Low-dimensional dynamics of a turbulent axisymmetric wake

Abstract

The coherent structures of a turbulent wake generated behind a bluff three-dimensional axisymmetric body are investigated experimentally at a diameter based Reynolds number ∼ 2×10 5 . Proper orthogonal decomposition of base pressure measurements indicates that the most energetic coherent structures retain the structure of the symmetry-breaking laminar instabilities and manifest as unsteady vortex shedding with azimuthal wavenumber m = ±1. In a rotating reference frame, the shedding preserves the reflectional symmetry and is linked with a reflectionally symmetric mean pressure distribution on the base. Due to a slow rotation of symmetry plane of the turbulent wake around the axis of the body, statistical axisymmetry is recovered in the time average. The ratio of the timescales associated with the slow rotation of the symmetry plane and the vortex shedding is of order 100.

High-frequency forcing of a turbulent axisymmetric wake

“…Figure 5 compares the premultiplied spectral density for the unforced and forced flows, the latter at maximum pressure recovery, C µ = 0.04 and St θ = 0.107. The unforced spectral density at this radius is qualitatively similar to the radially averaged result presented in figure 3 of Rigas et al (2014b). Within the pressure recovery regime, the effect of high-frequency forcing on pressure fluctuations is a broadband suppression occuring across all modes, without any obvious mode selection.…”

“…A full description of the unforced wake in the present experiment is provided by Rigas et al (2014b) who show that the coherent structures of the turbulent wake retain the symmetry-breaking properties of the laminar wake. Similarly, oscillatory bifurcations appearing at low Reynolds numbers (the ones at higher Reynolds numbers breaking reflectional symmetry) also appear in the turbulent wake as axisymmetric "bubble pumping" (Berger et al 1990) and as "vortex shedding" (Achenbach 1974;Taneda 1978;Fuchs et al 1979;Berger et al 1990), a large-scale anti-symmetric oscillation.…”

“…Similarly, oscillatory bifurcations appearing at low Reynolds numbers (the ones at higher Reynolds numbers breaking reflectional symmetry) also appear in the turbulent wake as axisymmetric "bubble pumping" (Berger et al 1990) and as "vortex shedding" (Achenbach 1974;Taneda 1978;Fuchs et al 1979;Berger et al 1990), a large-scale anti-symmetric oscillation. This has often been referred to as a "helical" mode when, in fact, as shown by Rigas et al (2014b), periodic shedding is perturbed by a random variation of the azimuthal shedding angle on a very long timescale. They further show that, in a statistical sense, the broken symmetries are restored at much higher Reynolds numbers (Rigas et al 2014a).…”

“…This has often been referred to as a "helical" mode when, in fact, as shown by Rigas et al (2014b), periodic shedding is perturbed by a random variation of the azimuthal shedding angle on a very long timescale. They further show that, in a statistical sense, the broken symmetries are restored at much higher Reynolds numbers (Rigas et al 2014a). Monkewitz (1988) conducted a linear stability analysis for a family of axisymmetric wake (parallel flow) profiles: he showed that this asymmetric mode is absolutely unstable, and in agreement with experimental observation by Taneda (1978), he noted that it is most clearly observed somewhat downstream of the body.…”

Low-frequency behavior of the turbulent axisymmetric near-wake

“…Such anti-symmetric oscillations have been later found to be a major feature of the wake of other more complex configurations such as truncated cylinders with afterbody. 6,7 In a recent investigation, Rigas et al 8 experimentally characterized the unsteady base pressure field of an axisymmetric truncated model. Based on the analysis of the base flow pressure dynamics, the authors identified a second, yet important very-low frequency contribution of the anti-symmetric m = 1 mode, possibly associated with a rotation of the shedding plane and corresponding instantaneous offset of the base pressure centroid.…”