On the Batchelor constant in decaying isotropic turbulence

Direct numerical simulations of a passive scalar mixed in decaying homogeneous isotropic turbulence indicate that, when the Schmidt number is close to or exceeds unity, the Batchelor constant is about 3. This is smaller by nearly a factor of 2 than that inferred from stationary turbulence simulations. In the present case, Batchelor’s spectrum approximates the present data well in the viscous-convective range while Kraichnan’s spectrum provides a very good fit at large wavenumbers.