TY - JOUR

T1 - Hysteresis and bifurcations at spin up and spin down of a two-liquid vortex

AU - Skripkin, Sergey G.

AU - Tintulova, Maria V.

AU - Naumov, Igor V.

AU - Shtern, Vladimir N.

N1 - The study was supported by the Russian Science Foundation (Grant No. 24-19-00233). The experimental facilities were provided under state contract with IT SB RAS (No. 121031800229-1).

PY - 2025/5/12

Y1 - 2025/5/12

N2 - Our experiments revealed an interesting nonlinear physics phenomenon: a triple hysteresis and a few bifurcations in a compact two-liquid vortex flow driven by the bottom disk rotation. Two immiscible liquids fill a vertical cylindrical container. The slow rotation drives toroidal axisymmetric steady circulations of both liquids. The lower liquid moves up near the sidewall and down near the axis, eventually forming a funnel filled with the upper liquid. If the angular velocity ωd of the disk exceeds the first critical value ω1, then the flow pattern loses axial symmetry and, in particular, the funnel in the horizontal cross section from circular becomes ellipsoidal. If ωd exceeds the second critical value ω2, then the flow becomes oscillatory in time. If ωd exceeds the third critical value ω3, then the elliptical funnel splits into two funnels whose axes differ from the axis of the cylinder. If we now start eventually reducing ωd, then the flow in the reversed order passes qualitatively the same states, but with smaller critical values of ωd. These three different critical values of ωd indicate a triple hysteresis. A hysteresis—the dependence of flow state on the prehistory—is a typical feature of compact two-fluid rotating flows. However, the triple hysteresis discovered here is a new striking flow phenomenon.

AB - Our experiments revealed an interesting nonlinear physics phenomenon: a triple hysteresis and a few bifurcations in a compact two-liquid vortex flow driven by the bottom disk rotation. Two immiscible liquids fill a vertical cylindrical container. The slow rotation drives toroidal axisymmetric steady circulations of both liquids. The lower liquid moves up near the sidewall and down near the axis, eventually forming a funnel filled with the upper liquid. If the angular velocity ωd of the disk exceeds the first critical value ω1, then the flow pattern loses axial symmetry and, in particular, the funnel in the horizontal cross section from circular becomes ellipsoidal. If ωd exceeds the second critical value ω2, then the flow becomes oscillatory in time. If ωd exceeds the third critical value ω3, then the elliptical funnel splits into two funnels whose axes differ from the axis of the cylinder. If we now start eventually reducing ωd, then the flow in the reversed order passes qualitatively the same states, but with smaller critical values of ωd. These three different critical values of ωd indicate a triple hysteresis. A hysteresis—the dependence of flow state on the prehistory—is a typical feature of compact two-fluid rotating flows. However, the triple hysteresis discovered here is a new striking flow phenomenon.

UR - https://www.mendeley.com/catalogue/f90fc0cd-dff5-33f3-85ea-117065aff0b4/

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-105005144341&origin=inward&txGid=df6f6615f6b1aac28752bc29adf00d59

U2 - 10.1063/5.0271831

DO - 10.1063/5.0271831

M3 - Article

VL - 37

JO - Physics of Fluids

JF - Physics of Fluids

SN - 1070-6631

IS - 5

M1 - 054102

ER -