Stabilities of two-dimensional plane jet which is ejected from between two parallel plates are studied numerically.
Firstly, by investigation of the basic flow which is obtained by numerical simulation we have found that there is a new local similarity and the basic flow can be represented by similarity variables of ξ(=x/$Re_L$), η(=y/h) irrespective of the Reynolds number $Re_L$.
Secondly, stabilities of plane jet are investigated numerically on the entire region including the nozzle exit. When the Reynolds number is large the varicose mode`s disturbances grow very rapidly at frequency of $St_L\cong 0.31$ and the sinuous mode`s disturbances at frequency of $StL\cong 0.2$. And the spatial growth rates and phase velocities depend on local similarity variable ξ rather than Reynolds number $Re_L$.
Thirdly, stabilities of plane jet flow are studied at a location of x=X by a local analysis method. The results show that the stability characteristics are well matched with that of global analysis at $x\gtrsim 3$ and the local similarity can be used in the linear stability analysis if the Reynolds number is moderately large( $Re_L$>100 ). In the case of low Reynolds numbers, since the nonparallel effects become apparent it is needed to carry out the stability analysis by using the basic flow`s local similarity which can reproduce the velocity distribution at certain Reynolds number from a known one. And the neutral stability curves which are not coincide before reaching the similarity region with that of Bickley jet are presented by considering the local similarity variable ξ( =x/$Re_L$ ) as a parameter. However there is a limitation in usage of this local similarity, which is also discussed.
The unstable disturbances grow very rapidly near the nozzle exit and then reach linearity limit where the spatial growth rates begin to decrease. After that the disturbances are saturated and transit to turbulence. These nonlinear phenomena can not be observed by a linear analysis method. So, fourthly, we have investigated the nonlinear stability of plane jet where the periodic disturbances show more complicate appearance. Varicose mode`s disturbances grow rapidly near the nozzle exit and saturate generating harmonic frequencies. And since sinuous mode`s disturbances shed anti-symmetrically these make an effect on the flow near the nozzle exit. This feed back effect makes the flow more complicate and seems to cause the flow transit to turbulence.
Finally, we have investigated 3-D stabilities of a pulsating jet which is generated by a periodic pressure pulsation inside the nozzle. Since the pulsating jet is not a parallel one, the Squire`s theorem is not valid any more and 3-D disturbances can grow from the nozzle exit and may grow more rapidly than 2-D disturbances. The results show that 3-D disturbances have a frequency which is resonated with a 2-D pulsating frequency and grow most rapidly when the spanwise wave number κ is about π/2~π.
