The growth of a cylinder wake in turbulent flow

Abstract

In the absence of ambient turbulence, the width of the downstream wake of a cylinder grows diffusively either through viscous effects or entrainment at the outer wake edge, depending on the characteristic Reynolds number, and in both the cases it increases as x ^1/2, where x is the distance downstream of the cylinder. We examine the effect of ambient turbulence on the downstream wake of a cylinder, where this turbulence is treated as homogeneous and isotropic. Wake spreading becomes affected when the velocity deficit has decayed sufficiently that it is comparable with the root mean square velocity of the ambient turbulence. A new model is developed to explain how and when the ambient turbulence is sufficiently strong, and the wake is passively advected by the turbulence in the freestream. In this case, when the wake width is smaller than the integral length scale, the wake grows linearly with distance downstream (i.e. proportional to x), whereas when the wake width is larger than the integral length scale, it grows diffusively (i.e. proportional to x ^1/2). A laboratory study of the decay of the velocity deficit behind a cylinder confirms the salient aspects of the new model predictions.

Keywords:

• isotropic turbulence
• external aerodynamic turbulence
• environmental turbulent flows
• turbulent mixing

Acknowledgements

IE is supported by a Senior Leverhulme Fellowship. PBJ acknowledges support from PhD supervisors Kevin Drake and Adam Wojcik, and an EPSRC doctoral training award.