Structure of critical perturbations in a horizontal layer of melted water with the prescribed heat flux at the boundaries

Abstract

Abstract. The paper deals with the investigation of critical perturbations structure in a horizontal layer of fluid with temperature inversion of density. The lower boundary of the layer is rigid and upper boundary is free and undeformable. The constant vertical heat flux is imposed at both boundaries. The thermocapillarity, evaporation and radiation are neglected. The temperature dependence of the density is assumed to be quadratic. The coordinate of the density inversion point which shows the position of the plane of maximal density in the fluid layer in the conductive state is used for the description of density inversion effect. The influence of the location of density inversion point on structure of critical perturbations is studied. It is shown that, depending on the location of the inversion point, velocity profile of longwave critical perturbations can have two-floor or three-floor structure. Stability to finitewavelength perturbations is studied for the entire range of their existence. The asymptotic formulas for critical values of the Rayleigh number and wave number are obtained, the structure of finite-wavelength critical perturbations .is determined.

Supercritical Convection of Water in an Elongated Cavity at a Given Vertical Heat Flux

“…For the case of an infinitely elongated layer, i.e. for L = ∞, the quiescent state of the fluid (12) becomes unstable with respect to small normal disturbances when the Rayleigh number exceeds the critical value Ra cr (∞) = 320 defined in [1] and confirmed in [7,8]. Hence, it follows that the critical Grashof number is equal to Gr cr (∞) = 45.7 for an infinitely elongated cavity L = ∞ and the value of the Prandtl number considered in this paper.…”