Abstract
We present numerical simulations of closed wavy Taylor vortices and of helicoidal wavy spirals in the Taylor–Couette system. These wavy structures appearing via a secondary bifurcation out of Taylor vortex flow and out of spiral vortex flow, respectively, mediate transitions between Taylor and spiral vortices and vice versa. Structure, dynamics, stability and bifurcation behaviour are investigated in quantitative detail as a function of Reynolds numbers and wave numbers for counter-rotating as well as corotating cylinders. These results are obtained by solving the Navier–Stokes equations subject to axial periodicity for a radius ratio η=0.5 with a combination of a finite differences method and a Galerkin method.
Highlights
Vortices [14] appear via primary bifurcations out of CCF in a symmetric Hopf bifurcation together with the RIB state
Besides the bifurcation behaviour exhibited in figure 1 as a function of R1, we investigated the wavenumber dependence of wavy structures for fixed R1 and R2
We have investigated the bifurcation behaviour, dynamics and structural properties of Taylor vortices, spiral vortices, and their corresponding modulated structures, namely toroidally closed wavy Taylor vortices and helical wavy spirals as well as the so-called ribbons in the Taylor–Couette system
Summary
We report the results obtained numerically for a Taylor–Couette system with co- and counterrotating cylinders, fixed radius ratio η = r1/r2 = 0.5, no-slip boundary conditions at the cylinder surfaces and axial periodic boundary conditions determining the axial wave number k. Cylindrical coordinates r, φ and z are used to decompose the velocity field into a radial component u, an azimuthal one v, and an axial one w:. Lengths are scaled by the gap width d and times by the radial diffusion time d2/ν for momentum across the gap, and the pressure p is scaled by ρν2/d2. R1 and R2 are just the reduced azimuthal velocities of the fluid at the cylinder surfaces; 1 and 2 are the respective angular velocities of the cylinders
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