ISSN:
1089-7666
Source:
AIP Digital Archive
Topics:
Physics
Notes:
Instability and transition in plane Poiseuille flow with spanwise system rotation is studied via direct numerical simulations with initial small-amplitude random disturbances. The results confirm and clarify the recent experimental findings of Alfredsson and Persson [J. Fluid Mech. 202, 543 (1989)]. A large computational domain is used to allow natural selection of the dominant spanwise wavelength of the observed streamwise vortices, and also the streamwise wavelength of the dominant secondary modes which subsequently develop in the presence of the streamwise vortices. Temporal evolutions of these vortices for several different cases are studied in detail. It is found that the spanwise wavelength of the streamwise vortices can be significantly different from that obtained from linear stability analysis. In all cases examined, the unstable primary three-dimensional waves, which develop during the linear stage, are still persistent in the nonlinear stage. It is also found that for the cases in which the primary three-dimensional waves decay, the finite-amplitude streamwise vortices can become unstable to two different three-dimensional secondary modes of instability, depending on the range of Reynolds number (Re) and rotation number (Ro). The first mode has a streamwise wavelength an order of magnitude longer than the spanwise wavelength; the other, referred to by Alfredsson and Persson as the "twisting mode'' because of its visual appearance, has a streamwise wavelength comparable to the spanwise wavelength, and is shown to consist of counter-rotating streamwise vortices whose centers oscillate mostly in the vertical direction. It is shown that these modes are nondispersive traveling waves.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.858070
Permalink