A direct numerical simulation display of the rotational frame preference of turbulence

Abstract

An elementary observation of a laminar cylindrical Poiseuille–Couette flow profile reveals no distinction in the parabolic streamwise profile, from one without a cross-stream flow, in whatever reference frame the observation is made. This is because the laminar flow is in solid-body rotation and there is no fluid intrinsic rotation. Hence, the main streamwise Poiseuille flow is unaffected. On the contrary, in turbulent (unsteady) cylindrical axial-Couette flow, the rotational reference frame must be considered, and any observation from an external inertial reference frame can give outright incorrect results. However, even in axial turbulent pipe flow with axial rotation, the resultant effect of azimuthal velocity on the flow profile is still usually too low. Hence, the importance of consideration in the rotational frame is often overlooked. A common misconception in the study of fluid mechanics is that the position of the observer does not matter. In this direct numerical simulation study, firstly turbulent flow in a pipe with axial rotation is established. Then turbulent flow in the concentric pipe, with inner wall rotation, is used to show how tilted wall streak direction is oriented by the rotational reference frame and not the inertial reference frame.