Context. During their journey to perihelion, comets may appear in the field-of-view of space-borne optical instruments, showing in some cases a nicely developed plasma tail extending from their coma and exhibiting an oscillatory behaviour. Aims. The oscillations of cometary tails may be explained in terms of vortex shedding because of the interaction of the comet with the solar wind streams. Therefore, it is possible to exploit these oscillations in order to infer the value of the Strouhal number $St$, which quantifies the vortex shedding phenomenon, and the physical properties of the local medium. Methods. We used the Heliospheric Imager (HI) data of the Solar TErrestrial Relations Observatory (STEREO) mission to study the oscillations of the tails of the comets 2P/Encke and C/2012 S1 (ISON) during their perihelion in Nov 2013, determining the Strouhal numbers from the estimates of the halo size, the relative speed of the solar wind flow and the period of the oscillations. Results. We found that the estimated Strouhal numbers are very small, and the typical value of $Stsim0.2$ would be extrapolated for size of the halo larger than $sim10^6$ km. Conclusions. Despite the vortex shedding phenomenon has not been unambiguously revealed, the findings suggest that some MHD instability process is responsible for the observed behaviour of cometary tails, which can be exploited for probing the physical conditions of the near-Sun region.
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