A theory of whistler wave propagation in axially symmetric density ducts is developed. Both density crests and troughs are considered. The duct width is assumed to be large compared with the parallel wave length. All considerations are based on the Maxwell equations. A number of effects that are not included in the ray theory and (or) the Schrödinger-type equations are elucidated. Among them is whistler detrapping from a density crest at ω < ½ωH. An analytical theory of the detrapping is developed and the corresponding wave attenuation rate in the duct is calculated.

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Uncertainty Quantification (UQ) for fluid mixing depends on the length scales for observation: macro, meso and micro, each with its own UQ requirements. New results are presented here for macro and micro observables. For the micro observables, recent theories argue that convergence of numerical simulations in Large Eddy Simulations (LES) should be governed by space-time dependent probability distribution functions (PDFs, in the present context, Young measures) which satisfy the Euler equation. From a single deterministic simulation in the LES, or inertial regime, we extract a PDF by binning results from a space time neighborhood of the convergence point. The binned state values constitute a discrete set of solution values which define an approximate PDF. The convergence of the associated cumulative distribution functions (CDFs) are assessed by standard function space metrics.

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