Corrections to 'Nonlinear stability of boundary layers for disturbances of various sizes'

Abstract

Dr P . Hall has kindly pointed out an error in § 2 of the paper; namely, that (2.10a) renders X complex whenever a is complex, so that inter alia a spatial growth or decay can appear in Ein (2.9). The following alterations and reinterpretations correct for this fault and some minor misprints. Equation (2.10a) should read ‘X( = X ) = h~2X X is then real and can be identified with X throughout the paper, while the terms multiplied by a 2 in (2.11), (2.12), (2.13c), (2.34a, d),(2.35), (2.37), (2.38) should be omitted. The sentence starting two lines below (2.106) should then be replaced by ‘Here, working with a wavenumber a. close to the neutral value a l5 we will keep the reference Reynolds number Re, length scale l*, frequency and velocity U* fixed and suppose that the position x = xx -f h2x2 under investigation is close to the neutral position x = xx for the particular fixed frequency disturbance considered. So the skin friction factor A = Aj + h2X + 0(h3)(2.106') is also slightly perturbed from the neutral value A = Al5 where Ax = from just below (2.2). Notice that this treatment of the nearly neutral state differs from that usually applied to parallel flows where the Reynolds number is usually varied instead’. From (2.106') onwards Ax should replace A. A term — A^ioq ZUX+ kj) should be added to the right side of (2.13c). Equation (2.146) should give U1-*XxA 1, ?72->A1A2but f^3->A1^43+ (2.17) should have A 1 = A 1(X)E-f-c.c. and the right sides of (2.30), (2.31) should be multiplied by —Ay1, Xj1 respectively. An extra term + + should be included in the right side of (2.32) and (2.34c) should have Ax 4- In (2.37) the term — 6AA31 should be replaced by — 6(A1^431 + A2H1) and — A^bX2A 1 should be added to the right side of (2.38). X should replace X in the definition of SF2{u, v,p), just above (2.13a), in TJXx in (2.136) and in U2x + U2 U