Natural Transition in Plane Poiseuille Flow

Abstract

We present numerical and theoretical results on the natural transition in a plane Poiseuille flow. The natural transition is often studied in boundary layers, but the analysis in a parallel flow allows the use of the Reynolds number as a control parameter. The results indicated that the classical scenarios described in the literature play a role in natural transition and can lead to turbulent spots. In natural transition the wave systems are modulated in streamwise and spanwise directions and cause premature nonlinearity [1]. Spikes and turbulent spots are often present in natural transition, but the classical routes, namely, K-type and H-type instabilities and the oblique transition, have not been linked to these phenomena. Therefore, many questions remain regarding the relevance of these studies to natural transition. For instance, it is unknown whether such classical routes actually occur in natural transition, whether they occur simultaneously or interact, whether there is a dominant mechanism under some circumstances, etc. Such questions motivated the present work. Numerical simulation of the incompressible three-dimensional Navier-Stokes equations in a vorticity velocity formulation was performed using high accurate numerical schemes. Owing to the complexity of the natural transition, the streamwise modulation was initially not considered. Therefore, only the three dimensionality was studied yielding spanwise modulated wavetrains. Two cases were judiciously selected at Re = 8000. One case was located near the first branch of the two-dimensional stability diagram where the linear process is dominated by three-dimensional Tollmien-Schlichting (TS) waves. The other case was located far from the first branch where the linear process is dominated by a two-dimensional TS waves. Preliminary results can be found in [2]. Similar studies, but for boundary layers, can be found in [3].