Growth of unsteady Hopf bifurcation modes and their swapping in a transitional coupled wake

• Published in: Physics of fluids (1994) 2008-10, Vol.20 (10)
• Main Author: Sau, Amalendu
• Format: Article
• Language: English
• Subjects: Exact sciences and technology; Fluid dynamics; Fundamental areas of phenomenology (including applications); Hydrodynamic stability; Nonlinearity (including bifurcation theory); Physics; Rotational flow and vorticity; Separated flows; Turbulent flows, convection, and heat transfer; Wakes
• ISSN: 1070-6631; 1089-7666
• DOI: 10.1063/1.2989147

The present work is devoted to unfolding the flow physics and the growth of different higher order Hopf bifurcation modes in the supercritical transitional coupled wake of two square cylinders in side-by-side arrangement. Depending on gap to diameter ratio g ∗ between the cylinders, the coupled growths of the wakes (and therefore the corresponding Benard von Karman streets) through of each of the antiphase, in-phase, and biased patterns were found to be essentially governed by several dominant unsteady modes of Hopf bifurcations, occurring along the spanwise extended corelines of the shedded vortices. During the transient process of synchronized/biased wake evolution there noted significant spanwise pressure, velocity, and vorticity oscillations along the vortex corelines, which considerably amplified, as the flows reached transitional state. Such an unsteady spanwise oscillation of the wake facilitated the growth of higher order Hopf bifurcation modes and their frequent/random swapping. Instantaneous wakes (synchronized/biased) thereby evolved either through a particular mode of Hopf bifurcation or there remained simultaneous presence of multiple bifurcation modes. The growth of a number of instantaneous local pressure maxima over the spanwise extended corelines of the shedded vortices and the gradual decrease in pressure along two sides of the maximum pressure regions, together with the developed azimuthal pressure fluctuation around the vortex corelines, are found to be responsible for initiating the bifurcations. Notably, the present findings, while remaining closely consistent with recent experimental measurements (performed with a pair of circular cylinders) and the existing theoretical predictions (made on the basis of Landau/Ginzburg–Landau equations), clearly demonstrate the existence of five different transient modes of Hopf bifurcating solutions of the Navier–Stokes equations in the wake of two side-by-side square cylinders. Flow transition in the wake is noted to occur essentially through random swapping of these unsteady Hopf bifurcation modes with arbitrarily varying length scales.