VELCJC[TI - John List for numerous discussions on the analysis and physical interpretation of t

m 0 GG

G G G G G G G G G G G (3 cj3G (3 G G G G G G G G

a Cl

..,,

::0 r J:l

c

... ...

z

CJ U1 ti) ...

...

N N f"T1 rr1

< rn

I G

n

1--i -I

-< <

U) -I t--i 3;

rn

.

V1 0. ro rr Pl '-s (D () 0 '"1 0.

.

I\) 0 -l

...

3: 1"11 ,..., (f) 1"11

n

w Ol 0 w Cl) 0 U1 I\) 0

(3 G

G G G G G G

VELOC£Tl'

I-' 0 (.) Ill ("1" ... 0 ::I 0

VELLJC I TI

..J OJ a ..J Cl) 0 co CJ CJ co I\) a co .i:: 0 CXl CJ) 0 co l\J 0 IC II= CJ IC Ol a co OJ CJ

...

0 CJ CJ

...

0 l\J CJ

...

G G G

G G ~ G G G G G ~ ... ...._._ ... .._._,_._.._.__._._. ... ~11:1.1 CJ

G G

O'l

G3

G G

G G G G G G G G G G Gd3 G(j3 G G G G G G

(3 C") :::IJ JJ ...

z

(/) ... N rn G

tO 0

.,,

r c ... 0 (/) ... N rn

location 1.80, Figure 8.1.4, are very similiar to those obtained at location 2.70. At location 1.20, Figure 8.1.5, a wavy character is again observed. The oscillations are now due to intermittent

undulations in the sediment bed. Many of the sediment grains lag the nearby fluid. The effect of bed undulations is seen most clearly in Figure 8.1.6, location 0.75. The velocimetry record contains periods in which little or no data was collected. The gaps in the data are caused by undulations in the sediment bed which completely blocked the laser light beams.

Figures 8.1.7 and 8.1.8 illustrate the effects of the filter used on the fluid velocity measurements in the preceding figures. The

unfiltered data appear in the lower plot of each figure. Trends in the fluid velocity data record are more easily seen in the filtered plot.

The filtered plots must be viewed with care, however, when comparing the fluid and the sediment grain velocity. The velocity of some of the sediment grains seems very different from the nearby filtered fluid velocity measurements. Filtering the fluid velocity removes many of -

the extreme fluctuations. Comparison of the filtered plots to the unfiltered plots shows that this apparent difference in the sediment grain and fluid velocity is primarily due to the filtering. The

sediment grain velocity is seen to be quite similiar, in most cases, to the nearby fluid velocity.

Some grains are observed to have a velocity different from that of the surrounding unfiltered fluid, but this still may not be the case within the flow. The fluid velocity data record may lack measurements of the "surrounding" fluid velocity. Portions of the unfiltered data

.µ (1j

(1j

t..

.µ Q)

s Q)

·rio

() 0 0 • ,..., l.D Q) > ^i:::

Q) ·ri .-I .µ Cl. lil Cl) ,...,

mg

i:-

.

...

0 N

w w

N N

o z

E) E) E)

0 ₀

.U I J013A

r-0

0 (J)

0 OCl

0 r-

0 '°

u w

(f) o~

If)

0 ::I'

0 ('()

0 (\J

0 I -

D lD 0

lf') E)

El ^{E) E)} E)

E) El E)E) E)

€) E) El

E) El ^E)

'Cl

Q) El

.µ Q) §

,..., .,..;

c....

Fl 10 ^EID

El El

w w

N N

D z

:;::) a:

_J :]i

l.J_

0 £

-

.U1J013A

>- I- ... u 0 __J w > >- I- ... u 0 __J w >

Figure 8.1.8 Sample velocimetery data record, filtered and unfiltered, location 1. 80 100[ I I I I I I I I ' j I i i I i I I I I I I I I I I I I I I j I I i I i I I I I j I i I i I I i I I J I I i I i I I I I I I I I I I I I I I j I I I I I I I i I j I I I I I I I I I j I I I I I I I I I_] so 50

FLUrD SflE m GRAIN SIZE (!) (!) (!)

