Abstract
Language  English 

Qualification  PhD 
Awarding Institution 

Supervisors/Advisors 

Award date  1 Jun 2012 
Place of Publication  Edinburgh 
Publication status  Published  2 Apr 2012 
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Keywords
 direct numerical simulation
 isotropic turbulence
 energy
 statistical field theory
 renormalized perturbation theory
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Investigation of the transfer and dissipation of energy in isotropic turbulence. / Yoffe, Samuel R.
Edinburgh, 2012. 292 p.Research output: Thesis › Doctoral Thesis
TY  THES
T1  Investigation of the transfer and dissipation of energy in isotropic turbulence
AU  Yoffe, Samuel R.
PY  2012/4/2
Y1  2012/4/2
N2  A parallel pseudospectral code for the direct numerical simulation (DNS) of isotropic turbulence has been developed. The code has been extensively benchmarked using established results from literature. The code has been used to conduct a series of runs for freelydecaying turbulence. We explore the use of powerlaw decay of the total energy to determine an evolved time and compare with the use of dynamic quantities such as the peak dissipation rate, maximum transport power and velocity derivative skewness. Stationary turbulence has also been investigated, where we ensure that the energy input rate remains constant for all runs. We present results for Reynolds numbers up to R{\lambda} = 335 on a 1024^3 lattice. An exploitation of the pseudospectral technique is used to calculate second and thirdorder structure functions from the energy and transfer spectra, with a comparison presented to the realspace calculation. An alternative to ESS is discussed, with the secondorder exponent found to approach 2/3. The dissipation anomaly is considered for forced and freedecay. The K\'arm\'anHowarth equation (KHE) is studied and a derivation of a new work term presented. The balance of energy represented by the KHE is then investigated. Based on the KHE, we develop a model for the behaviour of the dimensionless dissipation coefficient that predicts C{\epsilon} = C{\epsilon}(\infty) + C_L/R_L, with C{\epsilon}(\infty) = 0.47 and C_L = 19.1 obtained from DNS data. Theoretical methods based on RG and statistical closures are still being developed to study turbulence. The dynamic RG procedure used by Forster, Nelson and Stephen (FNS) is considered in some detail and a disagreement in the literature is resolved here. The application of statistical closure and renormalized perturbation theory is discussed and a new twotime model probability density functional presented.
AB  A parallel pseudospectral code for the direct numerical simulation (DNS) of isotropic turbulence has been developed. The code has been extensively benchmarked using established results from literature. The code has been used to conduct a series of runs for freelydecaying turbulence. We explore the use of powerlaw decay of the total energy to determine an evolved time and compare with the use of dynamic quantities such as the peak dissipation rate, maximum transport power and velocity derivative skewness. Stationary turbulence has also been investigated, where we ensure that the energy input rate remains constant for all runs. We present results for Reynolds numbers up to R{\lambda} = 335 on a 1024^3 lattice. An exploitation of the pseudospectral technique is used to calculate second and thirdorder structure functions from the energy and transfer spectra, with a comparison presented to the realspace calculation. An alternative to ESS is discussed, with the secondorder exponent found to approach 2/3. The dissipation anomaly is considered for forced and freedecay. The K\'arm\'anHowarth equation (KHE) is studied and a derivation of a new work term presented. The balance of energy represented by the KHE is then investigated. Based on the KHE, we develop a model for the behaviour of the dimensionless dissipation coefficient that predicts C{\epsilon} = C{\epsilon}(\infty) + C_L/R_L, with C{\epsilon}(\infty) = 0.47 and C_L = 19.1 obtained from DNS data. Theoretical methods based on RG and statistical closures are still being developed to study turbulence. The dynamic RG procedure used by Forster, Nelson and Stephen (FNS) is considered in some detail and a disagreement in the literature is resolved here. The application of statistical closure and renormalized perturbation theory is discussed and a new twotime model probability density functional presented.
KW  direct numerical simulation
KW  isotropic turbulence
KW  energy
KW  statistical field theory
KW  renormalized perturbation theory
UR  https://www.era.lib.ed.ac.uk/handle/1842/7541
UR  http://arxiv.org/abs/1306.3408
M3  Doctoral Thesis
CY  Edinburgh
ER 