Convection in spherical Taylor–Couette flow under the influence of the dielectrophoretic force

This study investigates convection in a non-isothermal spherical Taylor–Couette flow (sTC) under the influence of the dielectrophoretic (DEP) force. The convective flow is driven by differential rotation of the inner and outer boundaries rotating with $\varOmega$ and $\Delta {\varOmega }$ in combination of an electric tension applied between both shells to induce thermo-electrohydrodynamic (TEHD) convection. To understand the interaction between DEP force-driven and rotation-driven mechanisms, we first analysed TEHD convection and non-isothermal sTC flow independently. For the TEHD case, we establish scaling relations for heat transport by expressing the Nusselt number, ${\textit{Nu}}$ , as a function of the electric Rayleigh number, ${\textit{Ra}}_{{E}}$ , and the kinetic energy density, $\tilde {E}_k$ . These relations are evaluated against classical models of convection to assess consistency and deviations. A similar approach was applied to the non-isothermal sTC flow in the absence of the DEP force, where we identified axisymmetric and non-axisymmetric flow regimes which were classified by ${\textit{Nu}}$ , $\tilde {E}_k$ and $\Delta {\varOmega }$ , and developed corresponding scaling relations. When both mechanisms were active, ${\textit{Nu}}$ generally increased, however, the DEP force locally suppressed angular momentum transport, especially near the equator. This interplay revealed three distinct regimes: (A) DEP force-dominated TEHD convection, (C) rotation-dominated non-isothermal sTC flow and (B) a transitional regime with reduced heat transport. A decomposition of a derived inflow Nusselt number, ${\textit{Nu}}^q$ , based on conductive and convective contributions, further elucidated the underlying heat transport mechanism.