Objectivity or material frame indifference is the indifference of material behavior to a Euclidean transformation (a general change of observer). This paper considers the objectivity of turbulent fields under a time-periodic change of the observer. At a given phase, the fluctuating velocity and Reynolds stress tensor fields are shown to be objective. This is further illustrated by presenting one-point statistics of two canonical flows: homogeneous isotropic turbulence and turbulent channel flow. The results also highlight that statistical symmetries such as homogeneity and stationarity found in the objective fields are carried over after a change of observer. The paper concludes with some final thoughts on objectivity and its usefulness for the advancement of turbulent theory.
Arosemena et al. (Sat,) studied this question.