately above the canopy. In the sparse regime, turbulence penetrates relatively unhindered into the canopy, whereas in the dense regime, this penetration is limited. It is shown that the common measure of canopy density based on frontal density λ_f does not accurately predict the density regime for practical canopies with anisotropic layouts, which suggests that λ_f does not necessarily encapsulate the key physics governing canopy density. Instead, we focus directly on whether the overlying turbulence penetrates or not to determine if a canopy behaves as dense or sparse. We propose metrics that measure turbulence penetration by focusing on individual turbulent eddies, particularly structures of intense Reynolds shear stress u'v'. These metrics indicate whether such eddies penetrate within the canopy or are precluded from doing so. We use these metrics to analyse a series of isotropic and anisotropic canopies across a range of frontal densities λ_f≈0.01-2.04, heights h^+≈44-266 and Reynolds numbers Re_τ≈180-2000. Our findings suggest that the penetration of overlying eddies and whether a canopy behaves as dense or sparse essentially depend on the spanwise gap between canopy elements and how that compares to the typical spanwise width of the overlying eddies, which scale in inner units at low Re_τ. At higher Re_τ, these eddies are expected to scale in outer units. In essence, a canopy is sparse if the characteristic turbulent eddies near the canopy-tip plane fit between the elements, while a canopy is dense if these eddies are too large compared to the spanwise gap, where turbulence penetration is precluded. In the second part of the thesis, we assess outer-layer similarity in flows over canopies from sparse to dense, with λ_f≈0.01-2.04, at moderate-to-high Reynolds numbers Re_τ≈550-2000. The canopies have heights h^+≈110-220, and are used as an instance of obstructing substrate for the assessment of outer-layer similarity. 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_τ. Instead, we determine the zero-plane displacement 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. In addition, we explore the possibility of the zero-plane displacement and the friction velocity being set independently, but find that outer-layer similarity is more consistently recovered when they are coupled. We observe that although the Kármán constant κ may not have smooth-wall-like values, the flow statistics are smooth-wall-like in the logarithmic layer (and above) if the surface effect is limited within the near-wall region. This suggests a modified outer-layer similarity, where κ 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 κ≈0.39 and origin essentially at the tip plane. For canopies with intermediate density, the overlying flow perceives a deeper zero-plane displacement into the canopy, which is consistent with observations reported by previous studies, but exhibits a lower Kármán constant, κ≈0.34-0.36. For sparse canopies, κ 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 κ never exceeds 15%, which is significantly less than that obtained in some previous works using conventional methods to assess outer-layer similarity.","abstract_has_math":false,"creators":["Chen, Zishen"],"institution":"University of Cambridge","degree_name":"Doctor of Philosophy (PhD)","degree_level":"Doctoral","degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["García-Mayoral, Ricardo"],"committee_chairs":[],"committee_members":[],"year":2025,"date_issued":"2025-02-28","date_published":"2025-02-28","updated_at":"2026-07-22T22:24:06Z","subjects":["Turbulent boundary layers","Turbulence simulation"],"languages":[],"rights":[],"rights_urls":["https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/da85f1ed-1c07-4c63-b654-35c990ed48a4/download","https://creativecommons.org/licenses/by/4.0/"],"identifier_entries":[]},"links":{"outbound_url":"https://doi.org/10.17863/CAM.119863","outbound_label":"DOI","outbound_source":"dc:identifier.doi"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["García-Mayoral, Ricardo"]},{"key":"dc:contributor.sponsor","label":"Sponsor","values":["This work was supported in part by the UK Engineering and Physical Sciences Research Council (EPSRC) under grant EP/S013083/1. Computational resources were provided by the University of Cambridge Research Computing Service under EPSRC Tier-2 grant EP/P020259/1 (project cs155), and by the UK 'ARCHER2' system under PRACE project pr1u1702 and EPSRC Access to HPC projects e776 and e800."]