A Similarity Hypothesis for the Two-Point Velocity Correlations in a Temporally Evolving Wake

Abstract

It has long been recognized (e.g. Towsend, 1956) that the governing equations for the single-point moments in several free-shear flows admit similarity solutions if the flows evolve from virtual sources. These similarity solutions, however, do not provide information about many important features of the flow, such as how the turbulent kinetic energy is distributed amongst the different scales of motion. In order to gain this information it is necessary to consider more complex statistical measures of the flow, such as the two-point correlations.Most of the previous analyses of the two-point equations have considered decaying isotropic turbulence (e.g., Batchelor, 1948 or George, 1992) or homogeneous shear turbulence (George and Gibson, 1992). Ewing (1995) later demonstrated that the equations for the two-point velocity correlation in the far fields of the axisymmetric and planar jets admit similarity solution. However, no attempt was made to test the hypotheses using data from these non- homogeneous flows. Here, data from two Direct Numerical Simulations of the temporally evolving wake (Moser and Rogers, 1994) are used to test the similar hypothesis for the two-point correlations in this flow.