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Bed topography in the bend
ROZOVSKII (1957), showed theoretically that the deviation angle δ can be expressed for smooth
channels by:
tanδ
and for rough channels by:
tanδ
v r
= ---- =
v θ
g
v
F
---- r 1 1
( z)
–
κ
---------- ⋅
⋅ C
F ( z ) 2 h
---- ------------------------------------------------ s
v θ κ 2 ⋅ ⋅ ---- k h s
= = = ⋅ ----
g
1 +
κ
----------- ⋅ (
⋅ C
1 + ln z
r r
)
1
----
κ 2
g
F 1
( z)
–
κ
---------- ⋅ [
⋅ C
F ( z ) + 0.8 ⋅ ( 1 + lnz)
]
2
⋅ --------------------------------------------------------------------------------------------- ⋅
g
1 +
κ
----------- ⋅ (
⋅ C
1 + ln z )
(3.69)
(3.70)
where z is the elevation above bed level and the functions F 1
and F 2
are given with:
2 ⋅ lnz
F 1 ( z)
= ∫
-------------- d and (3.71)
z – 1
z
ln
F 2 ( z)
2 z
= ∫---------- dz
z – 1
In both equations (3.69, 3.70), a variation of the Chezy coefficient has only a small influence on
the deviation angle δ . Approaching these equations by a linear equation, the coefficient k (eq.
3.69) takes the value of 10 to 12 for smooth and of 11 to 11.5 for rough surfaces.
ROZOVSKII compared his equation with a factor k = 11 against laboratory data of nine other
authors and his own laboratory data, covering a large range of parameters
( V = 0.01 ÷ 0.68 m ⁄ s, Fr = 0.03 ÷ 0.68 , Re = 3 000 ÷ 300 000 , h ⁄ B = 0.02 ÷ 1.20 ,
h ⁄ R c
= 0.01 ÷ 2.40 ) with rectangular, triangular and parabolic cross-sections. He completed his
data set with measurements on the Desna River in a reach located between Chernigov (Ukraine)
and the confluence with the Dnjepr. The Desna has a very tortuous course flowing through sandy
alluvial bed material ( R c
≈ 400 m ). Comparisons show an excellent agreement between measured
and computed values (see Fig. 3.9).
h
---- s
r
EPFL Ph.D thesis 2632 - Daniel S. Hersberger November 9, 2002 / page 45