},{"key":"dc:creator","label":"Author","values":["Chen, Zishen"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.issued","label":"Date","values":["2025-02-28"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["University of Cambridge"]},{"key":"dc:relation.isreferencedby.uri","label":"Dc Relation Isreferencedby URI","values":["https://www.repository.cam.ac.uk/handle/1810/386833"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["Doctoral"]},{"key":"dc:type.qualificationname","label":"Dc Type Qualificationname","values":["Doctor of Philosophy (PhD)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Turbulent boundary layers","Turbulence simulation"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/da85f1ed-1c07-4c63-b654-35c990ed48a4/download","https://creativecommons.org/licenses/by/4.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.doi","label":"DOI","values":["https://doi.org/10.17863/CAM.119863"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/52b85bae-f491-4f06-aa3f-d7f46587fcd6/download"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["This thesis investigates turbulent flow regimes over canopies using direct numerical simulations. The term `canopy' refers to a group of substantial roughness elements protruding into the flow, which generally results in two distinct regions of interest: the near-canopy region, where the flow is directly influenced by the canopy, and the outer layer, where the flow sufficiently far above the canopy is minimally disturbed. The first part of the thesis aims to identify and characterise the canopy density regime, which has a direct impact on the flow within and immediately above the canopy. In the sparse regime, turbulence penetrates relatively unhindered into the canopy, whereas in the dense regime, this penetration is limited. It is shown that the common measure of canopy density based on frontal density λ_f does not accurately predict the density regime for practical canopies with anisotropic layouts, which suggests that λ_f does not necessarily encapsulate the key physics governing canopy density. Instead, we focus directly on whether the overlying turbulence penetrates or not to determine if a canopy behaves as dense or sparse. We propose metrics that measure turbulence penetration by focusing on individual turbulent eddies, particularly structures of intense Reynolds shear stress u'v'. These metrics indicate whether such eddies penetrate within the canopy or are precluded from doing so. We use these metrics to analyse a series of isotropic and anisotropic canopies across a range of frontal densities λ_f≈0.01-2.04, heights h^+≈44-266 and Reynolds numbers Re_τ≈180-2000. Our findings suggest that the penetration of overlying eddies and whether a canopy behaves as dense or sparse essentially depend on the spanwise gap between canopy elements and how that compares to the typical spanwise width of the overlying eddies, which scale in inner units at low Re_τ. At higher Re_τ, these eddies are expected to scale in outer units. In essence, a canopy is sparse if the characteristic turbulent eddies near the canopy-tip plane fit between the elements, while a canopy is dense if these eddies are too large compared to the spanwise gap, where turbulence penetration is precluded. In the second part of the thesis, we assess outer-layer similarity in flows over canopies from sparse to dense, with λ_f≈0.01-2.04, at moderate-to-high Reynolds numbers Re_τ≈550-2000. The canopies have heights h^+≈110-220, and are used as an instance of obstructing substrate for the assessment of outer-layer similarity. 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_τ. Instead, we determine the zero-plane displacement 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. In addition, we explore the possibility of the zero-plane displacement and the friction velocity being set independently, but find that outer-layer similarity is more consistently recovered when they are coupled. We observe that although the Kármán constant κ may not have smooth-wall-like values, the flow statistics are smooth-wall-like in the logarithmic layer (and above) if the surface effect is limited within the near-wall region. This suggests a modified outer-layer similarity, where κ 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 κ≈0.39 and origin essentially at the tip plane. For canopies with intermediate density, the overlying flow perceives a deeper zero-plane displacement into the canopy, which is consistent with observations reported by previous studies, but exhibits a lower Kármán constant, κ≈0.34-0.36. For sparse canopies, κ 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 κ never exceeds 15%, which is significantly less than that obtained in some previous works using conventional methods to assess outer-layer similarity."]