Predicting the upper bound of two-dimensional flow regimes of symmetric objects through two-dimensional computations

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The onset of secondary wake instability is generally predicted via experiments, linear stability analysis, and three-dimensional direct numerical simulations. The current work stems from an open question that is very intriguing and fundamental: Can the upper bound of a two-dimensional flow be predicted purely on the basis of two-dimensional computational results? It is found that spatial distribution of a field variable, i.e., streamwise velocity in the vortex formation region, aids in determining the upper limit of a two-dimensional flow regime of a symmetric object. The vortex formation length attains its least value at the second critical Reynolds number. In addition, streamwise extents of mean wake and vortex formation region along wake axis become the same. Under this circumstance, the streamwise velocity at the terminal point of vortex formation region is such that its mean value vanishes while intensity of fluctuations or corresponding Reynolds stress becomes the maximum. The predicted values of critical Reynolds numbers for circular, square, and diamond cross sections exhibit excellent agreement with the results available in the literature.