One-dimensional turbulence: Variable-density formulation and application to mixing layers

One-dimensional turbulence (ODT), a method for one-dimensional stochastic simulation of turbulent flow, is generalized to incorporate variable-density effects. This formulation is used to investigate variable-density effects in planar mixing layers. Computed results are compared to direct numerical simulations of temporally developing mixing layers and to measurements performed in spatially developing mixing layers. Dependencies of mean flow structure and fluctuation statistics on the free-stream density ratio $s$ are examined, including $s$ values beyond the range of previous experimental and computational studies. For temporally developing mixing layers, the previously noted decrease of the layer growth rate as $s$ deviates from unity is reproduced. For spatially developing mixing layers, dependence on $s$ is sensitive to whether the high-speed or the low-speed stream is denser; by convention, the latter case corresponds to $s>1$⁠. Experimental results indicating that layer growth is an increasing function of $s$ have previously been interpreted on the basis of models that imply the continuation of this monotonic trend for all $s$⁠. ODT reproduces the observed trend within the experimentally accessible range, but predicts a reversal of the trend slightly beyond that range and a subsequent decrease of the growth rate as $s$ increases. This and related results suggest a closer analogy between the behaviors of temporally and spatially developing mixing layers than has previously been recognized. An experimental test of the predicted trend reversal in spatially developing mixing layers is proposed.