  The temporal statistics of incompressible fluid velocity and passive scalar
fields in developed turbulent conditions is investigated by means of direct
numerical simulations along the trajectories of self-propelled point-like
probes drifting in a flow. Such probes are characterised by a propulsion
velocity which is fixed in intensity and direction; however, like vessels in a
flow they are continuously deviated by their intended course as the result of
local sweeping of the fluid flow. The recorded time-series by these moving
probes represent the simplest realisation of transect measurements in a fluid
flow environment. We investigate the non trivial combination of Lagrangian and
Eulerian statistical properties displayed by the transect time-series. We show
that, as a result of the homogeneity and isotropy of the flow, the single-point
acceleration statistics of the probes follows a predictable trend at varying
the propulsion speed, a feature that is also present in the scalar
time-derivative fluctuations. Further, by focusing on two-time statistics we
characterize how the Lagrangian-to-Eulerian transition occurs at increasing the
propulsion velocity. The analysis of intermittency of temporal increments
highlights in a striking way the opposite trends displayed by the fluid
velocity and passive scalars.
