ENERGY DISTRIBUTION IN MODES IN THE WAKE OF A FINITE-LENGTH CYLINDER BEFORE AND AFTER TRANSITION

The flow in the wake of a finite-length cylinder has been studied experimentally both before and after the transition to turbulence. This instability occurs at Reynolds numbers around 180–190. One end of the cylinder was fixed to the bottom of the test-section of a wind tunnel, whilst the other terminated in the open flow (free end). For these boundary conditions four main frequency modes within the wake can be identified. These are a centre-cell mode at the Strouhal frequency, end-cell modes with a frequency below the Strouhal frequency, a mode exhibiting the difference frequency between the centre-cell and end-cell modes, and a low-frequency mode (appearing only after transition to turbulence). In this work the energy content of these four modes has been determined throughout the wake, both before and after transition to turbulence. For three of the modes, the energy content is the same before and after transition, whereas the low-frequency mode exhibits energy two to four orders of magnitude greater after transition than before. Hence it is clear that the additional turbulence energy appearing in the wake after transition is located predominantly in this low-frequency mode. The appearance of this low-frequency mode is characterized by the simultaneous appearance of a peak in the power spectra of the velocity fluctuations centred about zero frequency (but with finite width). Consequently, the appearance of this zero frequency peak can be taken as the signature of the onset of turbulence. By considering the downstream growth rates of this low-frequency mode, evidence is presented which suggests that transition to turbulence may occur as a result of wake transition in the downstream central plane of the cylinder.