By Stephen B. Pope
ISBN-10: 0521591252
ISBN-13: 9780521591256
Turbulent Flows is an up to date and accomplished graduate textual content in this vital subject in fluid dynamics. The publication contains elements: half I presents a basic advent to turbulent flows, how they behave, how they are often defined quantitatively, and their basic actual strategies. half II is worried with diverse methods for modeling, or simulating, turbulent flows. Key appendices current the mandatory mathematical options. whereas basically meant for engineering graduate scholars, this publication can be worthwhile to scholars in utilized arithmetic, physics, oceanography and atmospheric sciences, in addition to to researchers and training engineers.
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61) dt which, apart from the viscous term, is identical to the vorticity equation. Hence, in inviscid flow, the vorticity vector behaves in the same way as an infinitesimal material line element (Helmholtz theorem). If the strain rate produced by the velocity gradients acts to stretch the material line element aligned with ω, then the magnitude of ω increases correspondingly. This is the phenomenon of vortex stretching, which is an important process in turbulent flows, and ω · ∇U is referred to as the vortex-stretching term.
54). , ρ, ν, and Γ), and hence it has no effect on the flow. The scalar φ can represent various physical properties. It can be a small excess in temperature – sufficiently small that its effect on material properties is negligible. In this case Γ is the thermal diffusivity, and the ratio ν/Γ is the Prandtl number, Pr. Alternatively, φ can be the concentration of a trace species, in which case Γ is the molecular diffusivity, and ν/Γ is the Schmidt number, Sc. An important property of the scalar is its boundedness.
Hence, in inviscid flow, the vorticity vector behaves in the same way as an infinitesimal material line element (Helmholtz theorem). If the strain rate produced by the velocity gradients acts to stretch the material line element aligned with ω, then the magnitude of ω increases correspondingly. This is the phenomenon of vortex stretching, which is an important process in turbulent flows, and ω · ∇U is referred to as the vortex-stretching term. For two-dimensional flows, the vortex-stretching term vanishes, and the one non-zero component of vorticity evolves as a conserved scalar.
Turbulent Flows by Stephen B. Pope
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