Astron. Astrophys. 342, L1-L4 (1999)

## 3. Hypersonic flow

When a large meteoroid enters the Earth's atmosphere, it has a speed in the range  km/s, hence it moves at hypersonic speed (that is, with Mach number greater than about 5). Since here we are interested in the dynamics of a meteoroid large enough to reach the lower atmosphere, the fluid can be treated as a continuum. Thus, we can use current knowledge about hypersonic aerodynamics in order to understand meteoroid airbursts. For thorough presentations of this theory, the reader is referred to the books of Shapiro (1954), Landau & Lifshitz (1987), and Holman (1989).

It is important to note that for large Mach numbers the linearized equations for the speed potential are not valid, so we cannot use laws holding for supersonic speeds. In hypersonic flow, Mach waves and oblique shock waves are emitted at small angles with the direction of the flow, of the order of the ratio between body thickness and length, and thus tend to follow the surface of the body. Under these conditions, the atmospheric path of a large meteoroid can be seen as a long cylinder, generating pressure waves that can detected as infrasonic sound (Cumming 1989, ReVelle 1976).

The small angle of Mach and oblique shock waves gives also rise to the concept of hypersonic boundary layer near the surface. In front of the meteoroid there is a bow shock, that envelopes the body. The shock is stronger on the symmetry axis, because at this point it is normal to the stream. Then, we find a zone where molecular dissociation is the main process and even closer to the body surface, we find the boundary layer, where viscous effects are dominant. As the air flows toward the rear of the meteoroid, it is reattracted to the axis, just like in a Prandtl-Meyer expansion. As a consequence, there is a rotation of the stream in the sense opposite to that of the motion (rectification); this creates an oblique shock wave, which is called wake shock. Since the pressure rise across the bow shock is huge when compared to the pressure decrease across the Prandtl-Meyer expansion, one can assume, as a reasonable approximation, that there is a vacuum in the rear of the meteoroid. For illustrative images of a hypersonic flow, we refer to Chapter 19, Volume 2, of Shapiro (1954).

The fluid temperature increases in the boundary layer, because the speed must decrease to zero at the meteoroid surface; moreover there are heating effects due to viscous dissipation. There are also regions (like in the Prandtl-Meyer expansion) in which the presence of vacuum or near-vacuum strongly reduces heat transfer, and this contributes to the increasing body temperature. If the generation of heat increases so quickly that the loss of heat may be inadequate to achieve an equilibrium state, we may have a thermal explosion. This explosion generates pressure waves that can be detected on the ground by seismographs. Note that after the Tunguska event no meteorite was recovered, so the argument the meteorites are usually cold immediately after landing does not rule out this kind of thermal explosion in this case.

Current models of the Tunguska event consider, as a reference, the stagnation pressure only (e.g. Hills & Goda 1993), although, for the reasons outlined above, a realistic physical description should account for heat transfer and generation processes as well. A similar conclusion on the need for a coupled radiation-hydrodynamical model has been recently reached by Borovika et al. (1998a, 1998b), following a detailed analysis of theories and observations for the Beneov bolide.

© European Southern Observatory (ESO) 1999

Online publication: December 22, 1998