{"id":{"repo_id":"bradford","oai_identifier":"oai:bradscholars.brad.ac.uk:10454/20906"},"canonical_url":"https://search.dev.ndltd.org/etd/bradford/oai:bradscholars.brad.ac.uk:10454/20906","repository":{"repo_id":"bradford","name":"University of Bradford","base_url":"https://bradscholars.brad.ac.uk/oai/request"},"display":{"title":"Turbulence Modelling of Tidal Currents in Rectangular Harbours","abstract":"In this study turbulence refinements have been made to existing computational models for the prediction of currents and water levels in coastal and estuarine waters via the numerical solution of the depth- and layer-integrated Reynolds equations. As most flows in practice are always turbulent, it is necessary to try and model the turbulence as accurately as possible. Various turbulence models including the mixing length, k-s and algebraic stress turbulence models all adopting a time average statistical approach, and the Smagorinsky model of the Large Eddy Simulation type were considered in a 2-D model. Likewise, the two-layer mixing length and the k-s turbulence models were included in a 3-D model to calculate the vertical Reynolds stresses. As for the hydrodynamic equations, the finite difference method has been used for the discrete equations of the turbulence parameters. Likewise, the Alternating Direction Implicit scheme has again been used for solving the discretized turbulence equations. In the hydrodynamic equations the advective acceleration terms have been treated using the third-order upwind scheme, whereas the counterpart terms in the turbulence equations have been treated using the exquisite scheme. In the finite difference representation various closed boundary conditions, including the no-slip, semi-slip and partial-slip, have been considered for the turbulence diffusion terms in the hydrodynamic equations and in using zero-equation turbulence models. These closed boundary conditions have been found to lead to a significant difference in the predicted flow patterns, both in the 2-D and 3-D models. However, in using more sophisticated turbulence models only the common no-slip closed boundary condition has been used for the turbulence diffusion terms as well as the turbulence parameters. The modified 2-D model has been applied to the predictions of tidal flow in rectangular harbours with large and small aspect ratios, as well as to a practical case study (i.e. Rattray Island), whereas the refined 3-D model has been applied to the predictions of steady state flow in a channel, wind-induced currents in a channel, tidal flow in rectangular harbours and steady flow in a practical case study (i.e. Blithfield Reservoir). The predicted numerical model results have been compared with the measured laboratory and field data and an encouraging degree of similarity has been obtained for all of the case studies. In particular, the partial-slip condition, incorporated with the zero-equation turbulence model, gave close agreement with the experimental data. More sophisticated turbulence models were found to give closer agreement with the experimental data.","abstract_html":"In this study turbulence refinements have been made to existing computational models for the prediction of currents and water levels in coastal and estuarine waters via the numerical solution of the depth- and layer-integrated Reynolds equations. As most flows in practice are always turbulent, it is necessary to try and model the turbulence as accurately as possible. Various turbulence models including the mixing length, k-s and algebraic stress turbulence models all adopting a time average statistical approach, and the Smagorinsky model of the Large Eddy Simulation type were considered in a 2-D model. Likewise, the two-layer mixing length and the k-s turbulence models were included in a 3-D model to calculate the vertical Reynolds stresses. As for the hydrodynamic equations, the finite difference method has been used for the discrete equations of the turbulence parameters. Likewise, the Alternating Direction Implicit scheme has again been used for solving the discretized turbulence equations. In the hydrodynamic equations the advective acceleration terms have been treated using the third-order upwind scheme, whereas the counterpart terms in the turbulence equations have been treated using the exquisite scheme. In the finite difference representation various closed boundary conditions, including the no-slip, semi-slip and partial-slip, have been considered for the turbulence diffusion terms in the hydrodynamic equations and in using zero-equation turbulence models. These closed boundary conditions have been found to lead to a significant difference in the predicted flow patterns, both in the 2-D and 3-D models. However, in using more sophisticated turbulence models only the common no-slip closed boundary condition has been used for the turbulence diffusion terms as well as the turbulence parameters. The modified 2-D model has been applied to the predictions of tidal flow in rectangular harbours with large and small aspect ratios, as well as to a practical case study (i.e. Rattray Island), whereas the refined 3-D model has been applied to the predictions of steady state flow in a channel, wind-induced currents in a channel, tidal flow in rectangular harbours and steady flow in a practical case study (i.e. Blithfield Reservoir). The predicted numerical model results have been compared with the measured laboratory and field data and an encouraging degree of similarity has been obtained for all of the case studies. In particular, the partial-slip condition, incorporated with the zero-equation turbulence model, gave close agreement with the experimental data. More sophisticated turbulence models were found to give closer agreement with the experimental data.","abstract_has_math":false,"creators":["Hakimzadeh, Habib"],"institution":"University of Bradford","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Falconer, Roger A."],"committee_chairs":[],"committee_members":[],"year":null,"date_issued":"","date_published":null,"updated_at":"2026-07-24T01:14:08Z","subjects":["Numerical modelling","Turbulence modelling","Coastal hydrodynamics","Tides","Harbours","Closed boundary conditions","Finite difference method","Tidal currents","Rectangular harbours"],"languages":["en"],"rights":["\"Creative
The University of Bradford theses are licenced under a Creative Commons Licence."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://bradscholars.brad.ac.uk/handle/10454/20906","outbound_label":"Repository record","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Falconer, Roger A."]},{"key":"dc:creator","label":"Author","values":["Hakimzadeh, Habib"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2026-05-13T13:44:28Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2026-05-13T13:44:28Z"]},{"key":"dc:publisher.department","label":"Dc Publisher Department","values":["Department of Civil and Environmental Engineering"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["University of Bradford"]},{"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":["PhD"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Numerical modelling","Turbulence modelling","Coastal hydrodynamics","Tides","Harbours","Closed boundary conditions","Finite difference method","Tidal currents","Rectangular harbours"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["\"Creative
