ENTRAINMENT IN A SHEAR-FREE TURBULENT MIXING LAYER

Results from a direct numerical simulation of a shear-free turbulent m ixing layer are presented. The mixing mechanisms associated with the t urbulence are isolated. In the first set of simulations, the turbulent mixing layer decays as energy is exchanged between the layers. Energy spectra with E(k) similar to k(2) and E(k) similar to k(4) dependence at low wavenumber are used to initialize the flow to investigate the effect of initial conditions. The intermittency of the mixing layer is quantified by the skewness and kurtosis of the velocity fields: resul ts compare well with the shearless mixing layer experiments of Veerava lli & Warhaft (1989). Eddies of size of the integral scale (k(3/2)/eps ilon) penetrate the mixing layer intermittently, transporting energy a nd causing the layer to grow. The turbulence in the mixing layer can b e characterized by eddies with relatively large vertical kinetic energ y and vertical length scale. In the second set of simulations, a force d mixing layer is created by continuously supplying energy in a local region to maintain a stationary kinetic energy profile. Assuming the s patial decay of r.m.s. velocity is of the form u proportional to y(n), predictions of common two-equation turbulence models yield values of n ranging from -1.25 to -2.5. An exponent of -1.35 is calculated from the forced mixing layer simulation. In comparison, oscillating grid ex periments yield decay exponents between n = -1 (Hannoun et al. 1989) a nd n -1.5 (Nokes 1988). Reynolds numbers of 40 and 58, based on Taylor microscale, are obtained in the decaying and forced simulations, resp ectively. Components of the turbulence models proposed by Mellor & Yam ada (1986) and Hanjalic & Launder (1972) are analysed. Although the is otropic models underpredict the turbulence transport, more complicated anisotropic models do not represent a significant improvement. Models for the pressure-strain tensor, based on the anisotropy tensor, perfo rmed adequately.