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 20483 grid points. When the Reynolds number Reλ is increased up to Reλ = 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 Cuθ = 1.50±0.08 at Reλ = 585. The Reλ effect on the scaling of the scalar flux spectrum is well compensated using the mean molecular destruction of the scalar flux uθ. The Reλ dependence of Cuθ is also compared with the results of previous studies, and its asymptotic state at an infinite Reynolds number is discussed