Table 1 Nomenclature and abbreviations of flow states.

From: Effects of an imposed axial flow on a Ferrofluidic Taylor-Couette flow

Abbreviation

Flow state & description

CCF

Circular Couette flow

TVF

Taylor vortex flow

m-wTVF

wavy Taylor vortex flow46 with major azimuthal wavenumber m (wTVF is also known as wavy vortex flow, WVF?)

m-\(wTV{F}_{l}\)

(axial) localized m-wTVF

m-\(wTV{F}_{{H}_{x}}\)

m-wTVF modified due to transverse magnetic field26 with m ± 2 modes

m-\(wTV{F}_{l,{H}_{x}}\)

(axial) localized m-\(wTV{F}_{{H}_{x}}\)

m1-m2-\(wTV{F}_{{H}_{x}}\)

\(wTV{F}_{{H}_{x}}\) with major azimuthal wavenumber m1 and minor azimuthal wavenumber m2

L[R]m-SPI

left- [right-] winding spiral vortex flow with azimuthal wavenumber m47

m-wSPI

wavy SPI with major azimuthal wavenumber m46

L[R]m-\(wSP{I}_{{H}_{x}}\)

left- [right-] modified winding m-wSPI with m ± 2 modes due to transverse magnetic field26

Lm1Lm2-MCS

left-winding Mixed-Cross-Spiral47 with major azimuthal wavenumber m1 and minor azimuthal m2 (right-winding counterparts exist simultaneously)

Lm1Lm2-\(MC{S}_{{H}_{x}}\)

modified Lm1Lm2-MCS with m ± 2 modes due to transverse magnetic field

Lm1Lm2Lm3-\(mMC{S}_{{H}_{x}}\)

left-winding modulated \(MC{S}_{{H}_{x}}\) with a combination of azimuthal wavenumbers m1, m2 and m3

  1. In the presence of a transverse magnetic field (\({s}_{x}\ne 0\)), all flow state are inherently 3D and have stimulated 2-fold symmetry20,26, which are indicated by a small label Hx. The index l highlights the (axial) localization of the wavy flow structure.