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Effect of large bulk viscosity on large-Reynolds-number flows. (English) Zbl 1329.76305
Summary: We examine the inviscid and boundary-layer approximations in fluids having bulk viscosities which are large compared with their shear viscosities for three-dimensional steady flows over rigid bodies. We examine the first-order corrections to the classical lowest-order inviscid and laminar boundary-layer flows using the method of matched asymptotic expansions. It is shown that the effects of large bulk viscosity are non-negligible when the ratio of bulk to shear viscosity is of the order of the square root of the Reynolds number. The first-order outer flow is seen to be rotational, non-isentropic and viscous but nevertheless slips at the inner boundary. First-order corrections to the boundary-layer flow include a variation of the thermodynamic pressure across the boundary layer and terms interpreted as heat sources in the energy equation. The latter results are a generalization and verification of the predictions of G. Emanuel [Phys. Fluids, A 4, No. 3, 491–495 (1992; Zbl 0748.76067)].

MSC:
76N20 Boundary-layer theory for compressible fluids and gas dynamics
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