Experimental investigations have indicated that some essential features of the instability properties cannot be described by the linearized stability theory of temporal growing disturbances. In this paper, linear stability theory used for analysis of spatially growing disturbances in mixing layer is studied. A tangent mapping of is used to map the doubly infinite domain of y into the computational domain [-1,1]. We solve the Orr-Sommerfeld equation by means of spectral method. The eigen functions and eigenvalue problem were solved for complex wave numbers and real frequencies where a hyperbolic tangent profile is taken for the velocity U(y). Results show that, contrary to the temporal case, real and imaginary values of eigen functions of mixing layer, are not symmetric and asymmetric. The results indicate that the theory of spatially growing disturbances, describes the instability properties of a disturbed mixing layer more precisely, at least for small frequencies.

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