Lorenz model of instability in porous media for van der Waals gas

The article is devoted to the study of the nonlinear instability of the van der Waals gas in a gap with a porous medium of finite thickness heated from below. A fixed temperature difference is set between the upper cold surface and the lower hot one. The Lorenz approach was used to solve the problem. During a numerical solution, criteria for monotonic instability Racr1 and oscillating instability Racr2 were obtained. The results of calculations of the criterion Racr3 for the appearance of a strange attractor in the phase space are presented, which can be interpreted as a criterion for the generation of undamped turbulent fluctuations. The nature of the dependences of the critical Rayleigh numbers on the physical properties of the gas, the porosity of the medium, and the parameters of the van der Waals equation of state Waa and Wab is analyzed.The phenomenon of instability (formation of vortices in liquids or gases) in the space between two horizontal boundaries, when the lower one is heated, is widespread in technical applications. Lorenz developed a non-linear approach to the study of this phenomenon. This approach makes it possible to determine the criteria for the emergence of vortices and their transformation. This article uses the Lorenz approach to obtain instability criteria for a real gas whose properties are described by the van der Waals equation of state. This gas is in a porous medium. This combi-nation of gas and medium has a wide technological application in the food, chemical and other industries. That is why the present study focused on this problem.