On the global nonlinear instability of the rotating-disk flow over a finite domain

Direct numerical simulations based on the incompressible nonlinear Navier–Stokes equations of the flow over the surface of a rotating disk have been conducted. An impulsive disturbance was introduced and its development as it travelled radially outwards and ultimately transitioned to turbulence has been analysed. Of particular interest was whether the nonlinear stability is related to the linear stability properties. Specifically three disk-edge conditions were considered; (i) a sponge region forcing the flow back to laminar flow, (ii) a disk edge, where the disk was assumed to be infinitely thin, and (iii) a physically-realistic disk edge of finite thickness. This work expands on the linear simulations presented by Appelquist et al. (J. Fluid. Mech., vol. 765, 2015, pp. 612-631), where, for case (i), this configuration was shown to be globally linearly unstable when the sponge region effectively models the influence of the turbulence on the flow field. In contrast, case (ii) was mentioned there to be linearly globally stable, and here, where nonlinearity is included, it is shown that both case (ii) and (iii) are nonlinearly globally unstable. The simulations show that the flow can be globally linearly stable if the linear wavepacket has a positive front velocity. However, in the same flow field, a nonlinear global instability can emerge, which is shown to depend on the outer turbulent region generating a linear inward-travelling mode that sustains a transition-front within the domain. The results show that the front position does not approach the critical Reynolds number for the local absolute instability, R = 507. Instead, the front approaches R = 583 and both the temporal frequency and spatial growth rate correspond to a global mode originating at this position.Swedish Research Counci

Global stability of a jet in crossflow

International audienceA linear stability analysis shows that the jet in crossflow is characterized by self-sustained global oscillations for a jet-to-crossflow velocity ratio of 3. A fully three-dimensional unstable steady-state solution and its associated global eigenmodes are computed by direct numerical simulations and iterative eigenvalue routines. The steady flow, obtained by means of selective frequency damping, consists mainly of a (steady) counter-rotating vortex pair (CVP) in the far field and horseshoe-shaped vortices close to the wall. High-frequency unstable global eigenmodes associated with shear-layer instabilities on the CVP and low-frequency modes associated with shedding vortices in the wake of the jet are identified. Furthermore, different spanwise symmetries of the global modes are discussed. This work constitutes the first simulation-based global stability analysis of a fully three-dimensional base flow. © 2009 Cambridge University Press