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