The asymptotic form of the stationary separated circumfluence of a body at high reynolds numbers

Abstract

An asymptotic theory of the stationary separated circumfluence of bodies at high Reynolds numbers, Re, is constructed. It is shown that the length and width of the separated zone (SZ) is proportional to Re and that the drag cofficient is proportional to Re −1. A cyclic boundary layer is located around the separated zone with a constant vorticity. In the scale of the body, the flow tends towards a Kirchhoff flow with a velocity on a free line of flow of the order of Re − 1 2 which satisfies the Brillouin-Villat condition. A review of the attempts which have been made to describe the two-dimensional separated circumfluence of a body at high Reynolds numbers is given in /1, 2/. Certain features of the asmyptotic structure of the solution based on qualitative arguments were pointed out in /3, 4/. The corresponding shape of the separated zone was calculated in /5/. However, no complete theory was constructed in these papers. The appearance of the numerical calculations in /6, 7/ stimulated further investigations and a model with a non-zero jump in the Bernoulli constant on the boundary of the separated zone was proposed in /8/. A number of hypotheses concerning the limiting structure of the flow were put forward in /9/. In the solution obtained below the flow in the scale of the body is described as in /1, 2/ but the velocity is of the order of Re − 1 2 . The flow characteristics in this zone are correspondingly renormalized. The flow in the scale of the separated zone corresponds to the assumptions made in /3, 4/. Unlike in /1–4/, the flow in the scale of the body is not directly combined with the flow in the scale of the separated zone. There are several embedded zones and the possibility of uniting these ensures the selfconsistency of the expansion. Moreover, the cyclic boundary layer on the boundary of the separated zone plays an important role.