In the region close to the thermodynamic critical point and in the proximity of the pseudoboiling (Widom) line, strong property variations substantially alter the growth of modal instabilities, as revealed in Ren et al. [J. Fluid Mech. 871, 831 (2019)0022-112010.1017/jfm.2019.348]. Here, we study nonmodal disturbances in the spatial framework using an eigenvector decomposition of the linearized Navier-Stokes equations under the assumption of locally parallel flow. To account for nonideality, a new energy norm is derived. Several heat transfer scenarios at supercritical pressure are investigated, which are of practical relevance in technical applications. The boundary layers with the fluid at supercritical pressure are heated or cooled by prescribing the wall and free-stream temperatures so that the temperature profile is either entirely subcritical (liquidlike), supercritical (gaslike), or transcritical (across the Widom line). The free-stream Mach number is set to 10-3. In the nontranscritical regimes, the resulting streamwise-independent streaks originate from the lift-up effect. Wall cooling enhances the energy amplification for both subcritical and supercritical regimes. When the temperature profile is increased beyond the Widom line, a strong suboptimal growth is observed over very short streamwise distances due to the Orr mechanism. Due to the additional presence of transcritical Mode II, the optimal energy growth at large distances is found to arise from an interplay between lift-up and Orr mechanism. As a result, optimal disturbances are streamwise-modulated streaks with strong thermal components and with a propagation angle inversely proportional to the local Reynolds number. The nonmodal growth is put in perspective with modal growth by means of an N-factor comparison. In the nontranscritical regimes, modal stability dominates regardless of a wall-temperature variation. In contrast, in the transcritical regime, nonmodal N factors are found to resemble the imposition of an adverse pressure gradient in the ideal-gas regime. When cooling beyond the Widom line, optimal growth is greatly enhanced, yet strong inviscid instability prevails. When heating beyond the Widom line, optimal growth could be sufficiently large to favor transition, particularly with a high free-stream turbulence level.

Ren et al. (2019) recently studied the stability of the boundary layer flow over a flat plate for supercritical CO2. While only one unstable mode usually exists for boundary layer flows, the authors found an additional unstable mode, whose origin has so far not been identified. In the present work, we carry out a stability analysis in the general case of a fluid following the Van der Waals equation of state and flowing over a heated flat plate in the limit of zero Eckert number. In this framework, the second unstable mode is also recovered, ruling out an acoustic origin. From the Rayleigh equation derived in the presence of density gradients, a generalised inflection point (GIP) criterion of instability exists, similar to that of fully compressible flows. Inviscid stability calculations confirm the existence of an unstable mode in the presence of a GIP, which is linked to the additional second mode found at finite Reynolds numbers. A theoretical analysis is then carried out by approximating the momentum equation for a base flow exhibiting strong gradients of dynamic viscosity. It is shown that the origin of the GIP, and hence the additional unstable mode, is associated with a minimum of kinematic viscosity at the Widom line. The universality of this result beyond supercritical fluids is eventually discussed.