(!) (!)

(!) (!) (!) ~ (!) (!)

(!)

SQ18l (!) (!) <®mg(!)

~(!) ~C)~

gi lC) 'l!iQJ ,wu,

~k~i~~

• H

~.F, ~J;I /V

~·!.~'~

.ln _t,], 1, ·; Ii ,.,,,~J

~

^·ii

^t¥

¹ ¹^~:1;^i:^v:~

Qlftf©. •_:i "'flcqf•!,r QJ 1£QJ ~·' ~ .!!.fn11 I C) & C) (!) ('.) (!) (!) ijQt1 I! I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I 0 10 20 30 1,10 50 60 70 80 90 100 T 1 ME (SE Cl filtered 100[ I I I I I I I I I j I I i I i I I I I I i I I I I I I I I j I i I I I I i i I I I I I I I I I i I j I I i I I I I I I I I i I I I I I i I i i I I I I I I I I i I I i i I I I i I I I I i t I I I I I I so

-FLUID SIZE e GRAIN SIZE (!)

SQ181 (!) 140r,,,,,,,,, 1,,,,, I,,, 1,,,,, , , , , 1,,,, , , , , , 1,,,,., , , , 1,,,,,,,, , 1,,,,,,,,, 1,,,,,,,,, 1,,, , , , , , , 1, , , , , , , , 11 0 10 20 30 1,10 50 60 70 80 90 LOO TJME CSECl unfiltered

records shown in the previous Figures are expanded in Figure 8.1.9 to allow each fluid velocity measurement to be identified with a second plotting symbol. At approximately t=17 seconds the fluid velocity data record from location 6.00 contains a gap. No measurements of the fluid velocity were made. The sediment grain velocity recorded at this time seems to differ from the plotted fluid velocity, but there are no measurements of the fluid velocity very near to the grain. The times of measurement of fluid and sediment grain velocity are not coincident and the resulting data records are not continuous.

8.2 Measurements of fluid and sediment grain velocity

Profiles of the mean velocity of the fluid, u, and the sediment grains,

u ,

_g are shown in Figure 8 .2. 1. The mean velocities computed from the different data records obtained at a single location are noted to vary. This is most probably due to slow, long time-scale

fluctuations in the flow. A comparison of u and u is presented in

Figure 8.2.2. In the lower portion of the flow, ug is less than u. At location 6.00, near the water surface, the sediment grains are observed to move significantly faster, in the mean, than the fluid.

Profiles of the standard deviation of the velocity of the fluid,

~and

the sediment grains,

'\/u

¹² ^, are shown in Figure 8.2.3.

Profiles of the relative velocity fluctuation, the local value of the standard deviation expressed as a percentage of the local mean, are given in Figure 8.2.4. The fluid velocity observations are in accordance with existing experimental measurements. Comparisons of

~and~

are given in Figure 8.2.5 and Figure 8.2.6. Throughout

Figure 8.1.9 Sample expanded scale velocimetry data records, locations 6.00 and 1.80 1201 I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I Ir I 110

x FLUID SIZE l!l GRAIN SIZE -FLUID SIZE SQ60l C) (!)

§ "°! ~\

I~ l~

~

iJ© ©1~ yf\ l ~

(!) 0 90 _J w > >- I- .._. u 0 _J w >

ao 70 601 I ! ! I ! I I I j } ! I ! ! I I I I I } t I ! ! I ! I ! 1 J I I I ! I I I I I I ! I I ! ! I ! ! I J 1 I I I I I I I I ! I I I I I I ! I ! I ! ! ! I I I ! ! I I I I I I I I I I I J t I I I I I I I I I 15 15.5 16 16.5 17 17.5 18 18.5 19 19.5 20 TI ME (SECl 1001 1 1 1 J 1 1 t 1 1 1 J 1 1 1 1 i Ji Iii iii i ii 1 1 I I Ii I I If I Ii I I I I I I I I I I I I I I I I I I I JI I I I I I I I I I I I I I I I I I If I I I I I I I I I j I I I Ii I I I ij 90 00 70

x FLUlD SIZE l!l GRAIN SIZE -FLUrD SIZE ~ )!; I ·11 (!) (!)(!) 601-l so

SQ18l "

