Area rule for the wake behind a three-dimensional body

In three-dimensional flows, the local characteristics of the medium in the wake behind a supersonic body at Reynolds numbers Re 5·10⁴ depend in a complicated manner on the coordinates. However, in a number of cases it is important to know only the parameters of the medium averaged over the transverse section of the wake. For example, for the diagnostics of the plasma of the wake behind a body by means of microwave resonators the electron density averaged over the section is used 1]. The chemiluminescent radia tion of the wake is also obtained in an averaged form 2]. It is therefore worthwhile obtaining the average characteristics of the medium without detailed study of the local parameters. In the present paper, a rule is established that makes it possible to use the results obtained for the far viscous wake behind an axisymmetric body in the case of the wake behind a three-dimensional body that is nearly axisymmetric, the flow conditions being similar. The three-dimensional wake is considered to the distances until it degenerates into an axisymmetric wake.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 148–150, May–June, 1980.We thank G. Yu. Stepanov and É. Z. Apshtein for helpful advice in a discussion of the results.