Vorticity and Vortex Dynamics 2011 Part 3 pptx
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...
Vorticity and Vortex Dynamics 2011 Part 8 pptx
... 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...
Vorticity and Vortex Dynamics 2011 Part 1 pps
... . . . . 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...
Vorticity and Vortex Dynamics 2011 Part 2 doc
... 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...
Vorticity and Vortex Dynamics 2011 Part 4 pdf
... 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...
Vorticity and Vortex Dynamics 2011 Part 6 pps
... 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...
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 ... 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;...
Vorticity and Vortex Dynamics 2011 Part 13 ppt
... 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...
Vorticity and Vortex Dynamics 2011 Part 14 pot
... 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...
Vorticity and Vortex Dynamics 2011 Part 15 ppsx
... (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...
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