Vortices on the Free Surface of a Normal Helium He-I Layer in a Wide Cell

Abstract

The appearance of a thermogravitational convective flow in the bulk of a layer of normal liquid helium He-I h ≈ 1–3 cm deep in a wide cylindrical cell, which is heated from above in the gravity field in the temperature range Tλ ≤ T ≤ Tm, is accompanied by the excitation of a vortex flow on the free surface of the liquid. Here Tλ = 2.1768 K is the temperature of transition of liquid 4He from the superfluid He-II to the normal He-I state at the saturated vapor pressure, and Tm ≈ 2.183 K is the temperature at which the He-I density passes through a maximum. Bulk convection serves as a source of energy pumped into the vortex system on the surface of He-I. The nonlinear interaction of vortices on the surface with each other and with convective vortex flows in the bulk of the layer leads to the formation of two large-scale vortices (vortex dipole) on the surface of He-I, and their sizes are limited to the diameter of the working cell and several times exceed the layer depth. This behavior corresponds to the transition from the vortex flow mode on “deep water” (vortices on the surface of a three-dimensional liquid layer) to vortices on the surface of “shallow water” (vortices on the surface of a two-dimensional layer) in time. When the layer is heated further above Tm, the convective flows in the bulk decay quickly, but the vortex motion on the surface of a two-dimensional He-I layer is retained. In the absence of energy pumping from the bulk, the total energy of the vortex system on the surface of a shallow water layer decreases in time according to a near-power law because of the nonlinear interaction of large-scale vortices with each other and friction against the cell walls. As a result, during long-term observations, small-scale vortices with sizes comparable to or less than the layer depth again begin to prevail on the surface of He-I, which corresponds to the transition from a two-dimensional to a three-dimensional liquid layer. The energy of the vortex flow on the surface of a deep water layer decreases according to a near-exponential law. Thus, long-term observations of the dynamic phenomena on the free surface of an He-I layer several centimeters deep in a wide temperature range above Tλ allowed us, for the first time, to study the excitation, evolution, and decay of the vortex flows on the surface of a deep or shallow water layer in one experiment.