The velocity signal of a wall-bounded turbulent flow at a given point can be divided into large scales and small scales by filtering. It is well known in literature that when the large- scale signal is positive, the small-scale signal has an increased amplitude or activity, and when the large-scale signal is negative, the amplitude of the small-scale is reduced. This phenomenon, now generally called amplitude modulation, has been conjectured to be caused by the fluctuation of the large-scale velocity gradient and, subsequently, the production term in the energy budget equation. However, recent findings have shown the need to verify the currently accepted conjectures on what causes small-scale amplitude modulation. This present work therefore aims not only to present an alternative method to quantify amplitude modulation but also to verify the conjectures put forward about what causes small-scale amplitude modulation in turbulent wall-bounded flows. To achieve the aims of the work, a program was developed to analyse the time-varying conditionally averaged velocity field around the zero-crossings of the large-scale fluctuation. Here, zero-crossings refer to positions in the time series where the large-scale fluctuation is zero, and they mark the switch between a period of increased and decreased small-scale activity. The method of calculating conditional statistics at zero-crossings was originally developed by Baars et al. (2017), and the method is modified here by using kinetic energy instead of a mathematically formulated envelope as an approximant for the amplitude of the small scales. A script was also written which calculates the probability density function of the intervals between zero-crossings. The methods developed were then applied to data obtained from the direct numerical simulation of a turbulent Poiseuille flow at a frictional Reynolds number of 1000. Comparisons are then made between the time derivative of the conditionally averaged small-scale kinetic energy and two different conditionally averaged production terms. The results show a very large disparity in the shape and magnitude of the time derivative of the kinetic energy and the production terms. These findings therefore suggest that current conjectures may be wrong, since if the conjectures are true it is expected that the time derivative of the kinetic energy and the production terms should have comparable shape and magnitude.     «

The velocity signal of a wall-bounded turbulent flow at a given point can be divided into large scales and small scales by filtering. It is well known in literature that when the large- scale signal is positive, the small-scale signal has an increased amplitude or activity, and when the large-scale signal is negative, the amplitude of the small-scale is reduced. This phenomenon, now generally called amplitude modulation, has been conjectured to be caused by the fluctuation of the large-scale vel...     »