The University of Bradford theses are licenced under a Creative Commons Licence."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://bradscholars.brad.ac.uk/handle/10454/20906"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In this study turbulence refinements have been made to existing computational models for the prediction of currents and water levels in coastal and estuarine waters via the numerical solution of the depth- and layer-integrated Reynolds equations. As most flows in practice are always turbulent, it is necessary to try and model the turbulence as accurately as possible. Various turbulence models including the mixing length, k-s and algebraic stress turbulence models all adopting a time average statistical approach, and the Smagorinsky model of the Large Eddy Simulation type were considered in a 2-D model. Likewise, the two-layer mixing length and the k-s turbulence models were included in a 3-D model to calculate the vertical Reynolds stresses. As for the hydrodynamic equations, the finite difference method has been used for the discrete equations of the turbulence parameters. Likewise, the Alternating Direction Implicit scheme has again been used for solving the discretized turbulence equations. In the hydrodynamic equations the advective acceleration terms have been treated using the third-order upwind scheme, whereas the counterpart terms in the turbulence equations have been treated using the exquisite scheme. In the finite difference representation various closed boundary conditions, including the no-slip, semi-slip and partial-slip, have been considered for the turbulence diffusion terms in the hydrodynamic equations and in using zero-equation turbulence models. These closed boundary conditions have been found to lead to a significant difference in the predicted flow patterns, both in the 2-D and 3-D models. However, in using more sophisticated turbulence models only the common no-slip closed boundary condition has been used for the turbulence diffusion terms as well as the turbulence parameters. The modified 2-D model has been applied to the predictions of tidal flow in rectangular harbours with large and small aspect ratios, as well as to a practical case study (i.e. Rattray Island), whereas the refined 3-D model has been applied to the predictions of steady state flow in a channel, wind-induced currents in a channel, tidal flow in rectangular harbours and steady flow in a practical case study (i.e. Blithfield Reservoir). The predicted numerical model results have been compared with the measured laboratory and field data and an encouraging degree of similarity has been obtained for all of the case studies. In particular, the partial-slip condition, incorporated with the zero-equation turbulence model, gave close agreement with the experimental data. More sophisticated turbulence models were found to give closer agreement with the experimental data."]},{"key":"dc:title","label":"Title","values":["Turbulence Modelling of Tidal Currents in Rectangular Harbours"]}]}],"canonical_facts":{"dc:contributor.advisor":["Falconer, Roger A."],"dc:creator":["Hakimzadeh, Habib"],"dc:date.accessioned":["2026-05-13T13:44:28Z"],"dc:date.available":["2026-05-13T13:44:28Z"],"dc:description.abstract":["In this study turbulence refinements have been made to existing computational models for the prediction of currents and water levels in coastal and estuarine waters via the numerical solution of the depth- and layer-integrated Reynolds equations. As most flows in practice are always turbulent, it is necessary to try and model the turbulence as accurately as possible. Various turbulence models including the mixing length, k-s and algebraic stress turbulence models all adopting a time average statistical approach, and the Smagorinsky model of the Large Eddy Simulation type were considered in a 2-D model. Likewise, the two-layer mixing length and the k-s turbulence models were included in a 3-D model to calculate the vertical Reynolds stresses. As for the hydrodynamic equations, the finite difference method has been used for the discrete equations of the turbulence parameters. Likewise, the Alternating Direction Implicit scheme has again been used for solving the discretized turbulence equations. In the hydrodynamic equations the advective acceleration terms have been treated using the third-order upwind scheme, whereas the counterpart terms in the turbulence equations have been treated using the exquisite scheme. In the finite difference representation various closed boundary conditions, including the no-slip, semi-slip and partial-slip, have been considered for the turbulence diffusion terms in the hydrodynamic equations and in using zero-equation turbulence models. These closed boundary conditions have been found to lead to a significant difference in the predicted flow patterns, both in the 2-D and 3-D models. However, in using more sophisticated turbulence models only the common no-slip closed boundary condition has been used for the turbulence diffusion terms as well as the turbulence parameters. The modified 2-D model has been applied to the predictions of tidal flow in rectangular harbours with large and small aspect ratios, as well as to a practical case study (i.e. Rattray Island), whereas the refined 3-D model has been applied to the predictions of steady state flow in a channel, wind-induced currents in a channel, tidal flow in rectangular harbours and steady flow in a practical case study (i.e. Blithfield Reservoir). The predicted numerical model results have been compared with the measured laboratory and field data and an encouraging degree of similarity has been obtained for all of the case studies. In particular, the partial-slip condition, incorporated with the zero-equation turbulence model, gave close agreement with the experimental data. More sophisticated turbulence models were found to give closer agreement with the experimental data."],"dc:identifier.uri":["https://bradscholars.brad.ac.uk/handle/10454/20906"],"dc:language.iso":["en"],"dc:publisher.department":["Department of Civil and Environmental Engineering"],"dc:publisher.institution":["University of Bradford"],"dc:rights":["\"Creative
The University of Bradford theses are licenced under a Creative Commons Licence."],"dc:subject":["Numerical modelling","Turbulence modelling","Coastal hydrodynamics","Tides","Harbours","Closed boundary conditions","Finite difference method","Tidal currents","Rectangular harbours"],"dc:title":["Turbulence Modelling of Tidal Currents in Rectangular Harbours"],"dc:type":["Thesis"],"dc:type.qualificationlevel":["doctoral"],"dc:type.qualificationname":["PhD"]},"updated_at":"2026-07-24T01:14:08Z"}