Linear stability analysis of differentially heated wall-bounded high-pressure transcritical fluids

Mixing and heat transfer rates are typically enhanced in high-pressure transcritical turbulent flow regimes. This is largely due to the rapid variation of thermophysical properties near the pseudo-boiling region, which can significantly amplify velocity fluctuations and promote flow destabilisation. The stability conditions are influenced by the presence of baroclinic torque, primarily driven by steep, localised density gradients across the pseudo-boiling line; an effect intensified by differentially heated wall boundaries. As a result, enstrophy levels increase compared with equivalent low-pressure systems, and flow dynamics diverge from those of classical wall-bounded turbulence. In this study the dynamic equilibrium of these instabilities is systematically analysed using linear stability theory. It is shown that under isothermal wall transcritical conditions, the nonlinear thermodynamics near the pseudo-boiling region favour destabilisation more readily than in subcritical or supercritical states; though this typically requires high-Mach-number regimes. The destabilisation is further intensified in non-isothermal wall configurations, even at low Brinkman and significantly low Mach numbers. In particular, the sensitivity of neutral curves to Brinkman number variations, along with the modal and non-modal perturbation profiles of hydrodynamic and thermodynamic modes, offer preliminary insight into the conditions driving early destabilisation. Notably, a non-isothermal set-up (where walls are held at different temperatures) is found to be a necessary condition for triggering destabilisation in low-Mach, low-Reynolds-number regimes. For the same Brinkman number, such configurations accelerate destabilisation and enhance algebraic growth compared with isothermal wall cases. As a consequence, high-pressure transcritical flows exhibit increased kinetic energy budgets, driven by elevated production rates and reduced viscous dissipation.