The stability of a two-dimensional laminar jet

This paper deals with the stability of a two-dimensional laminar jet against the infinitesimal antisymmetric disturbance. The curve of the neutral stability in the (α, R )-plane (α, the wave-number; R , Reynolds number) is calculated using two different methods for the different parts of the curve; the solution is developed in powers of (α R ) −1 for obtaining the upper branch of the curve and in powers of α R for the lower branch. The asymptotic behaviour of these branches is that for branch I, α → 2, \;\; c → 2/3 for R → ∞ ; and for branch II, R ~ 1·12α-1|2,\; c ~ 1· 20 α² for α → 0. Some discussion is given on the validity of the basic assumption of the stability theory in relation to the numerical result obtained here.