Abstract
This note presents using the LMSE model the exact solution for the concentration pdf (probability density function) equation for turbulent jets with an initial bi-valued scalar field. This solution generalises to inhomogeneous turbulence the solution of Dopazo and O'Brien (1978) for statistically homogeneous turbulence. It is shown that the concentration pdf preserves its shape and does not relax to an asymptotic self-similar shape as x tends to ∞. Therefore, the main drawback of this model, the inability to modify the (initial) pdf shape, noted by Dopazo and O'Brien (1978), still exists in inhomogeneous turbulent flows with initial bi-valued concentration field.
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