Restoring Property of the Michelson–Sivashinsky Equation. Issue 9 (2nd September 2019)

• Record Type: Journal Article
• Authors: Trucchia, Andrea; Pagnini, Gianni
• Is Part Of: Combustion science and technology. Volume 191:Issue 9(2019)
• Page Start: 1734
• Page End: 1741
• Publication Date: 2019-09-02
• Subjects: Turbulent premixed combustion -- Michelson–Sivashinsky equation -- G-equation -- fluctuations; Combustion -- Periodicals; Combustion engineering -- Periodicals; 541.36105
• DOI: 10.1080/00102202.2019.1632839
• Languages: English
• ISSNs: 0010-2202

Abstract

ABSTRACT: In this paper, we propose a derivation of the Michelson–Sivashinsky (MS) equation that is based on front propagation only, in opposition to the classical derivation based also on the flow field. Hence, the characteristics of the flow field are here reflected into the characteristics of the fluctuations of the front positions. As a consequence of the presence of the nonlocal term in the MS equation, the probability distribution of the fluctuations of the front positions results to be a quasi-probability distribution, i.e. a density function with negative values. We discuss that the appearance of these negative values, and so the failure of the pure diffusive approach that we adopted is mainly due to a restoring property that is inherent to the phenomenology of the MS equation. We suggest to use these negative values to model local extinction and counter-gradient phenomena.