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Asymptotic analysis of laminar boundary-layer flow over finely grooved surfaces. (English) Zbl 0835.76024
Summary: A set of matched asymptotic expansions is developed for laminar flow over grooved surfaces, which gives a formal mathematical justification and provides higher-order corrections to the separate study of the viscous sublayer pervading the grooves and of the essentially two-dimensional boundary layer far above. The question of whether, under various conditions, laminar drag is reduced or increased by grooves is answered with the aid of theoretical bounds concerning the protrusion height. The three-dimensional effect of the presence of grooves is reduced to an equivalent wall condition for the two-dimensional boundary layer equations.

76D10 Boundary-layer theory, separation and reattachment, higher-order effects
35Q35 PDEs in connection with fluid mechanics