The dynamics of towed objects in a ﬂuid environment is of interest for many practical situations. We investigate the stability of the trajectory of an object towed at the tip of the cable. We propose an experimental investigation of the Lagrangian dynamics of a spherical object towed at the tip of a cable. The towing conﬁguration is artiﬁcially obtained by considering a steady cable (with one ﬁx end and a free one to which a sphere is attached) in a low turbulence wind-tunnel (see ﬁgure 1).

This reproduces the situation of an object towed at constant speed. We consider three diﬀerent conﬁgurations of cable tip : (i) the cable free end by itself ; (ii) a light millimetric towed sphere made of expanded polystyrene and (iii) a denser millimetric towed sphere made of lead. For each situation a systematic study of the inﬂuence of Reynolds number is done by varying the mean velocity of the surrounding ﬂow. We recorded the lagrangian trajectories of the object towed at the tip of the cable and we analyzed statistics of position, velocity and acceleration for the three studied conﬁgurations.

From the mean height data we deduced the drag coeﬃcients of the aerodynamic forces acting on the cable, by ﬁtting our measurements with the predictions of a simple model for the cable shape and position 1 . The aerodynamical coeﬃcients deduced from the measurements are in agreement with typical values previously measured for drag coeﬃcients of cables and cylinders 2 . We then investigate the dynamical ﬂuctuations and the stability of the towed object. For the free end and light sphere case, we ﬁnd that the tip of the cable is stable (ﬂuctuations of position, velocity and acceleration remain marginal) only below a critical towing velocity.

Above this threshold, we observe a monotonic increase of ﬂuctuation levels with increasing towing velocity. The spectral analysis of the velocity, suggests that this instability is related to the propagation of waves downstream the cable when it aligns with the mean stream. No such threshold is observed for the heavy particle, for which the velocity and acceleration ﬂuctuations remain two order of magnitudes below that of the light particle and the free end. The dynamics is limited to low frequency oscillations, which may be associated to a pendular motion of the heavy particle.

*by M. Obligado, M. Bourgoin*