**INSTANTANEOUS SCALAR FIELD IN ISOTROPIC TURBULENCE**

**Geert Brethouwer* and Frans Nieuwstadt+
**

**Department of Mechanics, KTH, Stockholm, Sweden, and +Laboratory of Aero and Hydronamics, Delft University of
Technology, The Netherlands*
The picture shows the concentration of a passive scalar in isotropic
turbulence. It has been obtained from DNS. The Schmidt number of the scalar
is 25.

By
means of direct numerical simulations of a passive scalar with an imposed
linear and steady mean gradient in isotropic turbulence, the micro scales
of the scalar field has been studied for a wide range of Schmidt numbers.
The Schmidt number is the ratio of the kinematic viscosity of the fluid
to the diffusivity of the scalar and has an important influence on the
micro structure of the scalar field. The figure shows the instantaneous
scalar field on a two-dimensional plane through the computational domain
for a Schmidt number of 25. In this particular case the smallest length
scale of the scalar field, the so-called Batchelor scale, is about 5 times
smaller than the Kolmogorov length scale. At this high Schmidt number
we observe very thin, elongated structures with cross-sections that indicate
sheet-like structures in the scalar field. Many of the elongated structures
are more or less straight but at some places they are twisted and folded
or even rolled up. The typical spiral scalar structures, as observed in
the figure, appear only when the Schmidt number is larger than one. They
are formed by scalar sheets wrapping around turbulent vortices.

Reference:

G.
Brethouwer (2000) Mixing of passive and reactive scalars in turbulent
flows: A numerical study. Ph.D. dissertation, Delft University of Technology,
The Netherlands.