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Russian Academy of Science Institute for Problem in Mechanics
Roman N. Bardakov
Internal wave generation problem exact analytical and numerical solution
gvv
νzP
t 00
00v
zt0div v
pressuredensity,velocity,)zv,yv,x(v Pv
Basic set of equations
.0v
,22
v
0
0
zz
zxxUt
aUt
axU
Boundary conditions
Boundary conditions
02
2
2
2
2
2
22
2
2
2
2
2
2
zxtxN
zxt
.0
,22
0
0
z
z
x
xUta
Uta
xUz
Navier-Stokes equation for stream function
3
222 4
112
,Nkii
kkkw
3
222 4
112
,Nkii
kkki
dkkkUkkkUkee
eka
kiU
tzxiw
zkkUiikzkkUwikUtxik
,,2sin
1,,
,,
Exact solution for stream function
Dispersion equation
022222222
zkkikNzkk
Velocity absolute value
L = 1 cm, plate moving speed U = 0.25 cm/s, buoyancy
period Tb = 14 s. (Fr = U/LN = 0.55, Re =UL/ = 25,
= UTb = 3.5 cm).
Vertical component of velocity L = 1 cm, plate moving speed U = 0.25 cm/s,
buoyancy period Tb = 14 s. (Fr = U/LN = 0.55, Re =UL/n = 25, l = UTb = 3.5 cm).
Stream lines (N = 0.45 s-1, U=0.25 cm/s =UTb=3.5 cm, L=4 cm, Fr =
0.14)
Absolute value (left) and horizontal component (right) of velocity
boundary layer (U = 1 cm/s, L = 4 cm, Fr = 0.56, Re = 400, N = 0.45 s-
1, = UTb = 14 cm).
Vertical component of velocity boundary layer
(U = 1 cm/s, L = 4 cm, Fr = 0.56, Re = 400, N = 0.45 s-
1, = UTb = 14 cm).
0.2 0.4 0.6 0.80
1
2
3
2.5 см 5 см 10 см
Z/(a)-2
X
0.2 0.4 0.6 0.80.0
0.1
0.2
0.3
0.4
0.5
0.6
2.5 см 5 см 10 см
Z
X
=7.5 с, =0.11 см, =20 см, =2.6
0.11 cmN N 7.5 c,bT 20 cm,bUT 3 2.6,L g N
Vertical component of velocity (N = 0.45 s-1, U=0.25 cm/s, =UTb= 3.5 cm, Fr = 0.014,
Re = 1000)
Absolute value and vertical component of velocity. (N = 1 s-1, Tb = 6 s, U=0.01 cm/s, =UTb=0.06 cm, L=1
cm, Fr = 0.01, Re = 1)
Comparing with experimental results
Comparing with experimental results