High-Reynolds-number wake of a slender body

The high-Reynolds-number axisymmetric wake of a slender body with a turbulent boundary layer is investigated using a hybrid simulation. The wake generator is a 6 : 1 prolate spheroid and the Reynolds number based on the diameter D is Re = 10(5). The transition of the wake to a state of complete self-similarity is investigated by looking for the first time into the far field of a slender-body wake. Unlike bluff-body wakes, here the flow is not dominated by vortex shedding in the near wake. Instead, the recirculation region is very small, the near wake is quasi-parallel and is characterised by the presence of broadband turbulence. Until x/D approximate to 20, the wake decay of a slender body with turbulent boundary layer is very similar to the classic high-Re behaviour, U-d similar to x(-2/3). Extrapolation of this observation to larger x/D has led to the belief that these wakes decay following the asymptotic -2/3 decay law. Our results show, however, that this is not the case and the wake transitions to a faster decay rate once complete self-similarity is achieved. In this later region (20 < x/D < 80), mean and turbulence profiles are self-similar. Furthermore, despite the high global and local Reynolds numbers, the classic hypotheses that lead to the well-known decay exponents are not fulfilled. Instead, turbulent dissipation follows a non-equilibrium scaling and a new decay rate U-d similar to x(-6/5) is observed. The transition from U-d similar to x(-2/3) to U-d similar to x(-6/5) is preceded by the dominance of the azimuthal vertical bar m vertical bar = 1 mode and the emergence of a large-scale helical structure.

Automated summary

The characteristics of the wake of a slender body with a turbulent boundary layer at high Reynolds numbers are studied, showing a faster decay rate once complete self-similarity is achieved, which differs from the classic high Reynolds number decay law.