Estimation of River Banks Influence on Tachoida Shape at the Meridian - Experimental Methods in Hydraulic Research - page 219

where

C z ; C y ¼ const (16)

and furthermore:

Z

z
H

1

f 2 ð z Þ¼ d z (17)

K z ð z Þ

Z

y
B

1

f 1 ð y Þ¼ d y (18)

K y ð y Þ

Moreover, as it has already been assumed,

z
z 01

K z ð z Þ¼ K 0 z 1 þ (19)

y
z 02

K y ð y Þ¼ K 0 y 1 þ (20)

and

K 0 z
k z

K 0 y
k y

z 01 ¼

u z ;

z 02 ¼

u y

In the above equations, subindexes z and y indicate that the symbols are taken
along certain axes. The scheme of the flow elements is given in Fig. 3 . In the above
equations, K 0 z denotes the eddy viscosity coefficient at the bottom and K 0 y denotes
the eddy viscosity coefficient at the river bank. And furthermore, z 01 is the linear
measure of bed roughness, and z 02 the linear measure at the river bank roughness; k z
and k y denote von Karmann coefficients in vertical and horizontal directions,
respectively.

t 1

υ

B 1

1 y 1

x max

midstream

B

υ

x

B 2

2

y 2

t 2

Fig. 3 Scheme of changes of flow elements in the horizontal plane