Asymptotic and numerical analysis of momentumless turbulent wakes

The asymptotic behavior of turbulent axisymmetric and plane momentumless wakes was studied using the Reynolds-averaged momentum equations and the second-order model of turbulence. The similarity solutions were obtained analytically and the process of transition to self-similarity was studied numerically. It was found that a single-point spectrum of the solutions of the corresponding eigenvalue problem for turbulent energy and dissipation rate existed. However, the spectra of solutions for the normal components of the anisotropy tensor and for the mean velocity defect were discrete. The numerical solution of a non-self-similar problem shows, in accordance with experiments and analytic solutions, that mean and fluctuating velocities decay with different rates, shear stresses decay faster than normal stresses and the anisotropic component of normal stresses decays faster than the isotropic component. The analysis of solutions for a full system of the Reynolds stress equations showed the presence of 'partial similarity' of the turbulent momentumless wake when some variables (velocity defect and shear stress) remain non-similar in flow that is self-similar as a whole.