On the Spectral Decomposition of Skewness of Streamwise Velocity in a Zero Pressure Gradient Turbulent Boundary Layer

The skewness of the streamwise velocity is an important parameter in a zero-pressure gradient turbulent boundary layer (hereafter referred to as TBL). It is related to the energy cascade mechanism and is a measure of interactions between different scales in a turbulent flow. The contribution of different scales (frequencies) to the skewness is analyzed in terms of the bispectrum for near wall locations in a TBL (Reθ = 1770). Their contribution to the skewness is quantified and plotted as a function of interacting frequencies. The individual contributions are then summed up to produce the skewness of the original signals. The main contribution comes from the larger scales having frequencies f ∗ (= fδ/U∞) < 2. The frequencies in the range of ejection-sweep and sweep-ejection events play a crucial role in producing positive skewness for the near wall streamwise velocity. In fact, it is shown that, especially in the near wall region, the range of skewness producing frequencies matches closely with the probability density function of the frequency of the ejection-sweep and sweep-ejection events. Single point hot wire data and the variable interval time averaging (VITA) technique are employed to detect these events. Their role in skewness is quantified using a novel method for TBLs. Five different event sizes (T + w = 30, 60, 90, 120 and 195) are used and their contributions to skewness computed. Despite their short duration (1−30%), these events’ contribution to skewness can exceed 80% in the near wall region - also confirmed from the bispectrum. The contribution to skewness from the active signal for Reθ = 6700, 8300 and 39100 is always positive, but can be negative for Reθ = 1770. It is speculated that the skewness produced by these events in the near wall region ( y + < 15) may follow a near wall scaling. Similar analysis is done for a TBL (Reθ = 1770) with an active-large-scale-structure-actuator (ALSSA) in its outer layer. Both the passive and active ALSSAs reduce the frequency of these events in the near wall region by ≈ 20%. However, these events remain relevant to skewness production for such actuated TBL. Despite being less frequent, their contribution remains the same as in the canonical case till y + = 20. They produce 60% of the near wall positive skewness and 90% of the buffer and log layer negative skewness. In addition, the large-scale organized structures introduced by an active ALSSA influence these events. Although neither an active nor a passive ALSSA affect the randomness of these events, an active ALSSA organizes their occurrence. With an active ALSSA, despite having unchanged total event frequency in the region y + ≤ 30, the events occur more frequently in one half of the actuation cycle but less frequently in the other half. A similar trend is found for y + ≥ 30, although the plasma decreases the total event frequency. This indicates that the outer layer synthetic structures do not act as a trigger for these events but can create conditions favorable/unfavorable to these events. The periodicity of these events are in phase with phase averaged skewness, which further supports the proposition that these events are a key contributor to the near wall skewness for any Reynolds number. It is also discussed how the near wall third moment can be used as a representative of the relative strength of the ejection and the sweep events in wall bounded turbulent flows.