VELOCITY GRADIENT TENSOR ANALYSIS FOR TURBULENCE REFORMULATED IN TERMS OF NORMAL AND NON-NORMAL CONTRIBUTIONS. Keylock, C., J. Technical Report
VELOCITY GRADIENT TENSOR ANALYSIS FOR TURBULENCE REFORMULATED IN TERMS OF NORMAL AND NON-NORMAL CONTRIBUTIONS [pdf]Paper  abstract   bibtex   
Making use of a recently proposed, Schur decomposition approach to the analysis of the velocity gradient tensor (VGT), we provide a preliminary study of the resulting new terms for the case of a turbulent channel flow in the outer part of the logarithmic region. Previously, this approach has only been used for homogeneous, isotropic turbulence (HIT). In particular, we define six regions in the space of the second and third invariants of the tensor (the Q-R diagram) and condition our analysis on these regions and if the flow is undergoing a significant ejection or sweep event. When comparing the tendency for the VGT to form rod-like or disc-like structures, the results are very close to those for HIT. However, that the differences between ejections and sweeps are greater than this in the regions where Q and R are negative indicates a topological difference of potential significance for dissipation modelling. Where Q and R are negative, but the VGT's eigenvalues are complex we find a particularly strong tendency for the dynamics to be dominated by the non-normal contribution to the second order terms. In the more strongly vortical regions, the non-normal contribution to the sweeps is greater than for the ejections.
@techreport{
 title = {VELOCITY GRADIENT TENSOR ANALYSIS FOR TURBULENCE REFORMULATED IN TERMS OF NORMAL AND NON-NORMAL CONTRIBUTIONS},
 type = {techreport},
 id = {4f1217d0-99d3-3d35-8050-9012814a3157},
 created = {2020-05-26T19:15:55.845Z},
 accessed = {2020-05-26},
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 last_modified = {2020-05-26T19:15:58.312Z},
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 abstract = {Making use of a recently proposed, Schur decomposition approach to the analysis of the velocity gradient tensor (VGT), we provide a preliminary study of the resulting new terms for the case of a turbulent channel flow in the outer part of the logarithmic region. Previously, this approach has only been used for homogeneous, isotropic turbulence (HIT). In particular, we define six regions in the space of the second and third invariants of the tensor (the Q-R diagram) and condition our analysis on these regions and if the flow is undergoing a significant ejection or sweep event. When comparing the tendency for the VGT to form rod-like or disc-like structures, the results are very close to those for HIT. However, that the differences between ejections and sweeps are greater than this in the regions where Q and R are negative indicates a topological difference of potential significance for dissipation modelling. Where Q and R are negative, but the VGT's eigenvalues are complex we find a particularly strong tendency for the dynamics to be dominated by the non-normal contribution to the second order terms. In the more strongly vortical regions, the non-normal contribution to the sweeps is greater than for the ejections.},
 bibtype = {techreport},
 author = {Keylock, Chris J}
}
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