Linear instability in Taylor–Couette flows with non-ideal fluids

We present a systematic linear stability analysis of Taylor–Couette flows with non-ideal fluids, taking carbon dioxide near its critical point as a representative working fluid. By exploring different thermodynamic states (subcritical, transcritical, and supercritical), rotational configurations (single-, co-, and counter-rotation), and multiple equations of state, we reveal how thermodynamic non-ideality, compressibility, and rotational shear synergistically impact the flow stability. We show that the subcritical state is the most unstable state under counter-rotation, the transcritical state is the most complex state, and the supercritical state generally suppresses instability. However, compressibility exhibits state-dependent behavior: instability is enhanced with increasing fluid compressibility PrEc in the subcritical state but varies non-monotonically in the transcritical state. Significant discrepancies are found between real-fluid and ideal-gas predictions, particularly near the critical point, underscoring the necessity of an accurate thermodynamic model. Furthermore, modal analysis demonstrates that disturbances with azimuthal wavenumbers n=0−2 typically dominate, although higher-order modes may prevail under strong counter-rotation. Finally, by performing the energy budget analysis, we identify that the shear production is the primary energy source, while non-ideality modifies energy transfer via coupling thermal and velocity perturbations. Our findings may advance the fundamental understanding of Taylor–Couette flows with non-ideal fluids and provide insights for predicting and controlling the stability of real-fluid systems that operate near critical conditions.