Comparative study of convection characteristics for a system with deformable interface based on the Navier–Stokes and Oberbeck–Boussinesq equations

• Published in: Philosophical transactions of the Royal Society of London. Series A: Mathematical, physical, and engineering sciences Vol. 381; no. 2245; p. 20220078
• Main Authors: Bekezhanova, Victoria B., Goncharova, Olga N.
• Format: Journal Article
• Language: English
• Published: England 17.04.2023
• Subjects: Navier–Stokes equations; Oberbeck–Boussinesq approximation; thermocapillary convection
• ISSN: 1364-503X; 1471-2962; 1471-2962
• DOI: 10.1098/rsta.2022.0078

The right choice of the appropriate mathematical model is crucial for evaluating the physical plausibility of modelling results. The issue of the correct application of the classical Boussinesq approximation for studying the heat and mass transfer in fluidic systems with a deformable boundary is a subject of scientific discussions despite the good agreement of numerous theoretical and numerical results obtained within the convection models based on the Oberbeck–Boussinesq equations with the data of physical experiments and observations. A comparative analysis of the results of numerical simulations in the framework of two-sided models based on the Navier–Stokes equations, and their Boussinesq approximation, is performed in the context of a convection problem in a locally heated two-phase system with a deformable interface. It is demonstrated that the application of the standard Boussinesq approximation allows one to give a consistent description of the effect of interface deformations on combined buoyant–thermocapillary driven fluid motions. This article is part of the theme issue ‘New trends in pattern formation and nonlinear dynamics of extended systems’.