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Numerical simulations as well as recent experiments in turbulent three-dimensional flow show a trend of the gradient of a passive scalar to align with the compressional axis of the strain tensor. In two-dimensional flow, however, it has been proved that the most probable orientation of the scalar gradient can be different from the compressional direction. An idealized situation is used to address this question in the three-dimensional case and to suggest a possible way to reexamine the scalar gradient alignment in three-dimensional flow. This kind of analysis can be applied to the material line alignment as well.
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Garcı́a et al. (2006) studied this question.
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