On the Turbulent Far-Wake in Incompressible Axi-Symmetric Flow
MASSACHUSETTS INST OF TECH LEXINGTON LINCOLN LAB
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The arguments that lead to the xexpn 13 dependence of wake width and the xexpn -23 dependence of axial velocity on axial distance in the far turbulent wake are reviewed. Assuming similarity of mean velocity profiles, the dominant terms in the Navier-Stokes equations for turbulent wake flow are used to derive these profiles with the help of Boussinesqs and Prandtls hypotheses. The resulting profile has the same form as in the better known two-dimensional case. It is compared with an assumed Gaussian profile and both are compared with the Gaussian profile that results in the corresponding laminar case. The form of the eddy viscosity is also obtained in the two cases for the former it is zero on the axis and rises to a maximum before falling to zero again on the wake boundary whereas for a Gaussian profile it is constant across a cross section of the turbulent wake. In addition, the eddy viscosity has an xexpn -13 dependence in both cases, which is absent in the two-dimensional wake.
- Fluid Mechanics