Classification of forcing conditions in pulsatile turbulent pipe flow using Reynolds shear stress co-spectra

The turbulence dynamics of pulsatile pipe flow are investigated using data obtained from direct numerical simulations at a mean friction Reynolds number of 180, 270 and 360. The forcing conditions are achieved by applying a time-harmonic axial pressure gradient. This study directs attention towards the frequency response of single- and two-point turbulence statistics to systematic variations in the forcing frequency. We propose a classification of the applied forcing conditions based on the Reynolds shear stress frequency co-spectra and the applied forcing frequency. We perform simulations based on this classification to extend the physical understanding of the phase dependence of single- and two-point turbulence statistics under high, very-high and ultra-high forcing frequencies, focussed around the frequency response of turbulence dynamics in time (frequency) and space (wavenumber) domains. Results also reveal a decoupling behaviour when the frequency of the forcing is higher than the highest frequency (smallest time-scale) of the energy containing motions in the Reynolds shear stress co-spectra.