Three-dimensional instabilities in the wake of a circular cylinder

Three-dimensional Floquet stability analysis of the wake of a circular cylinder

“…The numerical studies discussed above (Thompson et al 1994(Thompson et al , 1996Zhang et al 1995) have managed to reproduce the long-and short-wavelength instabilities predicted by our calculations and observed in experiments. Direct numerical simulations will no doubt serve to improve our understanding of the physical mechanisms behind these instabilities.…”

“…In these calculations they observed a period-doubling bifurcation at Re = 300 and proposed that the wake might follow a period-doubling cascade leading to turbulence. Recently, a number of additional computational studies have appeared which examine the threedimensional flow that develops over this same range of Reynolds number (Zhang et al 1995;Mittal & Balachandar 1995;Thompson, Hourigan & Sheridan 1996). However, in none of these numerical studies was an attempt made to determine the onset of the secondary instability precisely because of the computational expense of such calculations using direct simulations.…”

LES of Flow past Circular Cylinder at Re = 3900

“…The flow remains steady and laminar for Reynolds number between 5 and 47 and the wake starts becoming unstable at a critical Reynolds number around 47, leading to the shedding of alternate vortices from the cylinder surface at definite frequencies, well known as the von Karman vortex street. The laminar vortex shedding is observed to be continuing up to a value of Re of about 190, beyond which the two-dimensional flow becomes unstable which leads to the formation and amplification of three-dimensional instabilities in the far wake region (Zhang et al 1995;Williamson 1996;Thompson et al 1996;Mittal and Balachandra 1997;Mittal 2001;Rajani et al 2009). These three dimensional disturbance leads to the simultaneous formation of spanwise and streamwise vortex structure along the spanwise direction and the far wake zone undergoes transition from laminar to turbulent state.…”

Vortex-induced vibration of a neutrally buoyant tethered sphere

“…Within each element, the mesh geometry as well as the velocity and pressure fields, were represented by eighth-order tensor-product polynomials associated with Gauss-Lobatto-Legendre quadrature points. Details of the approach and implementation have been provided by Thompson et al [17]. Higher-order boundary conditions in Karniadakis et al [7] are used for the pressure gradient at no-slip boundaries and at the far-field boundaries.…”