Vortex-Wave Interaction Theory: Exact Coherent Structures & Roughness

The interaction of waves and streamwise vortex structures in high Reynolds number shear flows is investigated. The theory applies to both inviscid and viscous (Tollmien-Schlichting) waves in fully developed or boundary layer flows. The different kinds of interactions possible at high Reynolds numbers are described and their application to understanding exact coherent structures is described. The predictions of the interaction equations are shown to be in remarkable agreement with finite Reynolds number calculations and to predict several features of fully turbulent shear flows. The interaction equations can also be used to describe how wall forcing, caused by for example transpiration or wall roughness, modifies exact coherent structures and indeed generates new coherent structures. The new type of structure is associated with streamwise mean flow waviness induced by the forcing which causes a new kind of instability.