Vorticity and Vortex Dynamics 2011 Part 3 pptx

... =const. (3. 132 ) This theorem has two important corollaries. First, setting S = X in (3. 131 ) and define Ω(X,τ) ≡ ω ρ · F −1 (3. 133 a) as the Lagrangian vorticity, which is the image of the physical vorticity ... (see Appendix A.4 and a comprehensive study of Casey and Naghdi 1991). Then by (2.1), (3. 107), and (3. 109), we have ∂Ω ∂τ = 0 or ω ρ = ω 0 ρ 0 · F, (3. 133 b) known a...

Ngày tải lên: 11/08/2014, 17:22

... amplitude and spectra of free-stream turbulence, aspect ratio of the cylinder, end conditions, and blockage ratio, etc. 7 .3 Steady Free Vortex- Layer Separated Flow 35 5 which by (4. 132 ) and (4. 133 ) is ... c is Re c = Wc/ν, (8 .34 ) implies that Batchelor’s linearized vortex- core theory is applicable at z ∼ 0.01cRe c A 2 , 7 .3 Steady Free Vortex- Layer Separated Flow 35 9...

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... . . . . 38 1 8 Core Structure, Vortex Filament, and Vortex System 38 3 8.1 Vortex Formation and Core Structure . . . . . . . . . . . . . . . . . . . . . . 38 3 8.1.1 Vortex Formation by Vortex- Layer ... vorticity and vortex dynamics. 2 The aim of this book is to present systematically the physical theory of vorticity and vortex dynamics. In this introductory ch...

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... b = e 3 direction and (3. 2) is reduced to ω = ωe 3 =  q r + ∂q ∂r  e 3 = 1 r ∂(rq) ∂r e 3 (3. 4) in which r = κ −1 is the radius of curvature and dr = −dn. An axisymmetric rectilinear vortex ... r 2 )ω dV, (3. 8) so M/ρ is solely related to vorticity moments. 74 3 Vorticity Kinematics (a) (c) B U (b) t 2 >t 1 t 1 A Fig. 3. 5. (a) Vorticity lines in a tornado-like...

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... model and interface flow is that, 186 4 Vorticity Dynamics 30 -30 0 30 -30 0 30 -30 0 30 -30 0 30 -30 0 30 -30 0 0 1.0 0 1.0 (a) (b) Fig. 4. 23. Rayleigh–Taylor instability of an interfacial vortex ... to C D = 12 Re  1+ 3 8 Re + 9 40 Re 2  ln Re + γ + 5 3 ln 2 − 32 3 36 0  + 27 80 Re 3 ln Re + ···  , (4.80) where γ =0.5772 is the Euler constant, exa...

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... vortical impulse I given by (3. 78) and Lamb’s second formula (3. 93) for kinetic energy K. The circular vortex ring is allowed to have arbitrary cross-sectional shape and vorticity dis- tribution ... magnitude but opposite sign are also called vortex dipoles. Lamb in 1895 and 1906 (the second and third editions of Lamb 1 932 ) and Chaplykin in 19 03 (see Meleshko and van...

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... efforts have naturally in turn enriched the content of vorticity and vortex dynamics (e.g., Melander and Hussain 1993a and 1994, Pradeep and Hussain 2000; Hussain 2002). We expect that the present ... Saffman and Baker 1979; Leonard 1985; Hunt 1987; Ashurst and Meiburg 1988; Virk and Hussain 19 93; Hunt and Vassilicos 2000; Lesieur et al. 2000; Schoppa and Hussain 2002;...

Ngày tải lên: 11/08/2014, 18:20

... body-volume integrals in (11 .31 ) and (11 .32 ) by the rate of change of identities (3. 80) and (3. 81a) applied to B. This yields F = −ρ dI f dt + ρ k d dt  ∂B x × (n × b)dS, (11 .33 ) M = ρ 2 dL f dt − ρ 2 d dt  ∂B x 2 n ... which brings in many unique and attractive topics to the vorticity dynamics and vortex motion in rotating fluid dynamics. In particular, the conservat...

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... considering the vortex- shape distortion. Crosses denote τ =1, 2, 3, 4. Adapted from Sutyrin and Flierl (1994) 12 .3 Quasigeostrophic Evolution of Vorticity and Vortices 681 130 10 15 20 25 30 40 50 35 45 135 ... of Vorticity and Vortices 685 and the other part is induced by distortions in the vortex shape (12.103b), due to the radial advection of contours relative t...

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... (x 1 ,x 2 ,x 3 )-frame read (∂ i f) ·e j =    c 11 c 12 c 13 c 21 c 22 c 23 ∂ 3 f 1 ∂ 3 f 2 ∂ 3 f 3    , (A.83a) where c 11 = ∂ 1 f 1 − κ 1 f 2 − b 11 f 3 c 12 = ∂ 1 f 2 + κ 1 f 1 − b 12 f 3 c 13 = ... Heidelberg New York 30 9 32 1. Lugt H.J. (19 83) Vortex Flow in Nature and Technology. Wiley-Interscience. Lugt H.J. (1996) Introduction to Vortex Theory. Vort...

Ngày tải lên: 11/08/2014, 18:20