Vortex Flow on the Surface Generated by the Onset of a Buoyancy-Induced Non-Boussinesq Convection in the Bulk of a Normal Liquid Helium

Abstract

The onset of the Rayleigh–Benard convection (RBC) in a heated from above normal He-I layer in a cylindrical vessel in the temperature range Tλ < T ≤ Tm (RBC in non-Oberbeck–Boussinesq approximation) is attended by the emergence of a number of vortices on the free liquid surface. Here, Tλ = 2.1768 K is the temperature of the superfluid He-II–normal He-I phase transition, and the liquid density passes through a well-pronounced maximum at Tm ≈ Tλ + 6 mK. The inner vessel diameter was D = 12.4 cm, and the helium layer thickness was h ≈ 2.5 cm. The mutual interaction of the vortices between each other and their interaction with turbulent structures appeared in the layer volume during the RBC development gave rise to the formation of a vortex dipole (two large-scale vortices) on the surface. Characteristic sizes of the vortices were limited by the vessel diameter. The formation of large-scale vortices with characteristic sizes twice larger than the layer thickness can be attributed to the arising an inverse vortex cascade on the two-dimensional layer surface. Moreover, when the layer temperature exceeds Tm, convective flows in the volume decay. In the absence of the energy pumping from the bulk, the total energy of the vortex system on the surface decreases with time according to a power law.