A novel analytic representation of the boundary layer velocity for uniform flow past a semi-infinite flat plate (Blasius solution) #

Edmund E Chadwick, Hamid A Adamu

15:50 Monday in 4Q08.

Part of the Boundary layer flows and stability session.

Abstract #

Consider the new theory by Chadwick (2019) on the applications of Navier-Stokeslet (NSlet) that describes boundary layer flow by a Green’s integral distribution of fundamental solutions in boundary layer flow which we call BL-l.ets. In particular, apply the theory to the classical non-linear problem of uniform flow past a semi-infinite flat plate, which results in the determination of the unknown strength function of a Wiener-Hopf type integral. The Fourier Transform of the BL-let is already analytic in the upper half plane, leading to a degenerate case of the Wiener-Hopf technique and the determination of the strength function going as the inverse square root. This is shown to be equivalent to and agree with other approaches by considering Oseenlets in the limit (Gautesen) and modified Bessel functions in the limit (Adamu) that both use the Wiener-Hopf technique, and also by Chadwick who appeals to self-similarity arguments. The velocity is then determined from the integral and shown to be the erf function of the self-similarity variable. However, the BL-let representation is only valid in the far-boundary layer and so this solution is a first approximation and not accurate. By relaxing the boundary condition at the leading edge, equivalent to assuming the BL-let approximation breaks down there, enables us to consider a strength function expansion and consequently a velocity expansion such that the erf function is only the first term. The resulting velocity expansion is continued into the boundary layer and shown to give a good representation of the flow even with just three terms, and is compared to the numerical Blasius shooting method and Kusukawa’s boundary layer expansion.