Analysis of kinetic energy spectra in oscillatory pipe flows

Kurzfassung

We present kinetic energy spectra calculated from DNS data of oscillatory pipe flows at several combinations of the Womersley Wo ϵ {13; 26; 52g} and the Reynolds Re ϵ {3000; 12000; 48000g} number. For all Wo, the mean flow oscillation frequency contains most of the energy. Besides that, we find a -5/3 energy decay in the spectra, either close to the wall but not at the pipe centre for the conditionally turbulent case or at the pipe centre and close to the wall for the turbulent case. For the laminar cases, we observe small peaks in the spectra at higher modes, indicating instabilities already known from stability analysis.