{"doi":"10.1098/rspa.2004.1426","title":"Transient growth in developing plane and Hagen Poiseuille flow","abstract":"<jats:title>Abstract</jats:title>\n                  <jats:p>The stability of developing entry flow in both two-dimensional channels and circular pipes is investigated for large Reynolds numbers. The basic flow is generated by uniform flow entering a channel/pipe, which then provokes the growth of boundary layers on the walls, until (far downstream) fully developed flow is attained; the length for this development is well known to be (Reynolds number)×the channel/pipe width/diameter. This enables the use of high-Reynolds-number theory, leading to boundary-layer-type equations which govern the flow; as such, there is no need to impose heuristic parallel-flow approximations. The resulting base flow is shown to be susceptible to significant, three-dimensional, transient (initially algebraic) growth in the streamwise direction, and, consequently, large amplifications to flow disturbances are possible (followed by ultimate decay far downstream). It is suggested that this initial amplification of disturbances is a possible and alternative mechanism for flow transition.</jats:p>","journal":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences","year":2005,"id":29599,"datarank":0.5936179485683986,"base_score":2.3978952727983707,"endowment":2.3978952727983707,"self_citation_contribution":0.3596842909197557,"citation_network_contribution":0.23393365764864288,"self_endowment_contribution":0.3596842909197557,"citer_contribution":0.23393365764864288,"corpus_percentile":null,"corpus_rank":null,"citation_count":10,"citer_count":8,"citers_with_citation_signal":6,"citers_with_endowment":6,"datacite_reuse_total":0,"is_dataset":false,"is_dataset_confidence":null,"is_data_producer":false,"deposit_databanks":null,"is_oa":false,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":null,"fair_score":null,"fair_percentile":null,"algorithm_id":"datarank_citation_only_1hop_v6","ranking_scope":"data_only","authors":[{"id":162832,"name":"Peter W Duck","orcid":null,"position":0,"is_corresponding":false}],"reference_count":0,"raw_metadata":{"has_enrichment":true,"base_score":2.3978952727983707,"endowment":2.3978952727983707,"datacite_reuse_total":0,"file_count":0,"downloads":0,"views":0,"has_version_chain":false,"is_dataset":false,"is_oa":false,"pmid":"18998881","pmcid":null,"openalex_id":"https://openalex.org/W2139580672","authors":[],"funders":[],"total_grants":0,"fwci":1.2743,"citation_percentile":0.80894006,"influential_citations":1,"citation_trend":[{"year":2013,"count":1},{"year":2021,"count":2},{"year":2022,"count":1},{"year":2026,"count":1}],"oa_status":"closed","license":"https://royalsociety.org/journals/ethics-policies/data-sharing-mining/","oa_locations":[{"url":"https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.2004.1426","host_type":"publisher"},{"url":"https://royalsocietypublishing.org/doi/full-xml/10.1098/rspa.2004.1426","host_type":"publisher"},{"url":"https://royalsocietypublishing.org/rspa/article-pdf/461/2057/1311/642846/rspa.2004.1426.pdf","host_type":"publisher"},{"url":"https://doi.org/10.1098/rspa.2004.1426","host_type":"journal"},{"url":"https://research.manchester.ac.uk/en/publications/1b9e3f62-3ef1-4898-a537-b61e0b645fef","host_type":"repository"},{"url":"https://www.research.manchester.ac.uk/portal/en/publications/transient-growth-in-developing-plane-and-hagen-poiseuille-flow(1b9e3f62-3ef1-4898-a537-b61e0b645fef).html","host_type":"repository"}],"fields_of_study":["Fluid Dynamics and Turbulent Flows","Fluid Dynamics and Vibration Analysis","Plant Water Relations and Carbon Dynamics","Mathematics","Engineering","Physics"],"mesh_terms":[],"keywords":["Reynolds number","Hagen–Poiseuille equation","Hele-Shaw flow","Open-channel flow","Mechanics","Flow (mathematics)","Laminar flow","Pipe flow","Boundary layer","Plug flow","Transient (computer programming)","Isothermal flow","Physics","Mathematics","Computer science","Turbulence"],"sdg_mappings":[{"sdg_number":0,"sdg_label":"Sustainable cities and communities"}],"linked_datasets":[],"clinical_trials":[],"software_tools":[],"database_accessions":[],"source":"live","citation_network_status":"fetched"},"created_at":"2026-06-09T00:16:24.766232Z","pmid":null,"pmcid":null,"fwci":null,"citation_percentile":null,"influential_citations":0,"oa_status":null,"license":null,"views":0,"total_file_size_bytes":0,"version_count":0,"fair_f":null,"fair_a":null,"fair_i":null,"fair_r":null,"fair_zscore":null,"fair_rationale":null,"fair_model":null,"fair_agent_version":null,"fair_fulltext_source":null,"fair_has_llm":null,"fair_computed_at":null,"clinical_trials":[],"software_tools":[],"db_accessions":[],"linked_datasets":[],"topics":[]}