0 2. Obtain a self-similar solution for the downstream evolution of the two-dimensional wake. We represent...

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0 2. Obtain a self-similar solution for the downstream evolution of the two-dimensional wake. We represent the mean streamwise velocity by U U = U(), and the Reynolds shear stress by - puv = pug(), where and g are functions of y/l only (with / being the transverse length scale of the flow.) (a) By substituting into the mean flow streamwise momentum equation, show that a self- similar solution is possible only if the quantities UodUs U dx S and Uo dl U dx are both independent of downstream location (x). (b) By making use also of the momentum integral, show that the self-similar solution has the forms s 1 = Ax/2, U = Bx-1/2, where A and B are constants to be determined. 0 2. Obtain a self-similar solution for the downstream evolution of the two-dimensional wake. We represent the mean streamwise velocity by U U = U(), and the Reynolds shear stress by - puv = pug(), where and g are functions of y/l only (with / being the transverse length scale of the flow.) (a) By substituting into the mean flow streamwise momentum equation, show that a self- similar solution is possible only if the quantities UodUs U dx S and Uo dl U dx are both independent of downstream location (x). (b) By making use also of the momentum integral, show that the self-similar solution has the forms s 1 = Ax/2, U = Bx-1/2, where A and B are constants to be determined.

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a To show that a selfsimilar solution is possible we substitute the given representations into the mean flow streamwise momentum equation The mean flow streamwise momentum equation can be written as d... View the full answer