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Even after several decades of experimental and numerical testing, our present-day knowledge of the axisymmetric turbulent boundary layer (TBL) along long thin circular cylinders still lacks a clear picture of many fundamental characteristics. The main issues causing this reside in the experimental testing complexities and the numerical simplifications. An important characteristic that is crucial for routine scaling is the boundary layer length scales, but the downstream growth of these scales (boundary layer, displacement, and momentum thicknesses) is largely unknown from the leading to trailing edges. Herein, we combine pertinent datasets with many complementary numerical computations (large-eddy simulations) to address this shortfall. We are particularly interested in expressing the length scales in terms of the radius-based and axial-based Reynolds numbers (Rea and Rex). Although the composite dataset gave an averaged shape factor H = 1.09 that is substantially lower than the planar value (H = 1.27), the shape factor distribution along the cylinder axis actually begins at the flat plate value then decays logarithmically to near unity. The integral length scales displayed power-law evolutions with variable exponents until high Rea (Rea > 35,000) where both scales then mimic streamwise consistency. Beneath this threshold, their streamwise growth is much slower than the flat plate (especially at low-Rea). The boundary layer thickness grew according to an empirical expression that is dependent on both Rea and Rex where its streamwise growth can far exceed the planar turbulent flow. These unique characteristics rank the thin cylinder axisymmetric TBL as a separate canonical flow, which was well documented by the previous investigations.

The formation and the downstream transport of the Strouhal vortices in the near wake of a circular cylinder are investigated using the large-eddy simulation (LES) method. The governing equations are formulated in curvilinear coordinates to accommodate a nonorthogonal grid with formal development of a dynamic model to account for the subgrid turbulent scales. Results were produced with and without use of the model. The focus of the investigation is at a subcritical Reynolds number of 5600. Using the dynamic model, the LES results compared best to the published experimental data in terms of both the global and local wake characteristics such as the drag and base pressure coefficients, shedding and detection frequencies, peak vorticity, and the downstream mean velocity-defect and Reynolds stresses. The results further showed streamwise filaments that connect subsequent Strouhal vortices. Qualitatively, the time-averaged Reynolds stresses of the formation region revealed similar symmetric characteristics over the range 525 ≤ Re ≤ 140,000.

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