It is usually assumed that the propagation of a turbulent jet traveling in a surrounding medium is basically determined by two parameters: the velocity ratio (m --u2/ul) and the density ratio (n p~/p~) of the surrounding medium and the jet [1]. However, in certain cases, for example for m m 1, the mixing intensity is apparently not only dependent on these factors but is also determined by the in i t i a l flow parameters (existence and state of the wall boundary layers in the nozzle, the intensity of the turbulence in the flow core, etc.). In this case, in order to relate the basic jet characteristics with these in i t ia l parameters we must know how the rearrangement of the "channel" flow into jet flow takes place. w The general qual i ta t ive picture of this transition [2] is characterized by alternation of various flow regimes which are unstable and transition from one to another. A complete analyt ic description of this transition has not yet been developed. Linear stabil i ty theory has had tire greatest success. Among its results we first note that the cr i t ical values of the Reynolds number obtained for jet flows of a viscous fluid [,3] are very low (R. m 4-5) . This means that in the majority of the real flows, in which R >> R., the process of unstable disturbance development in the jet may he satisfactorily described by stability theory for an ideal (inviscid) fluid. The instabili ty of the boundary layer thickness 6 in an ideal fluid was first studied by Rayleigh using the method of small disturbances. The disturbed motion was specified in the form A(y)exp[ ia(x e l ) l , where A(y) is the disturbance amplitude, a -= 27r/X is the wave number, X is the wavelength, c = c r + ic i, e r is the phase velocity, c i is the t ime amplif icat ion coefficient. It ~as shown that the maximum value of the disturbances spatial amplif icat ion coefficient (z =acSci/Cr), equal to 0.4, occurs for c~6 = 0.8. Here the phase velocity was equal to cr/U 0 = 0.5, where U 0 is the difference of the velocit ies at the boundaries of the layer. Further development of the linear theory of hydrodynamic instability of jet flows was presented in the studies of Schade and Michalke [4, 5]. In these studies the problem of free boundary layer instability was examined in an approximate formulation: the real velocity distribution was replaced by profiles consisting of linear segments. This assumption leads, as is known, to a considerable simplif ication of the corresponding differential equations and permits obtaining the solution in finite form.