We investigate the temporal evolution of the geometrical distribution of a passive
scalar injected continuously into the far field of a turbulent water jet at a scale
d smaller than the local integral scale of the turbulence. The concentration field
is studied quantitatively by a laser-induced- fluorescence technique on a plane cut
containing the jet axis. Global features such as the scalar dispersion from the source,
as well as the fine structure of the scalar field, are analysed. In particular, we define
the volume occupied by the regions whose concentration is larger than a given
concentration threshold (support of the scalar field) and the surface in which this
volume is enclosed (boundary of the support). The volume and surface extents,
and their respective fractal dimensions are measured as a function of time t, and
the concentration threshold is normalized by the initial concentration
Cs/C0 for
different injection sizes d. All of these quantities
display a clear dependence on t, d
and Cs, and their evolutions rescale with the variable
ξ = (ut/d)(Cs/C0),
the fractal dimension being, in addition, scale dependent. The surface-to-volume ratio and the
fractal dimension of both the volume and the surface tend towards unity at large ξ,
reflecting the sheet-like structure of the scalar at small scales. These findings suggest
an original picture of the kinetics of turbulent mixing.