Three-dimensional dynamics and transition to turbulence in the wake of bluff objects

Abstract

The wakes of bluff objects and in particular of circular cylinders are known to undergo a ‘fast’ transition, from a laminar two-dimensional state at Reynolds number 200 to a turbulent state at Reynolds number 400. The process has been documented in several experimental investigations, but the underlying physical mechanisms have remained largely unknown so far. In this paper, the transition process is investigated numerically, through direct simulation of the Navier—Stokes equations at representative Reynolds numbers, up to 500. A high-order time-accurate, mixed spectral/spectral element technique is used. It is shown that the wake first becomes three-dimensional, as a result of a secondary instability of the two-dimensional vortex street. This secondary instability appears at a Reynolds number close to 200. For slightly supercritical Reynolds numbers, a harmonic state develops, in which the flow oscillates at its fundamental frequency (Strouhal number) around a spanwise modulated time-average flow. In the near wake the modulation wavelength of the time-average flow is half of the spanwise wavelength of the perturbation flow, consistently with linear instability theory. The vortex filaments have a spanwise wavy shape in the near wake, and form rib-like structures further downstream. At higher Reynolds numbers the three-dimensional flow oscillation undergoes a period-doubling bifurcation, in which the flow alternates between two different states. Phase-space analysis of the flow shows that the basic limit cycle has branched into two connected limit cycles. In physical space the period doubling appears as the shedding of two distinct types of vortex filaments.Further increases of the Reynolds number result in a cascade of period-doubling bifurcations, which create a chaotic state in the flow at a Reynolds number of about 500. The flow is characterized by broadband power spectra, and the appearance of intermittent phenomena. It is concluded that the wake undergoes transition to turbulence following the period-doubling route.

Vortex dislocation in wake-type flow caused by local spanwise nonuniformity

“…The numerical code used in the present work has been verified first. It shows that evolution of the wake-type flow without the local spanwise non-uniformity results in a normal Kármán vortex street with a Strouhal number of 0.189, which is well compared with both numerical simulation of wake-type flow evolution (St=0.195, see Karniadakis & Triantafyllou, 1992) and DNS results of flow around cylinder (St=0.179, see Triantafyllou & Karniadakis, 1990). …”

Evolution of mushroom-type structures behind a heated cylinder

“…For the spatial discretization, a high-order Spectral Element Method ͑SEM͒ is used ͑Karniadakis and Triantafyllou, 24 Dauchy et al 25 ͒. Within an element, the equations are discretized using high-order approximation functions.…”

Vortex dislocations in wake-type flow induced by spanwise disturbances

“…The two-dimensional wake velocity profile is taken from the time-averaged streamwise velocity profile at the position in the near wake close to the cylinder, obtained by referring to previous DNS results 13,14 and the experimental measurements 15 of a cylinder wake flow. As discussed before, the profile flow has been shown to be absolutely unstable, resulting in a Kármán vortex street.…”