Vorticity and Vortex Dynamics 2011 Part 6 pps

... integral (6. 57), consider a circular line vortex of circulation Γ and radius r 0 at the z = 0 plane, with singular vorticity distribution ω θ = Γδ(r − r 0 )δ(z). (6. 62) Then, by (6. 60), (6. 56) becomes ψ(r, ... Batchelor (1 964 ). So the q -vortex is also called the Batchelor vortex. Evidently (6. 19) satisfies (6. 11). On the other hand, the vor- ticity has a Gaussian distribution,...

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... . . . . 268 6. 3 CircularVortexRings 272 6. 3.1 General Formulation and Induced Velocity. . . . . . . . . . . . 272 6. 3.2 Fraenkel–Norbury Family and Hill Spherical Vortex . . . . 277 6. 3.3 Thin-Cored ... 2 96 6.5.2 Strained Solution in Distant Vortex Dipole . . . . . . . . . . . 303 6. 5.3 Vortex in Triaxial Strain Field . . . . . . . . . . . . . . . . . . . . . . 3 06 6 ....

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... Burgers and Lamb-Oseen vortices in s strain field, J. Fluid Mech. 378: 145– 166 . Eloy C., Le Diz`es S. (2001) Stability of the Rankine vortex in a multipolar strain field. Phys. Fluids, 13(3): 66 0 67 6. Emanuel ... coherent structure and fine- scale turbulence. Phys. Rev. E, 48(4): 266 9– 268 9. Melander M.V., Hussain F. (1994) Core dynamics on a vortex column. Fluid Dyn. Res., 13:...

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... cast to the vorticity form, very important in vorticity and vortex dynamics: Du Dt = ∂u ∂t + ω × u + ∇  1 2 q 2  ,q≡|u|. (2. 162 ) Therefore, the advective acceleration consists of two parts. One ... −η  ), (2. 166 ) ∂ϑ ∂t + ∇ 2 H = −∇ · (L − η  ). (2. 167 ) While (2. 166 ) represents the general vorticity transport equation which char- acterizes all transverse interactions, (...

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... − 1 2 ∇|B| 2  = 1 µ m  ∇·(BB) − 1 2 ∇|B| 2  , 3 .6 Circulation-Preserving Flows 121 particles; while the observation following (3. 165 ) has indicated that the X enters the Lagrangian (3. 164 ) or (3. 166 ) only through the density ... the entire incompressible fluid dynamics falls into vorticity and vortex dynamics (complemented by the potential-flow theory of Sect. 2.4.4). 3.4.1...

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... photograph by Taneda (19 56) , Re= 36. 6 4 8 12 20 60 36. 6 Fig. 4.10. Separation bubble for small Reynolds-number flow over sphere. Repro- duced from Van Dyke (1975) 178 4 Vorticity Dynamics where the suffix ... (4. 166 ) Then symbolically the (u,p) formulation reads L(u)=−∇p, ∇·u =0. (4. 167 a,b) Similar to casting problem (4.157) and (4.159) to problem (4. 162 ) and (4. 163 ), we t...

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... aspect of vorticity and vortex dynamics, and so far one’s understanding of the flow has largely been based on experimental observations even for the simplest body geometries. On the other hand, in wake-flow ... chevron-shaped oblique vortex pattern (64 <Re<178), (b) quasi-periodic mode (Re < 64 ). From Williamson (1989) 7.3 Steady Free Vortex- Layer Separated Flow 361 (a)...

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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 ... Reynolds decomposition. A combination of triple decomposition and vortex dynamics has shed light on building up statistical vortex dynamics and may be a more powerful wa...

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... the trailing edge (Wu et al. 19 96) . 12 12 In Wu and Wu (1989) and Wu et al. (19 96) the drag formula is in error. 11.3 Vorticity Moments and Classic Aerodynamics 60 5 z zЈ yЈ x Ј x y 0 0Ј a R f Fig. ... which brings in many unique and attractive topics to the vorticity dynamics and vortex motion in rotating fluid dynamics. In particular, the conservation of the potential...

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... of Vorticity and Vortices 68 5 and the other part is induced by distortions in the vortex shape (12.103b), due to the radial advection of contours relative to the vortex center by the first part. Once ˆ φ j and ... observed a transitory square vortex in their laboratory. 66 2 12 Vorticity and Vortices in Geophysical Flows Thus, from (12.59) and (12 .62 ), (12 .61 ) ca...

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