On a small structure in velocity field within a contact region

Abstract

In a contact region (contact surface in Euler terms) connecting the two uniform regions in a flow field such as caused by the sudden break of a membrane in a shock-tube, there exists a small structure in velocity field, which has been reported earlier by the calculation based on the Boltzmann equation of the BGK type. Probably, the accepted view would be that the velocity within this region is uniform. Here this velocity structure is investigated thoroughly based on not only the Boltzmann equation but also the Navier–Stokes equations. Actually the velocity field has a hump or a pit, the width of which is found to be the same as the thickness of the region. The magnitude of the hump or the pit decreases with time, inversely proportional to the square root of time. At the so-called tailoring condition at which the contact region has so far been thought not to manifest itself, actually it does exist; the velocity structure does not appear of course but the temperature and, hence, the density still have structures, although they are small in magnitude.