Stability of three-dimensional rotating boundary layers

Abstract

This thesis investigates the effects of surface roughness on disturbances in the rotating disk boundary-layer. The stability of stationary and traveling waves using the YHP and MW models in the flow over a rotating disc was examined through linear stability analysis.The YHP modle imposes a specific roughness pattern (concentric grooves) as a surface shape function depending on the radial position but MW model allows some slippage, simulating the effect of distributed roughness. The roughness of the surface was simulated with no-slip (YHP) and slip boundary conditions which characterise concentric grooves, radial grooves and isotropic roughness. The impact on stationary crossflow and Coriolis instabilities was examined by applying slip conditions to undisturbed flow and linear disturbance based on the research of Cooper et al. (2015). This study examined how stationary and traveling disturbances impact stability. Traveling disturbances can induce instability at lower Reynolds numbers, potentially resulting in turbulence, a phenomenon first analyzed by Balakumar and Malik (1990) for flat disks. This study has built upon earlier linear stability studies on YHP by Garrett et al. (2016) for stationary disturbances. This study extends this analysis to include traveling wave instabilities. The Navier-Stokes equations are used to obtain the steady mean flow system, and linear stability equations are then formulated to obtain neutral stability curves. The results of the stability analysis are validated using linear growth rates and numerical analysis. Studies show that streamwise-aligned radial grooves significantly destabilize type II (viscous) instabilities, while concentric grooves and isotropic surface roughness stabilize boundary-layer flow against type I (inviscid or crossflow) instabilities. The asymptotic analysis of Hall(1986) has been extended to the YHP rough-wall model for the upper branch instability modes. By solving the neutral stability equations and determining the critical settings for linear instability, neutral stability curves were generated for a range of radial and azimuthal slip length values. The boundary layer profile has been investigated asymptotically in particular for the non-stationary perturbations. It has been found that, at very large Reynolds numbers, the upper branch for all waves tends asymptotically to the same wave number calculated by the linear stability method. The MW model applies slip to both base flow and perturbations, built upon the earlier work of Cooper et al. (2015) and Thomas et al. (2023). For the numerical analysis, we found that parameters that result in an increase or decrease in the critical Reynolds number led to a stabilization or destabilization of the flow, respectively. Finally, we compared the asymptotic and numerical stability results for both type I (inviscid or cross-flow) instabilities and type II (viscous) instabilities, followed by the critical Reynolds number comparisons, which were found to be consistent, in general, with results in the literature.