TY - JOUR
T1 - Viscosity renormalization based on direct-interaction closure
AU - Carnevale, George F.
AU - Frederiksen, Jorgen S.
PY - 1983
Y1 - 1983
N2 - Approximations in statistical turbulence theory often rely on modelling the decay in time of velocity correlations with a simple exponential decay. The decay rate is viewed as a renormalized viscosity. The three simplest implementations of this approximation scheme were originally given independently by Kraichnan, Edwards and Leslie. Each of these investigators used a different formalism and each achieved different renormalization prescriptions. These three different results are reexamined here entirely in terms of direct-interaction theory. The difference in the prescriptions of Kraichnan and Leslie is shown to be the product of different definitions of renormalized viscosity. Edwards’ prescription is shown to result from an inconsistent identification of the non-stationary energy-spectrum relaxation rate with the viscosity. An assessment of the validity of the Markovian closure approximation, and a prescription for non-stationary renormalized viscosity are provided.
AB - Approximations in statistical turbulence theory often rely on modelling the decay in time of velocity correlations with a simple exponential decay. The decay rate is viewed as a renormalized viscosity. The three simplest implementations of this approximation scheme were originally given independently by Kraichnan, Edwards and Leslie. Each of these investigators used a different formalism and each achieved different renormalization prescriptions. These three different results are reexamined here entirely in terms of direct-interaction theory. The difference in the prescriptions of Kraichnan and Leslie is shown to be the product of different definitions of renormalized viscosity. Edwards’ prescription is shown to result from an inconsistent identification of the non-stationary energy-spectrum relaxation rate with the viscosity. An assessment of the validity of the Markovian closure approximation, and a prescription for non-stationary renormalized viscosity are provided.
UR - http://www.scopus.com/inward/record.url?scp=0020767165&partnerID=8YFLogxK
U2 - 10.1017/S0022112083001330
DO - 10.1017/S0022112083001330
M3 - Article
AN - SCOPUS:0020767165
SN - 0022-1120
VL - 131
SP - 289
EP - 303
JO - Journal of Fluid Mechanics
JF - Journal of Fluid Mechanics
ER -