Full simulations of homogeneous isotropic turbulence containing a homogeneous passive scalar were made at low Reynolds numbers and various Prandtl numbers. The results show that the spectral behavior of the two fields are quite similar; both fields decay as power-law functions of time. However. the decay exponent is quite dependent on both the Reynolds and Prandtl numbers. The decay exponent of...

We study the eigenvectors of the renormalization-group matrix for scalar fields at the Gaussian fixed point, and find that that there exist “relevant” directions in parameter space. They correspond to theories with exponential potentials that are nontrivial and asymptotically free. All other potentials, including polynomial potentials, are “irrelevant,” and lead to trivial theories. Away from t...