Analysis of the Energy Budget of the Largest Scales in Turbulent Pipe Flow

Abstract

Very-large-scale motions (VLSM) in turbulent pipe flow become increasingly energetic with higher Reynolds numbers and contribute significantly to the turbulent kinetic energy budget. Although several investigations regarding energy mechanisms in wall-bounded turbulence were carried out in the past, the origin of the energy at the largest wavelengths has not been studied rigorously, yet. Consequently, we analysed the budget equation of the filtered streamwise velocity field with very large filter lengths to identify energy sources and sinks related to VLSM. While there was no inverse energy cascade found towards VLSM on average, conditional sampling revealed an inverse energy cascade related to low-speed structures, whereas high-speed structures were subject to a forward cascade. This behaviour is at odds with the mechanism relevant for the near-wall small-scale motions, where the inverse cascade correlates with high-speed fluid.