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The k-epsilon model in the theory of turbulence

Scott-Pomerantz, Colleen Dawn (2005) The k-epsilon model in the theory of turbulence. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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We consider the $k-varepsilon$ model in the theory of turbulence, where $k$ is the turbulent kinetic energy, $varepsilon$ is thedissipation rate of the turbulent energy, and $alpha,$ $eta,$ and $gamma$ are positive constants. In particular we examine the Barenblatt self-similar $k-varepsilon$ model, along with boundary conditions taken to ensure the symmetry and compactness of the support of solutions.Under the assumptions:$eta>alpha,$ $3alpha>2eta,$ and $gamma$>3/2,we show the existence of $mu$ for which there is a positive solutionto the system and corresponding boundary conditions by proving a seriesof lemmas. We also include graphs of solutions obtained by using XPPAUT 5.85.


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Item Type: University of Pittsburgh ETD
Status: Unpublished
CreatorsEmailPitt UsernameORCID
Scott-Pomerantz, Colleen
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairMcLeod, J. Brycemcleod@pitt.eduMCLEOD
Committee MemberBushell,
Committee MemberHastings, Stuartsph@pitt.eduSPH
Committee MemberMetzger, Thomasmetzger@pitt.eduMETZGER
Date: 31 January 2005
Date Type: Completion
Defense Date: 4 December 2004
Approval Date: 31 January 2005
Submission Date: 9 December 2004
Access Restriction: No restriction; Release the ETD for access worldwide immediately.
Institution: University of Pittsburgh
Schools and Programs: Dietrich School of Arts and Sciences > Mathematics
Degree: PhD - Doctor of Philosophy
Thesis Type: Doctoral Dissertation
Refereed: Yes
Uncontrolled Keywords: k-epsilon model; existence of solutions; turbulence; shooting methods
Other ID:, etd-12092004-201633
Date Deposited: 10 Nov 2011 20:09
Last Modified: 15 Nov 2016 13:54


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