#### DIMOTAKIS, P. E. & MILLER, P. L. 1990 "Some
consequences of the boundedness of scalar fluctuations," *Phys.
Fluids A *2(11), 1919-1920.

*Abstract*

Values of the scalar field c (x, t), if initially bounded,
will always be bounded by the limits set by the initial
conditions. This observation permits the maximum variance c'^{2}
to be computed as a function of the mean value c. It is argued
that this maximum should be expected in the limit of infinite
Schmidt numbers (zero scalar species diffusivity). This suggests
that c'/ c on the axis of turbulent jets, for example, may not
tend to a constant, i.e., independent of x/d, in the limit of
very large Schmidt numbers. It also underscores a difficulty with
the k^{-1} scalar spectrum proposed by Batchelor [J.
Fluid Mech. 5, 113 (1959)].