Turbulent far wake of a body of arbitrary shape

Laboratoire d'Hydrodynamique, CNRS, École polytechnique, Institut Polytechnique de Paris - 91120 Palaiseau, France

^(a) E-mail: martine.le-berre@u-psud.fr (corresponding author)

Received: 4 May 2023
Accepted: 6 September 2023

Abstract

Using a recently proposed closure for the Boussinesq-Reynolds turbulent stress we re-derive Prandtl's result for the turbulent wake width behind blunt bodies. We show that it is valid for a body of arbitrary shape, but only for wakes due to a drag oriented parallel to the incoming flow. If the geometry of the body resisting the flow lacks symmetries forbidding it, the force on the body has also a component orthogonal to the incoming velocity, called lift, that allows, for instance, planes to fly. Using our closure theory we show that this lift generates a wake wider than the drag, with a width growing like the one-half power of the distance to the body, instead of the one-third in the case of drag only. This has important consequences as it leads to a change of structure of the wake that remains turbulent all the way to infinity.