Transient energy growth of optimal streaks in parallel round jets

Abstract

OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. This is an author-deposited version published in : http://oatao. We present a linear optimal perturbation analysis of streamwise invariant disturbances evolving in parallel round jets. The potential for transient energy growth of perturbations with azimuthal wavenumber m 1 is analyzed for different values of Reynolds number Re. Two families of steady (frozen) and unsteady (diffusing) base flow velocity profiles have been used, for different aspect ratios ↵ = R/✓, where R is the jet radius and ✓ is the shear layer momentum thickness. Optimal initial conditions correspond to infinitesimal streamwise vortices, which evolve transiently to produce axial velocity streaks, whose spatial structure and intensity depend on base flow and perturbation parameters. Their dynamics can be characterized by a maximum optimal value of the energy gain G opt , reached at an optimal time ⌧ opt after which the perturbations eventually decay. Optimal energy gain and time are shown to be, respectively, proportional to Re 2 and Re, regardless of the frozen or diffusing nature of the base flow. Besides, it is found that the optimal gain scales like

Large-scale streaky structures in turbulent jets

“…The initial disturbance that generates the optimally-growing streaks can be seen in figure 14. The similarities with results from Jiménez- González & Brancher (2017) and with the optimal forcing from the resolvent analysis confirms that the streaks are generated via the lift-up mechanism. Initial perturbations in the shape of streamwise vortices are those that will suffer the largest growth, evolving into streamwise elongated streaks, resembling those found by Cossu et al (2009).…”

“…A transient growth study of Michalke's velocity profiles for jets and slowly diffusing jet flows was performed by Jiménez-González & Brancher (2017). In the present work, we extend the analysis to the turbulent jet, considering as base flow the experimental mean flow at x/D = 2, using an implementation similar to the resolvent analysis described in the previous section.…”

The effect of streaks on the instability of jets

“…The paper is organised as follows. In § 2, linearly optimal roll structures are computed, consistent with Jiménez-González & Brancher (2017), that maximise the transient temporal growth of streaks in an axisymmetric jet base flow. The nonlinear flow development, in the presence of finite-amplitude rolls, is then simulated in time.…”

“…We seek roll structures that lead to the fastest growth of streaks in a parallel and initially axisymmetric jet (Jiménez-González & Brancher 2017). The initial velocity in the streamwise direction is given by the usual profile of Michalke (1971): where represents the non-dimensional momentum shear-layer thickness and the radial coordinate.…”

“…A linear analysis of the growth of streaks in round jets was conducted by Jiménez-González & Brancher (2017), who computed optimal initial conditions for transient energy growth. These were found to take the shape of rolls, leading to the creation of streaks.…”