  A Lagrangian experimental study of an axisymmetric turbulent water jet is
performed to investigate the highly anisotropic and inhomogeneous flow field.
The measurements were conducted within a Lagrangian exploration module, an
icosahedron apparatus, to facilitate optical access of three cameras. The
stereoscopic particle tracking velocimetry results in three component tracks of
position, velocity and acceleration of the tracer particles within the
vertically-oriented jet with a Taylor-based Reynolds number $\mathcal R_\lambda
\simeq 230$. Analysis is performed at seven locations from 15 diameters up to
45 diameters downstream. Eulerian analysis is first carried out to obtain
critical parameters of the jet and relevant scales, namely the Kolmogorov and
large turnover (integral) scales as well as the energy dissipation rate.
Lagrangian statistical analysis is then performed on velocity components
stationarised following methods inspired by Batchelor (\textit{J. Fluid Mech.},
vol. 3, 1957, pp. 67-80) which aim to extend stationary Lagrangian theory of
turbulent diffusion by Taylor to the case of self-similar flows. The evolution
of typical Lagrangian scaling parameters as a function of the developing jet is
explored and results show validation of the proposed stationarisation. The
universal scaling constant $C_0$ (for the Lagrangian second-order structure
function), as well as Eulerian and Lagrangian integral time scales are
discussed in this context. $C_0$ is found to converge to a constant value (of
the order of $C_0 = 3$) within 30 diameters downstream of the nozzle. Finally,
the existence of finite particle size effects are investigated through
consideration of acceleration dependent quantities.
