Scalar flux spectrum in isotropic steady turbulence with a uniform mean gradient

The scaling law of a scalar flux spectrum (velocity-scalar cospectrum) in the inertial convective range of passive scalar turbulence under a uniform mean scalar gradient is examined using direct numerical simulation with a resolution of up to 2048(3) grid points. When the Reynolds number Re-lambda is increased up to Re-lambda=585, the scalar flux spectrum tends to obey the power law k(-7/3), as predicted by Lumley [J. Atmos. Sci. 21, 99 (1964); Phys. Fluids 10, 855 (1967)], with a nondimensional constant of C-u theta=1.50 +/- 0.08 at Re-lambda=585. The Re-lambda effect on the scaling of the scalar flux spectrum is well compensated using the mean molecular destruction of the scalar flux (epsilon) over bar (u theta). The Re-lambda dependence of C-u theta is also compared with the results of previous studies, and its asymptotic state at an infinite Reynolds number is discussed. (c) 2007 American Institute of Physics.