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( ) .., .. () . . ON EXACT SOLUTION OF A PROBLEM OF WIND FLOW IN CLOSED RESERVOIR (THREE-DIMENSIONAL CASE) Gavrilova L.V., Kompaniets L.A. (Krasnoyarsk) An exact solution of wind motion model of a homogeneous fluid in a closed shallow reservoir is obtained when flow is stationary and coefficient of turbulent diffusion is constant. The solution can be used for testing of numerical algorithms. ( , , , , ). , , . . [1] [2, 3].
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g u u dz, - - lv = K - g x 0 x t z z z v v + lu = K t z z u v + x y T T T +u +v + t x y y w + = z T w = z -g - 0, T KT . z z g

0



0z



0

dz, y

(1)

u = u(t , x, y , z ) , v = v (t , x, y , z ) , w = w(t , x, y, z ) ­ V = (u, v, w) ; g ­ ; l ­ ; K ­ , K = K (t , x, y, z ) ; ­ ( x, y, z ) , = (T ) , 0 ­ ; T = T (t , x, y , z ) ­ ; ; KT ­ = (t , x, y ) ­ . z . (2) Vn = 0 ( 0) T (3) =0. n (, z 0 = 0 )
K u z =
z =0

Q T KT , = z C p 0 = w. t

v 1 ,K z 0

=
z =0

2 , 0
(4)

228


.. . -- -10, 2002, .227-229

z = - H ( x, y )
K u z
z =-H

= kbu V ,

K

v z

z=-H

= kb v V

(5)

H H w=u +v . x y

(6)

T (7) = 0. z (4) (6) Q1 Q2 + + = 0, (8) t x y
Q1 =
-H



0

u dz , Q2 =

-H



0

v dz.

= ( 1 , 2 ) ­ ; n ­ ; k b ­ ; Q ­ , ; C p ­ . , , x = 0 , y = 0 , , . (1) (2) ­ (7) . . 1. . 2. . (1) (8)
229



- lv + g
lu + g

u = K , x z z

(9) (10)

v = K , y z z
y

-H

(u

0

x

+v

)

dz = 0,

(11) (12)

u v w + + = 0. x y z

(9) ­ (12) . (9) ­ (12) , (9) ­ (11) (12). u v. . 3. ( , [5]). 4. u v ( kb = 0 ). 5. ( K = const ). 6. ( H = const ).
g g
0

u = K , x z z = y z
x

(13) (14)

v K z

,

-H

(u

+v

y

)

dz = 0,

(15)

230


.. . -- -10, 2002, .227-231


u
n

= 0, = 1 (x, y ), 1 (x , y ) = = 2 (x, y ), 2 (x, y ) = = 0,
z=-H

(16)

K

u z v z u z v z

z =0

1 (x , y ) , 0 2 (x , y ) , 0

(17) (18) (19) (20)

K

z =0

K

K

= 0,
z=-H

u = (u, v ) . (x, y ) z 2 H u= 1 + z + ,
K 2H 3 v=

2 (x , y ) z 2 H +z+
K 2H 3

(13) ­ (15) (17) ­ (20). (16) 1 ( x, y ) , 2 ( x, y ) . , ­ , un = 0 , 1 ( x, y ) = - x , 2 ( x, y ) = y

231


. 1.

, [5] (9) ­ (12) . [4] , (9) ­ (12) , , . (1) . , . 1 ( ) ( ) 450 10 , 2 3 . (18) 1 ( x, y ) = - x 10-8 2/2,

2 ( x, y ) = y 10

-8

2/2,

.

K = 10 -6 , 2/. , -

232


.. . -- -10, 2002, .227-233

. 2. z=0, .

. 3. z=0, .

CRDF, REC-002.

. 1. .., .., .. . , 3, 1981 ., . 91 ­ 99. 2. .. -. , , 1979, 5, . 129 ­ 137. 3. .. . , , , 84, 1988, . 62 ­ 75. 4. .. . ­ .: , 1978. 5. .. . ­ .: , 1983.

233