Oscillation, bifurcation and growth of modal instability in bluff-body wakes: a new understanding

Past experimental findings suggest during nucleation of a vortex over a bluff body the near-wake instability initiates a wavy trail even at \textit{Re}=30, and wavelength of this oscillation decreases with increasing \textit{Re} while amplitude increases. We discovered that, such a wavy oscillation has a strong spanwise counterpart which gets fast augmented with \textit{Re}, and enforces growth of a new class of bifurcations along the K\'{a}rm\'{a}n vortex cores. Notably, the detected pressure oscillation along a vortex core reaches a threshold value at the onset of shedding process and initiates growth of a Hopf bifurcation in spanwise coordinate. With \textit{Re} the pressure oscillation gains momentum; enforcing occurrence of multiple local pressure maxima and bifurcations along a vortex coreline. Our detailed simulations with square cylinders of different aspect ratios and \textit{Re} up to 240 unfold development of two physically distinct stages of spanwise wake undulations and bifurcations. While growth of uniform length-scaled bifurcations and their spatio-temporal swapping initiate formation of ``Mode A'' instability structures, a transition scenario for the ``Mode B'' is prompted with the eruption of variable length-scaled spanwise bifurcations.