On the Lagrangian description of unsteady boundary-layer separation. Part 1. General theory

摘要: Although unsteady, high-Reynolds number, laminar boundary layers have conventionally been studied in terms of Eulerian coordinates, a Lagrangian approach may significant analytical and computational advantages. In coordinates the classical layer equations decouple into momentum equation for motion parallel to boundary, hyperbolic continuity (essentially conserved Jacobian) normal boundary. The equations, plus energy if flow is compressible, can be solved independently equation. Unsteady separation occurs when becomes singular as result touching characteristics, condition which expressed solution equations. solutions remain regular. Asymptotic structures number unsteady 3-D separating flows follow depend on symmetry properties flow. absence any symmetry, singularity structure just prior found quasi 2-D with displacement thickness form crescent shaped ridge. Physically singularities understood behavior fluid element inside contracts direction expands it, thus forcing above it ejected from layer.