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The Axisymmetric Turbulent Wake

Doktorsavhandling, 2002

This thesis presents a theoretical and experimental study of the turbulent axisymmetric wake.
In the theoretical part, an equilibrium similarity solution of the far wake was derived that was found to admit to two different solutions for this flow. The high Reynolds number solution predicts that the flow grows as the cube root of the distance downstream, whereas the low Reynolds number solution grows as the square root of the downstream distance. None of these solutions had unambiguously been confirmed in earlier work. The analysis also provided necessary criteria for when to expect either solution.
In the experimental part, data was obtained by hot-wire anemometry using arrays of 13 and 15 probes. For the first time, experimental data was proven to behave like the high Reynolds number equilibrium similarity solution predicted. These multi-point probe rakes were also used to measure cross-spectra in cross-sections of the flow from 10 to 150 disk diameters downstream.
The cross-spectra obtained from the measurements were Fourier transformed in the azimuthal direction and used in the kernel for a proper orthogonal decomposition (POD). The POD was shown to order the energetic structure in a highly organized manner, with approximately 56% of the resolved energy in the first mode. The decomposition revealed that the initial wake region from 10 to 30 diameters downstream was dominated by an azimuthal mode-1 type of motion, but also that the importance of this mode vanishes as the flow evolves. Instead the far wake from 30 diameters downstream on was found to be dominated by a mode-2 type of azimuthal motion. This was found to coincide very well with the position at which the similarity solution became valid. This mode-2 dominance continued throughout the whole range of the investigation, with virtually no change in the modal decomposition. The mode-1 was interpreted as a convected structure associated to the vortex shedding in the near wake that was just swept by the probes and dies off downstream, and the mode-2 was postulated to be associated with a global instability manifested as a slow movement of the whole mean velocity field.
The findings of the experiment triggered new theoretical investigations, and a re-visit of the classical linear temporal stability analysis. It was found that the theory permits unstable solutions of mode-0, 1, and 2 kind, contrary to the previous view that only azimuthal mode-1 can be unstable.