Uncertainty evaluation due to the difference in definitions of the acceleration parameter to examine the influence of mean flow acceleration on the experimental turbulent flows

This study presents the uncertainty arising from the difference among three definitions of acceleration parameter. Previous studies have used two definitions of the acceleration parameter, denoted as the first and second definitions in this study. In the present study, an intermediate definition is introduced in addition to the two definitions. Then, mean velocity profile functions represented by each of these definitions are derived. If the magnitude of the acceleration parameter is sufficiently small, the mean velocity profiles represented by the definitions can result in the same with each other and are derived to be a linear function. The difference magnitude in the mean velocity profile among these definitions is of the order of the square of the acceleration parameter magnitude. The difference in the values obtained experimentally for the acceleration parameter can be larger than the order of the typical magnitude in experimental uncertainty. The present study derives a simple formula to estimate a value of the second definition from that of the first definition. The deviation uncertainty of this derived formula is found to be smaller than the magnitude of this typical experimental uncertainty.