r
(3) - 29.2 ´10-4 k(N × kg -1)
6
(1) z = 35828(km)
(2) T = 86165(s) = 23h56m5s
7
-
1
uur N
ur ´V
r
8
(1) Ñ2fa = 0
(2) Ñ2fe = -2W2
(3) Ñ2f = -2W2
9
9
ur
ur
(1) Ñ ×V a = Ñ ×V
9
(VG Vg
)max
=
2
10 (1) VG = Vg (2) VG = Vi = const. 11 Vg = 25.1, a = 34o17'
12
12 -4.24 ´10-4o C × s-1或 -1.5o C × day-1
13 -4.09 ´10-5o C × s-1或 - 3.5o C × day-1
r j
+
k
2
z
r k
(3)
存在j＝kx2 -
ky2 2
-
kz2 2
+ C,不存在y
20 y = kxy + C
21
æ ç
-2xy
(1)
ur Ñ ´V
= (y2
r ur + x2)k,Ñ ×V
ç
=
0,
A
=
ç ç
1 2
(
y
2
- x2)
1 (y2 - x2) 2
2 xy
0
ö ÷
÷
0
÷ ÷
ç ççè
0
0
0
=－t2 6
+
3 t－ 4 23
(2)流线：ìíîzx=2－0 2y＋2tx
=0（4）迹线：íï ï
y
=
t2 2
-
1 2
即：íìî zy
= =
-3x 0
ïz = 0
ï
î
12
uur (1) Ñ ´Vh = 0 (2) j=-2axy+C
(3)y2 - x2 = 3
13 v = -2axy
14 u = -2x( y +1) + f ( y)
(2)
¶ ¶z
(
¶z ¶x
)
p
=
1 T
( ¶T ¶x
dt ¶t
2
2
ur
r
(1) V a = (u + WR)i
(2)
ur daV a
= -(u2
ur + 2Wu + W2R)R0
dt
R
3 g=g0 (1-2z/a)
4
(1) A = 310.2´10-4 (m × s-2 )
ur ur
r
(2) a = 0.628´10-4 (m × s-2 ) 5 2W ´V = -0.4375k(m × s-2 )
=
N2Hr +V
×Ñ) p
+
w
¶ ¶p
=
(¶ ¶t
ur +V
× Ñ)s
+ s& ¶ ¶s
11
习题四 自由大气中的平衡运动
1 tga = 1.0523´10-4
2 ug = 13m × s-1
3
ìïug ï
=
(
f
+
1 ugtgj )ra
¶p ¶j
ï
a
í ïïvg ïî
=
2m
h
(2) Q = - hU + r g sin a h3;U = r g sina h2
2 12m
6m
(3) u = r g sina h2 z + r g sina (z2 - hz) = r g sin a (z2 - 2hz )
6m
2m
2m
3
10
11
VB
= [2rm
gh
r
(1
-
s
2 B
]
16 1.46cm
17 7.8m，向东位移
18 0.018kg, 增加
19 -126.3m, 落在发射点的西边
20 556m
21 ¶T = -2.1oC × hr-1,降温 ¶t
22
( ¶ ¶t
+u
¶ ¶x
+v
¶ )
¶y
¶f ¶p
+s sw
+
a rCp
e
=
0
10
23
ss
=
¶ 2f ¶p2
f (5)
9 0.0286o < j < 0.286o
10 z = H ln( gH ) C pT0
11 z = T0 ,g = g 时，¶p = 0且 ¶2 p < 0
g R ¶t
¶t 2
12 39.9m × s-1
13 H = 7987(m)
14 ¶T = -0.034(oC × m-1) ¶z
¶t
+
u
¶v ¶x
+
v
¶v ¶y
=
-
1 r
¶p ¶y
ï ï-(u î
¶w ¶x
+
v
¶w ) ¶y
-
1 r
¶p ¶z
-
g
=
0
(2)不再成立
4 H = 8261m
5 H = RT0 g
6 ¶r = 0 ¶z z=H
7
(1) u =
u02
+
v02
sin(
ft
+
tan -1
u0 v0
),
v
=
(2) Ti
15 z = T0 [1- ( p0 )-Rg / g ]
g
p
16
z
=
Hq
[1 -
(
p0 p
)-R/Cp
]
16
17 O(w) = O(¶p w) ¶z
18
O(Dp
)
=
o(w) P0
= 10-6 (s-1)
19 Dp≈D,ζp≈ζ
20
(1)
tga
=
d d
x z
=
1 T
( ¶T ¶x
¶2z ) p ( ¶x2 ) p
1
习题一 流体力学基础
r
r
r
r
r
1 a = ( yz + xz2t2 )i + (xz + y2 z2t) j = 1604i + 3202 j
2
(1) 三维 （2）不是
r rr r （3）a = 27i + 9 j＋64k
3
流线：ìíîxzy==11
迹线：ìíî zx
+ =
y 1
=
-2
4
(1)
r
（3）V=xi - y j, a=xi + y j
8
(1) ¶T = -5.18 ° C / 天 ¶t
(2) ¶T = -2.68 °C / 天 ¶t
9
(1) Eulerian ur
(2) ¶V =(0,3,0) ¶rt r
(3）(V ×Ñ)V=(34+2vz,4uy+4vx,0) ur
(4) dV =(34+2vz,4uy+4vx+3,0) dt
ur
ur ur
(2) Ñ ´V a = Ñ ´V + 2W
10 d ( rv ) = 0 dt rd
11
(1) w0 = 0.2(m × s-1) , 爬坡 (2) ¶p = 0.0501(N × m-2 × s-1) = 5.5(hPa / 3hr)
¶t (3) w = -0.731´10-2 (m × s-1),下坡
（2） 941.3hPa
17 -852km
18 8.213´10-5o C × s-1或7.1oC × day-1
19
(1)13.7m × s-1 (2)11m × s-1, -11m × s-1
20
(1) 31m × s-1 (2) 59m × s-1
21 a = 28 '32 ''
22
13
《新编动力气象学》习题答案
李 国 平 编
成都信息工程学院 大气科学学院
二 O O 八年十二月
目录
习题一 流体力学基础 习题二 流体运动方程组 习题三 大气运动坐标系与方程组 习题四 自由大气中的平衡运动 习题五 尺度分析与方程组的简化 习题六 量纲分析与 Π 定理 习题七 环流定理与涡度方程 习题八 准地转动力学基础 习题九 大气边界层 习题十 大气能量学 习题十一 大气波动 习题十二 地转适应过程 习题十三 波动的不稳定理论 习题十四 热带大气动力学基础
(a
+
c)
6
x
=
x1eat
-
2 a3
-
1 a
(t 2
+
2t a
),
y
=
y1ebt
+
2 b3
+
1 b
(t 2
+
2t a
),
其中x1
=
x0
+
2 a3
, x0
=
x
t=0 ; y
=
y0
+
2 b3
, y0
=
y
t =0