Towards the solution of Feynman's turbulence problem

0582842 - ASÚ 2024 US eng C - Konferenční příspěvek (zahraniční konf.)
Macháček, Martin
Towards the solution of Feynman's turbulence problem.
Mathematical Modeling For Sustainable Development. Melville: AIP Publishing, 2023, č. článku 120026. AIP Conference Proceeding, 2872. ISBN 978-0-7354-4657-1. E-ISSN 1551-7616.
[Mathematical Modeling For Sustainable Development /11th/. virtual (RS), 05.09.2022-08.09.2022]
Klíčová slova: pipe flow * stationary turbulence * invariant measure
Obor OECD: Applied mathematics

In this paper we present further analytical results in the process of solving this algebraic system for the pipe flow, in particular of obtaining the mean values of the first-order Hermite-polynomials 〈vI〉. If we were able to calculate these mean values numerically, then we could also calculate the long-time mean velocity 〈v(x)〉 = ∑I 〈vI〉 wI (x) (i. e. the mean velocity of the stationary turbulent flow), hence give the ab initio answer to Feynman’s question he poses as the prototype of the turbulence problemml: ‘to push a given amount of water through that pipe, how much pressure is needed?’
Trvalý link: https://hdl.handle.net/11104/0350896