Approximate higher order polynomial inversion of the top-hat filter is
developed with which the turbulent stress tensor in large-eddy simula
tion can be consistently represented using the filtered field. General
ized (mixed) similarity models are proposed which improved the agreeme
nt with the kinetic energy transfer to small scales. These similarity
models are analyzed for random periodic signals and the ensemble avera
ged spectra of the turbulent stress tensor and the corresponding model
s are compared. (C) 1997 American Institute of Physics. [S1070-6631(97
)02712-8].