* *

U\1\ I C) LJ.otj , , , , , , , , 1 , , , , , , , , , 1 , , , , , , , , , 1 , , , , , , , • , 1 , , , , , , , , , 1 , , , , , , , , , 1 , , , , 1 , , , , 1 , , , , , , , , , , , , , , , , , , , , , , , I , , ! , 1 , 15 15.5 16 16.5 17 17.5 18 18.5 19 19.5 20 TI ME (SE Cl

100 i" "'" i I j Iii I I; i I if iii I I Ii 11 j It i I Ii Iii I I I Ii I I} I ij I Ii I I I I I I j FLUID SIZE .Y

d

10-1 lll 16

# IA

u

u*b

4/~

100 I' I''''''' I''''' I''' I''''''''' I'''''' .. ' I''''''''' I''''}'''' I y

d

GRAIN SIZE x x

I( + & A/A 10-1 I 1 f I I 1191 I I I I I I I I I I I I (I I I I I I I I If I If I I I I I I JI I I I I I I I I! I I! I! I I! If 11.l 1 6 18 20 2 2 214 26 Ug

u*b

Figure 8.2.1 Profiles of mean velocity

100

~ y=6.00 cm

)( y=4.00 cm + y=2. 70 cm

.& y=l.80 cm x y=l.20 cm 90 _l!l y=0.75 cm

u

(cm/sec) +

(cm/sec)

Figure 8.2.2 Comparison of fluid and sediment grain mean velocity

100

~~7...,....,-,-,...,...,..,,...,...,...,...,...,-rr-r-r-100 fLUID SIZE

~~7...-.--.-.,....,....,...T"'""'"""""..,...,...,....~- GRAIN SIZE 4 4

• •

)( II( + +

J

y I + +

~I dr 1 I

A A IA AA A ))!: x )¢( I 0-1

l

I I I I I I I I 1.'

5

I I ' I I E!!i I I

2

I I I I I I I I

2: 5

I I I I ' ' ' '

3

10-1 l -1.5 2 2.5 3

~ ~

u*b __ g u*b Figure 8.2.3 Profiles of velocity standard deviation

100 I''''''''' I' I' I I'' I' I'''''' I'' I''''''''' I''''''''' I''''''''' I y

d

FLUID SIZE

• • "'

+ + & & & 10

~% u

)( x

100 I''''''''' I''''''''' I'''''''' I I''''''''' I''''''' I 'I I'''''''' I 1. d

GRRIN SIZE

• •

I( + + ... & xx 10 16

./UW

g O/o Ug Figure 8.2.4 Profiles of relative velocity fluctuation

• y=6.00 cm )( y=4 .00 cm + y=2.70 cm

A y=l.80 cm x y=l.20 cm

1:!1 y=O. 75 cm

l!l

x x

6 7 B

J-Ul2

Figure 8.2.5 Comparison of fluid and sediment grain velocity standard deviation

• y=6.00 cm x y=4 .00 cm + y=2.70 cm

£ y=l.80 cm ll.I x ^y=l.20cm

l.!J y=0.75 cm

l.!J x

12 xx

~ u

O/o

6 8 10 12

~ _g

%

Figure 8.2.6 Comparison of relative rluid and sediment grain velocity fluctuation

most of the water

column,~

is greater than Vu ¹2

• Near the

sediment

bed,~

and the relative fluctuation in the fluid velocity is much greater than"Vu¹2

• Near the water

surface,~

is much

g g

greater

than~

but their relative fluctuations are nearly equal.

The velocity probability density functions for each data record are shown in Figure 8.2.7. The fluid velocity probability density function is given by the solid line; that of the sediment grains by the dashed line. The mean fluid velocity and the

mean sediment grain velocity are noted with plotting symbols.

