Modal and nonmodal stability of a stably stratified boundary layer flow

We investigate the modal and nonmodal linear stability of a stably stratified Blasius boundary-layer flow, composed of a velocity and a thermal boundary layer. The nonmodal analysis, based on optimization of a weighted sum of the kinetic and potential energies, provides oblique optimal structures close to the wall at short target times and spanwise-homogeneous rolls at the freestream for long target times. The latter disappear when variation of stratification strength with height is accurately accounted for in the norm definition, underlining the importance of the choice of a meaningful norm for thermal boundary layer optimization.