{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,17]],"date-time":"2025-10-17T13:34:51Z","timestamp":1760708091419},"reference-count":16,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2009,4]]},"abstract":"<jats:p> A method for finding reduced-order approximations of turbulent flow models is presented. The method preserves bounds on the production of turbulent energy in the sense of the [Formula: see text] norm of perturbations from a notional laminar profile. This is achieved by decomposing the Navier\u2013Stokes system into a feedback arrangement between the linearized system and the remaining, normally neglected, nonlinear part. The linear system is reduced using a method similar to balanced truncation, but preserving bounds on the supply rate. The method involves balancing two algebraic Riccati equations. The bounds are then used to derive bounds on the turbulent energy production. An example of the application of the procedure to flow through a long straight pipe is presented. Comparison shows that the new method approximates the supply rate at least as well as, or better than, canonical balanced truncation. <\/jats:p>","DOI":"10.1142\/s0218127409023615","type":"journal-article","created":{"date-parts":[[2009,8,17]],"date-time":"2009-08-17T09:02:26Z","timestamp":1250499746000},"page":"1267-1278","source":"Crossref","is-referenced-by-count":10,"title":["MODEL REDUCTION OF TURBULENT FLUID FLOWS USING THE SUPPLY RATE"],"prefix":"10.1142","volume":"19","author":[{"given":"A. S.","family":"SHARMA","sequence":"first","affiliation":[{"name":"Departments of Electrical and Electronic Engineering, Aeronautics, South Kensington Campus, Imperial College London, London SW7 2BY, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1063\/1.1398044"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1016\/S0376-0421(00)00016-6"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1063\/1.858894"},{"key":"rf4","volume-title":"Linear Robust Control","author":"Green W. J.","year":"1995"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1080\/00207170410001713448"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112005004295"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1016\/S0021-9991(03)00029-9"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.1981.1102568"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127405012429"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1146\/annurev.fluid.38.050304.092139"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1126\/science.261.5121.578"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1063\/1.1566753"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112004009346"},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1007\/BF00276493"},{"key":"rf17","doi-asserted-by":"publisher","DOI":"10.1007\/BF00276494"},{"key":"rf18","doi-asserted-by":"crossref","first-page":"228","DOI":"10.1109\/TAC.1966.1098316","volume":"11","author":"Zames G.","journal-title":"IEEE Trans. Automatic Contr."}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127409023615","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T00:02:22Z","timestamp":1565136142000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127409023615"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,4]]},"references-count":16,"journal-issue":{"issue":"04","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2009,4]]}},"alternative-id":["10.1142\/S0218127409023615"],"URL":"https:\/\/doi.org\/10.1142\/s0218127409023615","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,4]]}}}