The Lagrangian spectral relaxation model of the scalar dissipation in homogeneous turbulence

Lagrangian pdf methods are employed to extend the spectral relaxation (SR) model of the scalar dissipation of an inert, passive scalar (1 less than or equal to Sc) in homogeneous turbulence. The Lagrangian spectral relaxation (LSR) model divides wavenumber space into a finite number (the total number depending on the Taylor-scale Reynolds number R-lambda and the Schmidt number Sc) of wavenumber bands whose time constants are determined from the mean turbulent kinetic energy and instantaneous turbulent energy dissipation rate. The LSR model accounts for the evolution of the scalar spectrum (viz., pdf) from an arbitrary initial shape to its fully developed form. The effect of turbulent-frequency fluctuations on the instantaneous scalar dissipation rate following a Kolmogorov-scale fluid particle is incorporated into the LSR model through a Lagrangian pdf model for the turbulent frequency, Model results are compared with DNS data for passive scalar mixing in stationary, isotropic turbulence. Two distinct causes of non-Gaussian scalar statistics are investigated: small-scale intermittency due to scalar-dissipation fluctuations at scales near the Kolmogorov scale, and transient large-scale inhomogeneities due to the form of the initial scalar spectrum at scales near the integral scale. Despite the absence of fitting parameters, the LSR model shows satisfactory agreement with available DNS data for both types of flows. (C) 1997 American Institute of Physics.