},{"key":"dc:format.checksum.md5","label":"Dc Format Checksum Md5","values":["0f31098800dce762aeff7a571d5fd4fe","87eda9de84448d1f82354d60eee3eb5f"]},{"key":"dc:title","label":"Title","values":["Flow regimes in canopy turbulence"]}]}],"canonical_facts":{"dc:contributor.advisor":["García-Mayoral, Ricardo"],"dc:contributor.sponsor":["This work was supported in part by the UK Engineering and Physical Sciences Research Council (EPSRC) under grant EP/S013083/1. 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In the sparse regime, turbulence penetrates relatively unhindered into the canopy, whereas in the dense regime, this penetration is limited. It is shown that the common measure of canopy density based on frontal density λ_f does not accurately predict the density regime for practical canopies with anisotropic layouts, which suggests that λ_f does not necessarily encapsulate the key physics governing canopy density. Instead, we focus directly on whether the overlying turbulence penetrates or not to determine if a canopy behaves as dense or sparse. We propose metrics that measure turbulence penetration by focusing on individual turbulent eddies, particularly structures of intense Reynolds shear stress u'v'. These metrics indicate whether such eddies penetrate within the canopy or are precluded from doing so. We use these metrics to analyse a series of isotropic and anisotropic canopies across a range of frontal densities λ_f≈0.01-2.04, heights h^+≈44-266 and Reynolds numbers Re_τ≈180-2000. Our findings suggest that the penetration of overlying eddies and whether a canopy behaves as dense or sparse essentially depend on the spanwise gap between canopy elements and how that compares to the typical spanwise width of the overlying eddies, which scale in inner units at low Re_τ. At higher Re_τ, these eddies are expected to scale in outer units. In essence, a canopy is sparse if the characteristic turbulent eddies near the canopy-tip plane fit between the elements, while a canopy is dense if these eddies are too large compared to the spanwise gap, where turbulence penetration is precluded. In the second part of the thesis, we assess outer-layer similarity in flows over canopies from sparse to dense, with λ_f≈0.01-2.04, at moderate-to-high Reynolds numbers Re_τ≈550-2000. The canopies have heights h^+≈110-220, and are used as an instance of obstructing substrate for the assessment of outer-layer similarity. 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_τ. Instead, we determine the zero-plane displacement 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. In addition, we explore the possibility of the zero-plane displacement and the friction velocity being set independently, but find that outer-layer similarity is more consistently recovered when they are coupled. We observe that although the Kármán constant κ may not have smooth-wall-like values, the flow statistics are smooth-wall-like in the logarithmic layer (and above) if the surface effect is limited within the near-wall region. This suggests a modified outer-layer similarity, where κ 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 κ≈0.39 and origin essentially at the tip plane. For canopies with intermediate density, the overlying flow perceives a deeper zero-plane displacement into the canopy, which is consistent with observations reported by previous studies, but exhibits a lower Kármán constant, κ≈0.34-0.36. For sparse canopies, κ 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 κ never exceeds 15%, which is significantly less than that obtained in some previous works using conventional methods to assess outer-layer similarity."],"dc:format.checksum.md5":["0f31098800dce762aeff7a571d5fd4fe","87eda9de84448d1f82354d60eee3eb5f"],"dc:identifier.doi":["https://doi.org/10.17863/CAM.119863"],"dc:identifier.uri":["https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/52b85bae-f491-4f06-aa3f-d7f46587fcd6/download"],"dc:publisher.institution":["University of Cambridge"],"dc:relation.isreferencedby.uri":["https://www.repository.cam.ac.uk/handle/1810/386833"],"dc:rights":["https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/da85f1ed-1c07-4c63-b654-35c990ed48a4/download","https://creativecommons.org/licenses/by/4.0/"],"dc:subject":["Turbulent boundary layers","Turbulence simulation"],"dc:title":["Flow regimes in canopy turbulence"],"dc:type":["Thesis"],"dc:type.qualificationlevel":["Doctoral"],"dc:type.qualificationname":["Doctor of Philosophy (PhD)"]},"updated_at":"2026-07-22T22:24:06Z"}