Fully nonlinear mode competitions in magnetised Taylor-Couette flow
arXiv:2002.02630 · doi:10.1017/jfm.2020.365
Abstract
We study the nonlinear mode competition of various spiral instabilities in magnetised Taylor-Couette flow. The resulting finite-amplitude mixed-mode solution branches are tracked using the annular-parallelogram periodic domain approach developed by Deguchi & Altmeyer (2013). Mode competition phenomena are studied in both the anti-cyclonic and cyclonic Rayleigh-stable regimes. In the anti-cyclonic sub-rotation regime, with the inner cylinder rotating faster than the outer, Hollerbach, Teeluck & Rudiger (2010) found competing axisymmetric and non-axisymmetric magneto-rotational linearly unstable modes within the parameter range where experimental investigation is feasible. Here we confirm the existence of mode competition and compute the nonlinear mixed-mode solutions that result from it. In the cyclonic super-rotating regime, with the inner cylinder rotating slower than the outer, Deguchi (2017) recently found a non-axisymmetric purely hydrodynamic linear instability that coexists with the non-axisymmetric magneto-rotational instability discovered a little earlier by Rudiger, Schultz, Gellert & Stefani (2016). We show that nonlinear interactions of these instabilities give rise to rich pattern-formation phenomena leading to drastic angular momentum transport enhancement/reduction.
References in corpus (28)
- High Reynolds number Taylor-Couette turbulence
- Hydrodynamic turbulence cannot transport angular momentum effectively in astrophysical disks
- "Barber pole turbulence" in large aspect ratio Taylor-Couette flow
- Experimental evidence for magnetorotational instability in a helical magnetic field
- New type of magneto-rotational instability in cylindrical Taylor-Couette flow
- Analytic expression for Taylor-Couette stability boundary
- Helical magnetorotational instability in a Taylor-Couette flow with strongly reduced Ekman pumping
- Helical Magnetorotational Instability in Magnetized Taylor-Couette Flow
- Magnetorotational instability of dissipative Couette flow
- Non-axisymmetric Magnetorotational Instabilities in Cylindrical Taylor-Couette Flow
- Experimental evidence for non-axisymmetric magnetorotational instability in a rotating liquid metal exposed to an azimuthal magnetic field
- Experiments on the magnetorotational instability in helical magnetic fields
- Local instabilities in magnetized rotational flows: A short-wavelength approach
- Nonlinear stability of laboratory quasi-Keplerian flows
- The traveling wave MRI in cylindrical Taylor-Couette flow: comparing wavelengths and speeds in theory and experiment
- Stability and instability of hydromagnetic Taylor-Couette flows
- Boundary-layer turbulence in experiments of quasi-Keplerian flows
- Extending the range of the inductionless magnetorotational instability
- A unifying picture of helical and azimuthal MRI, and the universal significance of the Liu limit
- Competition between Traveling Fluid Waves of Left and Right Spiral Vortices and Their Different Amplitude Combinations
- Destabilization of rotating flows with positive shear by azimuthal magnetic fields
- Subcritical excitation of the current-driven Tayler instability by super-rotation
- Two types of axisymmetric helical magnetorotational instability in rotating flows with positive shear
- Turbulent Taylor-Couette flow with stationary inner cylinder
- Transport properties of the Azimuthal Magnetorotational Instability
- Nonaxisymmetric linear instability of cylindrical magnetohydrodynamic Taylor-Couette flow
- High-speed shear driven dynamos. Part 2. Numerical analysis
- High-speed standard magneto-rotational instability