Taylor-Couette (TC) flow involves fluid motion between rotating concentric cylinders, one of the key problems in fluid dynamics. Its behaviour varies from axisymmetric Taylor vortices to turbulence through different patterns. The flow dynamics become more complicated when a temperature difference is applied between the two cylinders, leading to radial heat transfer coupled with centrifugal acceleration. The combination is pivotal in altering the stability conditions of TC flow. In this study, we aim to focus on the effects of ‘sinusoidal’ radial heating on the TC flow dynamics.
In TC flow problems, most codes utilise the Fourier-spectral method in the axial and azimuthal directions due to the invariance of these directions. However, in our case, as we introduce sinusoidal heating, the Fourier-spectral approach becomes inadequate for the axial direction. This is where the capabilities of Nektar++ become valuable. In this context, we are developing a solver within the Nektar++ framework that operates in cylindrical coordinates. It uses spectral-element discretisation in the radial and axial plane while retaining the Fourier-spectral method in the azimuthal direction.