Weakly Damped Vortex Flow on the Free Surface of a Normal Helium He-I Layer

The buoyancy-driven thermogravitational Rayleigh–Benard convection (RBC) occurs in a 1–3 cm-deep layer of normal He-I in a wide experimental cell heated from above at temperatures below the liquid 4He density maximum T < Tm ≈ 2.183 K. It is established that the onset of RBC is accompanied by the appearance of a vortex flow on the free He-I surface. The interaction of these vortices between each other and with vertical vortex structures, which are formed in the bulk of the layer in the process of establishment of turbulent RBC, results in the appearance of large-scale vortices (vortex dipole), the dimensions of which were limited by the cell diameter d = 12.4 cm, on the surface. This corresponds to a transition from a 3D- to 2D-layer situation and the formation of an inverse energy cascade in the surface vortex system. As the temperature of the liquid at the cell bottom rises above Tm, the initial convective motion in the bulk of the non-uniformly heated He-I layer rapidly dies out; however, the vortex flow on the free surface of the liquid is maintained even without pumping energy from the bulk. The results of the long-term (up to ~ 800 s) studies on the evolution of the surface vortex system show that the decay of the total energy of the vortex system with time due to the nonlinear interaction between weakly damped large-scale vortices and their interaction with the cell boundaries can be described by the power law E ~ (1/τ)n with the exponent n≈ 1 ÷ 2 in different experiments. In the further observations (up to 2500 s), the appearance of small-scale vortices on a 2.5-cm-deep He-I surface layer was observed. Now, the decay of the total energy of the small-scale vortex system on the surface of a 3D-layer with time due to the viscous losses in the bulk could be described by the exponential law E ~ exp (− t/τ) with the characteristic time of τ ≈ 320 s.