Acta Mechanica 128, 253-258 (1998) ACTA MECHANICA 9 Springer-Verlag 1998 Note A note on the linear instability of the Blasius flow J. Dey and D. Das, Bangalore, India (Received February 12, 1997) Summary. It is found that in a ribbon-excited Blasius boundary layer, a wave Reynolds number defined here on the basis of phase speed and wave number of the disturbance remains nearly independent of the local mean flow Reynolds number, and so also of the streamwise distance, under the parallel flow approximation. Consequently, a limited similarity feature of the Orr-Sommerfeld equation has been found to exist for the streamfunction in the outer region of the boundary layer. 1 Introduction The linear instability of the Blasius flow has been the subject of many investigations in the past (see, for example, Drazin and Reid [1] for earlier work, and Bertolotti et al. [2] and Govindarajan and Narasimha [3] for recent development). For the flow in X direction with a free stream velocity U and under the parallel flow assumption, the linear instability of this flow with a small wavy disturbance superimposed on it is governed by the Orr-Sommerfeld equation [4], (r - cq2r (cqqSo' -/31) - cqCqSo'" = -iR-i(O .... - 2cqzr '' + cq4q~). (i) Here a prime denotes a derivative with respect to y (= Y/,~*), O(Y) is the perturbed stream function, ~1 (= c~c5")and/3i (=/36"/U) are the non-dimensional wave number and frequency, respectively, Co(Y)is the mean flow stream function, R (= U6*/v) is the Reynolds number based on the displacement thickness (6"), and v is the kinematic viscosity; c~ and/3 are dimensional quantities and are assumed here to be real. In a boundary layer excited by a ribbon oscillating at some (prescribed) frequency, a travelling wave is set-up. As the boundary layer grows along X, the values of the phase speed c (=/3/c0 and the wave number el for which the wave amplifies will depend on R, as given by the stability loop. It will be seen below that the disturbance parameter R~ =/31R/cq 2 is nearly independent of R (and so also of X) for a given value of/3, although 131 and cq change downstream with R. Consequently, a limited similarity for the normalized disturbance stream function is also seen in the outer region of the boundary layer. 2 Analysis /3 c We define a "wave Reynolds number", R~- - based on the phase speed and wave V~ 2 V~' number. The clue to the usefulness of such a non-dimensional number comes from the dis-