Stability and sensitivity of a cross-flow-dominated Falkner–Skan–Cooke boundary layer with discrete surface roughness

Abstract

Stability and sensitivity of a crossflow-dominated Falkner-Skan-Cooke boundary layer with discrete surface roughness. Journal of Fluid MechanicsAccess to the published version may require subscription. N.B. When citing this work, cite the original published paper. With the motivation of determining the critical roughness size, a global stability and sensitivity analysis of a three-dimensional Falkner-Skan-Cooke (FSC) boundary layer with a cylindrical surface roughness is performed. The roughness size is chosen such that breakdown to turbulence is initiated by a global version of traditional secondary instabilities of the crossflow (CF) vortices, instead of an immediate flow tripping at the roughness. The resulting global eigenvalue spectra of the systems are found to be very sensitive to numerical parameters and domain size. This sensitivity to numerical parameters is quantified using the "-pseudospectrum, and the dependency on the domain is analysed through an impulse response and an energy budget. It is shown that the growth rates increase with domain size, which originates from the inclusion of stronger CF vortices in the baseflow. This is reflected in a change in the rate of advective energy transport by the baseflow. It is concluded that the onset of global instability in a FSC boundary layer as the roughness height is increased does not correspond to an immediate flow tripping behind the roughness, but occurs for lower roughness heights if su ciently long domains are considered. However, the great sensitivity results in an inability to accurately pinpoint the exact parameter values for the bifurcation, and the large spatial growth of the disturbances in the long domains eventually becomes larger than what can be resolved using finite precision arithmetics.

On the linear global stability analysis of rigid-body motion fluid–structure-interaction problems

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“…The system is solved by estimating the eigenvalues of the time-stepping operator. The method was first used by Eriksson & Rizzi (1985) and has been used in several previous works by Barkley, Gomes & Henderson (2002), Bagheri et al (2009b) and Brynjell-Rahkola et al (2017) etc. The eigenvalue estimation is done using the implicitly restarted Arnoldi method (Sorensen 1992) implemented in the open source software package ARPACK (Lehoucq, Sorensen & Yang 1998).…”

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Transition to turbulence in the rotating-disk boundary-layer flow with stationary vortices

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