We analyse the azimuthal velocity fluctuation in the boundary layer driven by a rotating slender cone with a half-cone apex angle of 30 ∘. The flow is dominated by a centrifugal instability, which develops into randomly occurring spiralling vortices travelling on the cone surface. Such non-stationary vortices are observed as an irregular wave packet-like fluctuation signal by a hot wire fixed in the lab frame of reference and the spectral map at different radial positions forms a smooth ridge, which is in contrast to the periodic time signal due to stationary crossflow vortices on broad cones, which gives rise to sharp spectral ridges. The present analysis decomposes the wave packet-like fluctuation using a short-time Fourier transform (STFT), revealing that the smooth spectral peak at a given radial position consists of waves with different frequencies. The most probable fundamental frequency follows the most unstable frequency according to linear stability theory. Also, we evaluate the amplitude of the harmonics of the most energetic mode around transition; quadratic nonlinear growth is observed until the amplitude of the fundamental mode saturates at transition. This behaviour is similar to that on broad cones although the primary instability and vortex structures are different.
