Effect of the fluid velocity change on the linear stability of plane Poiseille flow

The numerical simulation has been done for the linear stability of plane Poiseille flow by varying the fluid velocity in the local flowing field. The analysis of the results showed that the influence of varying the fluid velocity on the linear stability bears some common characteristics. The relation curves between the unstable zone area encircled by the neutral curves and the different normal coordinates can be divided into four different functional regions, the approximately unchanged region of neutral curves, the region trending to stability, the region trending to instability, the obscure region trending to stability or instability. The susceptible region of stability change is made of the region trending to stability and the region trending to instability or unstable region. But that in which form the flowing field changes the unstable zone area encircled by the neutral curves depends on the forms of velocity changes. This study result will provide a fine platform for both the experimental study of the hydrodynamic stability and the further improvement of the coalescence theory.