Spatial optimal growth in three-dimensional compressible boundary layers

Abstract

AbstractThis paper represents a continuation of the work by Tempelmann et al. (J. Fluid Mech., vol. 646, 2010b, pp. 5–37) on spatial optimal growth in incompressible boundary layers over swept flat plates. We present an extension of the methodology to compressible flow. Also, we account for curvature effects. Spatial optimal growth is studied for boundary layers over both flat and curved swept plates with adiabatic and cooled walls. We find that optimal growth increases for higher Mach numbers. In general, extensive non-modal growth is observed for all boundary layer cases even in subcritical regions, i.e. where the flow is stable with respect to modal crossflow disturbances. Wall cooling, despite stabilizing crossflow modes, destabilizes disturbances of non-modal nature. Curvature acts similarly on modal as well as non-modal disturbances. Convex walls have a stabilizing effect on the boundary layer whereas concave walls have a destabilizing effect. The physical mechanisms of optimal growth in all studied boundary layers are found to be similar to those identified for incompressible flat-plate boundary layers.