ON THE STABILITY OF THE LAMINAR MIXING REGION BETWEEN TWO PARALLEL STREAMS IN A GAS

Abstract : The stability of the mixing of two streams was studied both for the interest in the problem and for clarifying certain points in the basic stability theory. It is shown that, when the relative speed of the two parallel streams exceeds the sum of their velocities of sound, subsonic oscillations cannot occur and the mixing region may be expected to be stable with respect to small disturbances. It is further shown that, when viscosity and heat conductivity are neglected, if the flow can execute a small neutral subsonic oscillation of finite wave length, it can also execute self-excited oscillations of longer wave lengths and damped oscillations of shorter wave lengths. Rigorous developments of the mathematical theory of asymptotic solutions confirm previous methods of solution of the stability equations in a compressible fluid. This theory also shows that, at high Reynolds numbers, the damped oscillations in a strictly parallel main flow have a structure similar to that of the vorticity field in fully developed turbulent flow. sample calculations are also included exhibiting various quantitative properties of these small oscillations.