Investigation of the transfer and dissipation of energy in isotropic turbulence

Research output: ThesisDoctoral Thesis

Abstract

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 freely-decaying turbulence. We explore the use of power-law 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 third-order structure functions from the energy and transfer spectra, with a comparison presented to the real-space calculation. An alternative to ESS is discussed, with the second-order exponent found to approach 2/3. The dissipation anomaly is considered for forced and free-decay. The K\'arm\'an-Howarth 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 two-time model probability density functional presented.
LanguageEnglish
QualificationPhD
Awarding Institution
  • University of Edinburgh
Supervisors/Advisors
  • McComb, W. David, Supervisor, External person
  • Berera, Arjun, Supervisor, External person
Award date1 Jun 2012
Place of PublicationEdinburgh
Publication statusPublished - 2 Apr 2012

Fingerprint

isotropic turbulence
dissipation
turbulence
direct numerical simulation
closures
skewness
decay
exploitation
energy
Reynolds number
energy spectra
derivation
perturbation theory
energy transfer
exponents
anomalies
coefficients

Keywords

  • direct numerical simulation
  • isotropic turbulence
  • energy
  • statistical field theory
  • renormalized perturbation theory

Cite this

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title = "Investigation of the transfer and dissipation of energy in isotropic turbulence",
abstract = "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 freely-decaying turbulence. We explore the use of power-law 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 third-order structure functions from the energy and transfer spectra, with a comparison presented to the real-space calculation. An alternative to ESS is discussed, with the second-order exponent found to approach 2/3. The dissipation anomaly is considered for forced and free-decay. The K\'arm\'an-Howarth 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 two-time model probability density functional presented.",
keywords = "direct numerical simulation, isotropic turbulence, energy, statistical field theory, renormalized perturbation theory",
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year = "2012",
month = "4",
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school = "University of Edinburgh",

}

Investigation of the transfer and dissipation of energy in isotropic turbulence. / Yoffe, Samuel R.

Edinburgh, 2012. 292 p.

Research output: ThesisDoctoral 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 freely-decaying turbulence. We explore the use of power-law 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 third-order structure functions from the energy and transfer spectra, with a comparison presented to the real-space calculation. An alternative to ESS is discussed, with the second-order exponent found to approach 2/3. The dissipation anomaly is considered for forced and free-decay. The K\'arm\'an-Howarth 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 two-time 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 freely-decaying turbulence. We explore the use of power-law 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 third-order structure functions from the energy and transfer spectra, with a comparison presented to the real-space calculation. An alternative to ESS is discussed, with the second-order exponent found to approach 2/3. The dissipation anomaly is considered for forced and free-decay. The K\'arm\'an-Howarth 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 two-time 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 -