Numerical Integration of the Lagrangian Renormalized Approximation

Abstract

The Lagrangian renormalized approximation (LRA) and the Modified Lagrangian renormalized approximation (MLRA) are integrated numerically for decaying homogeneous isotropic turbulences in two and three dimensions. At moderate Reynolds numbers the results are in good agreement with the direct numerical simulations by Herring et al. in two dimensions and with those by Orszag and Patterson in three dimensions. At high Reynolds numbers the one dimensional inertial and dissipation range spectra of the LRA and the MLRA agree well with the tidal channel data of Grant et al. The comparison with the DIA, TFM, ALHDIA and SBALHDIA shows that the MLRA behavior is very close to that of the TFM.