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Optimality conditions are derived, and semi-discrete a priori error estimates for all fluid variables are analyzed for both models. Numerical tests are performed to verify the accuracy of the theoretical findings and to demonstrate the effectiveness of optimal control. Given the proven utility of the NS-\n \n \n $$\\alpha $$<\/jats:tex-math>\n \n \u03b1<\/mml:mi>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n and NS-\n \n \n $$\\omega $$<\/jats:tex-math>\n \n \u03c9<\/mml:mi>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n models in fluid dynamics, this study addresses a significant gap by exploring the potential of optimal control to enhance the performance, efficiency, safety, and environmental impact of fluid systems.\n <\/jats:p>","DOI":"10.1007\/s11075-025-02013-z","type":"journal-article","created":{"date-parts":[[2025,1,30]],"date-time":"2025-01-30T02:56:31Z","timestamp":1738205791000},"page":"477-507","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Optimal Control problems of NS-$$\\alpha $$ and NS-$$\\omega $$ turbulence models: analysis and numerical tests"],"prefix":"10.1007","volume":"101","author":[{"given":"G\u00fclnur","family":"Ha\u00e7at","sequence":"first","affiliation":[]},{"given":"Aytekin","family":"\u00c7\u0131b\u0131k","sequence":"additional","affiliation":[]},{"given":"Fikriye","family":"Y\u0131lmaz","sequence":"additional","affiliation":[]},{"given":"Song\u00fcl","family":"Kaya","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,1,30]]},"reference":[{"issue":"24","key":"2013_CR1","doi-asserted-by":"publisher","first-page":"5338","DOI":"10.1103\/PhysRevLett.81.5338","volume":"81","author":"S Chen","year":"1998","unstructured":"Chen, S., Foid, C., Holm, D., Olson, E., Titi, E.S., Wynne, S.: Camassa-Holm equations as a closure model for turbulent channel and pipe flow. 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