Quasi-probability Approach for Modelling Local Extinction and Counter-gradient in Turbulent Premixed Combustion
Abstract
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.