Boundary-layer transition over a rotating broad cone

Abstract

The route to turbulence in the boundary layer on a rotating broad cone is investigated using hot-wire anemometry measuring the azimuthal velocity. The stationary fundamental mode is triggered by 24 deterministic small roughness elements distributed evenly at a specific distance from the cone apex. The stationary vortices, having a wave number of 24, correspond to the fundamental mode and these are initially the dominant disturbanceenergy carrying structures. This mode is found to saturate and is followed by rapid growth of the nonstationary primary mode as well as the stationary and nonstationary first harmonics, leading to transition to turbulence. The amplitudes of these are plotted in a way to highlight the continued growth after saturation of the fundamental stationary mode.

Instability and transition in the boundary layer driven by a rotating slender cone

“…2019 c ); the initial peak is smoother and the change in transition is more gradual, whereas spiky initial peaks and an abrupt transition are observed for the broad cone (Kato et al. 2019 a , b ). Figure 5 shows that the disturbance begins to grow around with .…”

“…), giving rise to counter-rotating vortices. Recent works provide further quantitative data for broad cones (Imayama, Alfredsson & Lingwood 2012, 2013, 2014; Kato, Alfredsson & Lingwood 2019 a ; Kato et al. 2019 b ).…”

“…ψ = 0 • ), giving rise to counter-rotating vortices. Recent works provide further quantitative data for broad cones (Imayama, Alfredsson & Lingwood 2012, 2013Kato, Alfredsson & Lingwood 2019a;Kato et al 2019b). However, such detailed experimental data on slender cones have up to now not been available.…”

Boundary layer instability over a rotating slender cone under non-axial inflow

“…2010). Recent experiments by Kato, Alfredsson & Lingwood (2019 a ) and Kato et al. (2019 b ) also show the existence of co-rotating spiral vortices (relating to the cross-flow instability) over a broad cone () rotating in still fluid.…”

“…This pressure gradient results in an inflectional profile of the mean streamwise velocity that leads to cross-flow instability (Kohama 1984b;Garrett et al 2010). Recent experiments by Kato, Alfredsson & Lingwood (2019a) and Kato et al (2019b) also show the existence of co-rotating spiral vortices (relating to the cross-flow instability) over a broad cone (ψ = 60 • ) rotating in still fluid. Overall, past research provides detailed insights into the formation, growth and breakdown of spiral vortices over a rotating cone, but all of these detailed studies are limited to axisymmetric inflow conditions.…”