The elephant mode between two rotating disks

Viaud, Bertrand; Serre, Éric; Chomaz, Jean‐Marc

doi:10.1017/s0022112007009962

Cited by 27 publications

(29 citation statements)

References 36 publications

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“…Although the local absolute instability only exists above R CA , as observed in the numerical study between two rotating disks (i.e. in an open rotating cavity) by Viaud, Serre & Chomaz (2008), the global mode is expected to connect smoothly to the upstream convectively unstable region, giving a nonlinear front straddling R CA . Therefore, as expected, the profile of the travelling disturbance at R = 490 indicates the upstream matching between travelling convectively and absolutely unstable regions.…”

Section: Comparisons Of Velocity-disturbance Spectramentioning

confidence: 81%

Experimental study of rotating-disk boundary-layer flow with surface roughness

2015

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Rotating-disk boundary-layer flow is known to be locally absolutely unstable at R > 507 as shown by Lingwood (J. Fluid Mech., vol. 299, 1995, pp. 17-33) and, for the clean-disk condition, experimental observations show that the onset of transition is highly reproducible at that Reynolds number. However, experiments also show convectively unstable stationary vortices due to cross-flow instability triggered by unavoidable surface roughness of the disk. We show that if the surface is sufficiently rough, laminar-turbulent transition can occur via a convectively unstable route ahead of the onset of absolute instability. In the present work we compare the laminarturbulent transition processes with and without artificial surface roughnesses. The differences are clearly captured in the spectra of velocity time series. With the artificial surface roughness elements, the stationary-disturbance component is dominant in the spectra, whereas both stationary and travelling components are represented in spectra for the clean-disk condition. The wall-normal profile of the disturbance velocity for the travelling mode observed for a clean disk is in excellent agreement with the critical absolute instability eigenfunction from local theory; the wall-normal stationary-disturbance profile, by contrast, is distinct and the experimentally measured profile matches the stationary convective instability eigenfunction. The results from the clean-disk condition are compared with theoretical studies of global behaviours in spatially developing flow and found to be in good qualitative agreement. The details of stationary disturbances are also discussed and it is shown that the radial growth rate is in excellent agreement with linear stability theory. Finally, large stationary structures in the breakdown region are described.

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Section: Comparisons Of Velocity-disturbance Spectramentioning

confidence: 81%

Experimental study of rotating-disk boundary-layer flow with surface roughness

2015

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“…Nevertheless, our simulations now confirm that the rotating-disk boundary layer can produce a linear amplified global mode. It would be interesting to investigate whether the rotating cavity simulated by Viaud, Serre & Chomaz (2008), for example, can be shown to become globally linearly unstable by moving the edge radially outwards, allowing the disturbances to grow, saturate and produce turbulence prior to the end of their domain.…”

Section: Discussionmentioning

confidence: 99%

Global linear instability of the rotating-disk flow investigated through simulations

et al. 2015

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Numerical simulations of the flow developing on the surface of a rotating disk are presented based on the linearized incompressible Navier-Stokes equations. The boundary-layer flow is perturbed by an impulsive disturbance within a linear global framework, and the effect of downstream turbulence is modelled by a damping region further downstream. In addition to the outward-travelling modes, inward-travelling disturbances excited at the radial end of the simulated linear region, r end , by the modelled turbulence are included within the simulations, potentially allowing absolute instability to develop. During early times the flow shows traditional convective behaviour, with the total energy slowly decaying in time. However, after the disturbances have reached r end , the energy evolution reaches a turning point and, if the location of r end is at a Reynolds number larger than approximately R = 594 (radius non-dimensionalized by √ ν/Ω * , where ν is the kinematic viscosity and Ω * is the rotation rate of the disk), there will be global temporal growth. The global frequency and mode shape are clearly imposed by the conditions at r end . Our results suggest that the linearized Ginzburg-Landau model by Healey (J. Fluid Mech., vol. 663, 2010, pp. 148-159) captures the (linear) physics of the developing rotating-disk flow, showing that there is linear global instability provided the Reynolds number of r end is sufficiently larger than the critical Reynolds number for the onset of absolute instability.

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“…A review of the subject can be found in Owen & Rogers (1995). The recent numerical work by Viaud, Serre & Chomaz (2008) (from now on labelled VSC) has demonstrated the similarity of the local velocity profiles in the boundary layers over a single rotating disc and in an annular rotating cavity with a forced throughflow. For the cavity, VSC have shown that the flow is linearly stable but nonlinearly unstable with large initial perturbation giving rise to self-sustained nonlinear global mode with a steep front located at the transition point between convective and absolute instability (the so-called elephant mode).…”

Section: Introductionmentioning

confidence: 95%

Transition to turbulence through steep global-modes cascade in an open rotating cavity

2011

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International audienceThe transition to turbulence in a rotating boundary layer is analysed via direct numerical simulation (DNS) in an annular cavity made of two parallel corotating discs of finite radial extent, with a forced inflow at the hub and free outflow at the rim. In a former numerical investigation (Viaud, Serre & Chomaz J. Fluid Mech., vol. 598, 2008, pp. 451-464) realized in a sectorial cavity of azimuthal extent 2p68, we have established the existence of a primary bifurcation to nonlinear global mode with angular phase velocity and radial envelope coherent with the so-called elephant mode theory. The former study has demonstrated the subcritical nature of this primary bifurcation with a base flow that keeps being linearly stable for all Reynolds numbers studied. The present work investigates the stability of this elephant mode by extending the cavity both in the radial and azimuthal direction. When the Reynolds number based on the forced throughflow is increased above a threshold value for the existence of the nonlinear global mode, a large-amplitude impulsive perturbation gives rise to a self-sustained saturated wave with characteristics identical to the 68-fold global elephant mode obtained in the smaller cavity. This saturated wave is itself globally unstable and a second front appears in the lee of the primary where small-scale instability develops. These secondary instabilities are identical for the 2p/68 and the 2p/4 long sectorial cavities, indicating that transition involves a Floquet mode of zero azimuthal wavenumber. This secondary instability leads to a very disorganized state, defining the transition to turbulence. The observed transition to turbulence linked to the secondary instability of a global mode confirms, for the first time on a real flow, the possibility of a direct transition to turbulence through an elephant mode cascade, a scenario that was up to now only observed on the Ginzburg-Landau model. © 2011 Cambridge University Press

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The elephant mode between two rotating disks

Cited by 27 publications

References 36 publications

Experimental study of rotating-disk boundary-layer flow with surface roughness

Experimental study of rotating-disk boundary-layer flow with surface roughness

Global linear instability of the rotating-disk flow investigated through simulations

Transition to turbulence through steep global-modes cascade in an open rotating cavity

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