Vorticity and Vortex Dynamics 2011 Part 16 potx
Vorticity and Vortex Dynamics 2011 Part 16 potx
... ∼,504–506 vortex collapse, 424 vortex core, 387–395, 485, 490, 496, 672,673, 680∼ dynamics, 395–399, 559–561 vortex dipole, 289–291, 303–306 vortex dynamics, 1, 3–8, 56, 67, 94, 173,451–698 vortex ... (Continued)normal vorticity continuity, 31surface-force continuity, 30, 146boundary enstrophy flux, 144, 147, 148,153, 166 , 171boundary layer, 3–7, 161 –172, 218, 651,687∼ equations, 159, 163 , 165 , 167 , 169 ,170, ... instability, 475∼ on free surface, 162 , 168 –172∼ on solid wall, 73, 162 167 , 591,627, 629∼ separation, (see separation,boundary layer), 7Blasius ∼, 166 , 167 , 476Lagrangian ∼ equation, 241,...
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Vorticity and Vortex Dynamics 2011 Part 1 pps
... . . . . . . 477 Part I Vorticity Dynamics PrefaceThe importance of vorticity and vortex dynamics has now been well recog-nized at both fundamental and applied levels of fluid dynamics, as alreadyanticipated ... vorticity and vortex dynamics. 2The aim of this book is to present systematically the physical theory of vorticity and vortex dynamics. In this introductory chapter we first locatethe position of vorticity ... vorticity and vortex dynamics in fluid mechanics, then brieflyreview its development. These physical and historical discussions naturallylead to an identification of the scope of vorticity and vortex dynamics, ...
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Vorticity and Vortex Dynamics 2011 Part 2 doc
... cast to the vorticity form, very important in vorticity and vortex dynamics: DuDt=∂u∂t+ ω × u + ∇12q2,q≡|u|. (2 .162 )Therefore, the advective acceleration consists of two parts. One ... fluid motion, and becomes a flexible extensionof the bodies whose movement generates the flow; bring the walls to rest and the fluid stops immediately.”Summary1. The vorticity and vortex dynamics ... to vorticity moments.74 3 Vorticity Kinematics(a)(c)BU(b)t2>t1t1AFig. 3.5. (a) Vorticity lines in a tornado-like vortex. (b) Vorticity lines in a cup ofrotating water. (c) Vortex...
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Vorticity and Vortex Dynamics 2011 Part 3 pptx
... 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 Vortical Impulse and Angular ImpulseIt has long ... 4.1.3.5.1 Vorticity Evolution in Physical and Reference SpacesThe time-evolution of vorticity in physical space comes from the curl of the vorticity form of the material acceleration, (2 .162 ), and ... Circulation-Preserving Flows 121particles; while the observation following (3 .165 ) has indicated that the Xenters the Lagrangian (3 .164 ) or (3 .166 ) only through the density ρ = J−1ρ0.Thus, the dynamics of...
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Vorticity and Vortex Dynamics 2011 Part 4 pdf
... with the kinematic prob-lem, say (4 .162 ) and (4 .163 ) with ϑ = 0. In (4 .168 b) and (4 .169 b) the accel-eration no-through and no-slip conditions, (2.70a) and (2.70b), are imposedrespectively. ... (4 .166 )Then symbolically the (u,p) formulation readsL(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 take the divergence of (4 .167 a) ... equations from ∇×ω = 0 and condition ∇·u = 0 for three4.2 Vorticity Field at Small Reynolds Numbers 1554.2.3 Separated Vortex and Vortical WakeFrom the point of view of vorticity dynamics, a remarkable...
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Vorticity and Vortex Dynamics 2011 Part 6 pps
... +Br, (6.20)where A and B are arbitrary constants. For a flow between two rotatingcoaxial circular cylinders with inner and outer radii R1 and R2 and angularvelocity Ω1 and Ω2, respectively, ... all vorticity lines being along the axis and all streamlines are closed circles centered at thez-axis. Then, if w is nonzero and r-dependent, ωθwill appear too such thatthe velocity and vorticity ... u and w by (3.57) butnot v:u = −1r∂ψ∂z,w=1r∂ψ∂r. (6.8)Thus, the velocity and vorticity, and hence their governing equations, can beexpressed in terms of two scalar functions, ψ and...
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Vorticity and Vortex Dynamics 2011 Part 8 pptx
... aspect of vorticity and vortex dynamics, and sofar one’s understanding of the flow has largely been based on experimentalobservations even for the simplest body geometries. On the other hand, inwake-flow ... Recr1. The vorticity generatedat the cylinder surface by a strong adverse pressure gradient (characterized8Core Structure, Vortex Filament, and Vortex System8.1 Vortex Formation and Core StructureThe ... (7.55), (7.57), and (7.58)are all necessary input. A major difficulty is that once the vortex sheet rollsinto a vortex with distributed vorticity and spiral arms (Chap. 8), inside the vortex core...
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Vorticity and Vortex Dynamics 2011 Part 12 ppt
... 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. Acombination of triple decomposition and vortex dynamics has shed light onbuilding up statistical vortex dynamics and may be a more powerful way outin turbulence studies. ... (10.1)where Φ is its time-mean, and ϕc and ϕrare its coherent and random compo-nents, respectively.Neglecting the correlation between the coherent and random motions, thecoherent energy...
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Vorticity and Vortex Dynamics 2011 Part 13 ppt
... which brings in many unique and attractivetopics to the vorticity dynamics and vortex motion in rotating fluid dynamics. In particular, the conservation of the potential vorticity is so fundamentalthat ... therest part of force and moment caused by attached vortex sheet with nonzerocirculation and free vortex sheet in the wake, denoted by suffix γ. We considera thing wing represented by a bound vortex ... derivative-momenttransformation, the new integrands (in the present theory, the first and secondmoments of ω) do not represent the local density of momentum and angular11.3 Vorticity Moments and Classic Aerodynamics 5990.80.60.40.20-0.2-0.40.9...
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Vorticity and Vortex Dynamics 2011 Part 14 pot
... 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 to the vortex center by thefirst part. Onceˆφj and ... (12.104b)Remarkably, owing to the vortex- patch approximation, the (q,φ)partisindependent of the vortex distortion ηjbut simply advected by the plane-tary vorticity r sin θ and the axisymmetric vortex with rate ... has two parts. One is expressed by (12.104) and generated directly by the advection of the planetary vorticity r sin θ,12.3 Quasigeostrophic Evolution of Vorticity and Vortices 679 vortex. Its...
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