Downflows on the solar surface are suspected to play a major role in the dynamics of the convection zone. We investigate the existence of the long-lasting downflows whose effects influence the interior of the Sun and the outer layers. We study the sets of Dopplergrams and magnetograms observed with SDO and Hinode spacecrafts and a MHD simulation. All of the aligned sequences, which were corrected from the satellite motions and tracked with the differential rotation, were used to detect the long-lasting downflows in the quiet-Sun at the disc centre. To learn about the structure of the flows below the solar surface, the time-distance local helioseismology was used. The inspection of the 3D data cube (x, y, t) of the 24-hour Doppler sequence allowed us to detect 13 persistent downflows. Their lifetimes lie in the range between 3.5 and 20 hours with sizes between 2 and 3 and speeds between -0.25 and -0.72 km/s. These persistent downflows are always filled with the magnetic field with an amplitude of up to 600 G. The helioseismic inversion allows us to describe the persistent downflows and compare them to the other (non-persistent) downflows in the field of view. The persistent downflows seem to penetrate much deeper and, in the case of a well-formed vortex, the vorticity keeps its integrity to the depth of about 5 Mm. In the MHD simulation, only sub-arcsecond downflows are detected with no evidence of a vortex comparable in size to observations at the surface of the Sun. The long temporal sequences from the space-borne allow us to show the existence of long-persistent downflows together with the magnetic field. They penetrate inside the Sun but are also connected with the anchoring of coronal loops in the photosphere, indicating a link between downflows and the coronal activity. A link suggests that EUV cyclones over the quiet Sun could be an effective way to heat the corona.
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