By Herbert Steinrück
A survey of asymptotic tools in fluid mechanics and functions is given together with excessive Reynolds quantity flows (interacting boundary layers, marginal separation, turbulence asymptotics) and coffee Reynolds quantity flows as an instance of hybrid tools, waves to illustrate of exponential asymptotics and a number of scales tools in meteorology.
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Extra resources for Asymptotic Methods in Fluid Mechanics: Survey and Recent Advances
In the oxygen distribution process of the micro-circulation, oxygen binds to its carrier, haemoglobin, in red blood cells, which transports it through the arterioles, branching to the capillary networks, to the collecting venules. In the capillaries, the oxygen is released from its carrier and diﬀuses into the surrounding tissue. The reviews of Popel (1989), Fletcher (1978), and the references in Titcombe and Ward (2000), provide substantial information on theoretical research in this area. x2 x3 x1 Capillary Cross-section 2-D cut Figure 2.
We then formulate the hybrid method for summing the inﬁnite-order logarithmic expansions that arise from the analysis. In the Stokes, or inner, region deﬁned by ρ = O(1), the stream function has an inﬁnite logarithmic expansion of the form u = ∂y ψ = sin θ ∂ρ ψ + cos θ ∂θ ψ , ρ v = −∂x ψ = − cos θ ∂ρ ψ + ∞ ν j ψj (ρ, θ) + · · · . ψs (ρ, θ) = (67) j=1 Here, we deﬁne ν = ν(εdf ) ≡ −1/ log εdf e1/2 , where df is a shapeparameter that is speciﬁed below in terms of the far-ﬁeld behavior of a Biharmonic problem.
Springer, 8th edition, 2000. M. Ungarish. Hydromechanics of Suspensions. Springer, 1993. M. Van Dyke. Perturbation Methods in Fluid Mechanics. The Parabolic Press, Stanford, annoted edition edition, 1975. ¨ Th. von Karman. Mechanische Ahnlichkeit und Turbulenz. Ges. Wiss. -Phys. , pages 58–76, 1930. J. D. A. Walker. Turbulent boundary layers ii: Further developments. In A. Kluwick, editor, Recent Advances in Boundary Layer Therory, volume 390 of CISM Courses and Lectures, pages 145–230. Springer, 1998.
Asymptotic Methods in Fluid Mechanics: Survey and Recent Advances by Herbert Steinrück