Quasi-probability Approach for Modelling Local Extinction and Counter-gradient in Turbulent Premixed Combustion
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In opposition to standard probability distributions, quasi-probability distributions can have negative values which highlight nonclassical properties of the corresponding system. In quantum mechanics, such negative values allow for the description of the superposition of two quantum states. Here, we propose the same approach to model local extinction and counter-gradient in turbulent premixed combustion. In particular, the negative values of a quasi-probability correspond to the local reversibility of the progress variable, which means that a burned volume turns to be unburned and then the local extinction together with the counter-gradient interpretation follows. We derive the Michelson-Sivashinsky equation as the average of random fronts following the G-equation, and their fluctuations in position emerge to be distributed according to a quasi-probability distribution displaying the occurrence of local extinction and counter-gradient. The paper is an attempt to provide novel methods able to lead to new theoretical insights in combustion science.