The probability density function of the fluid velocity near the

sediment bed is broader than that near the free surface. The sediment grain velocity distribution does not exhibit such a trend. The

sediment grain velocity tends to be less than the fluid velocity at locations 1.20 and 1.80. Also, at locations 1.20 and 0.75, the

distribution of the fluid velocity is broader than distribution of the sediment grain velocity. The fluid velocity is clearly less than the sediment velocity at location 6.00. At the remaining locations, the probability density functions of the fluid velocity and the sediment grain velocity are quite similiar.

The simple lag correlation coefficients of velocity fluctuations computed for one of the data records from location 1.80 are shown in Figure 8.2.8. Similiar results were obtained for each of the remaining data records. No correlation in the velocity of successive sediment grains was found in any of the data. Unfortunately, the subsequent calculation of the true auto-correlation function proved unreliable.

This calculation requires the inversion of a matrix with elements

:>.. 0.075 .µ

·ri r-1

·ri .0 0.05

.0 rt!

0 ~

p., 0.025

0so

>t il.075 .µ

·ri r-1

·ri ~ 0.05

.0 0 p., ~

FLUID SIZE GRAIN SIZE

1.10

FLUID SIZE GRAIN SIZE

1.10

70 80

Velocity

(cm/sec)

70 80 90

Velocity (cm/sec)

'; ,, .,,, ,, ,,. '

: ! ! ,;

\.!:::

-1 :

--. _-L

., ' ' ' ' ' ~Tj 1-,

..., •,.)'(" Ll --1

100

~--,

SIJ600

120

SC601

120

Figure 8.2.7.a Velocity probability density functions, location

6.oo

lSO

:;..,0.075 .µ .,;

,.-;

] 0.05 .Q m

0 ~

a.. 0.025

0so

- fLUlO SIZE -- CRR IN SIZE

1,!0 50 60

,-, •'

•:

70 BO 90 100

Velocity (cm/sec)

SIJIWl

110 120

Ftgure 8 .2. 7. b VeJ..,:;ci. ~.:y probability density function,

loc::~ t~;. :c. l\

·;on

1

130

0.075

:>..

.µ

·r-1 r-1

·r-1 0.05 .Q .Q rO

1-l 0 0.025 i:i.

~ ·r-1 r-1

0.075

·r-1 0.05

~ .Q 0 H 0.025 p..

- FLUID SIZE -· CllRill SIZE

1,10

SIZE SIZE

70 BO 90

Velocity (cm/sec)

70 BO 90

Velocity (cm/sec)

50271

100 1l0 120

50272

100 1l0 120

Figure 8.2.7.c Velocity probability density functions, location 2. 70

130

0.1

- FLUID SIZE -- CllR!N SIZE :;:... 0.0?5

.µ -..;

-..; r-l ..Q tU ..Q 0

&:

^0.025

\ID

0.1

- FLUID SIZE -- CllRIN SIZE .fj<o.0?5

.,.;

..-1

·n

.;a

^{0. 05}

..Q

~, "'I

0 I

30 \ID

i;'o.015

·n .-f

·..-l

.;a

^0.05

..Q 0 1-l A; 0.025

030

- FLUID SIZE -· CllRIN SIZE

110

70 BO QO

Velocity (cm/sec)

-I _I

J '-\_

^{I -}

_~~

^- ^'-1-

~ M ~ ~ ~

Velocity (cm/sec)

LOD

LOO

5D 60 ro ~ ~ LOO

Velocity (cm/sec)

50180

llD L2D

50181

do do

50182

llO L20

Figure 8.2.7.d Velocity probability density functions, lo ca ti on 1 • 80

L30

0.1

:;,...0.075 .µ . ^.;

r l

. ^.;

0.05 ..Q n1 ..Q

~ 0 0.025

0so

0.1

>.0.075 .µ . ^.;

.-I

·rl ..Q m ^0.05

,Q 0 1-1 p.. 0.025

0so

t'0.075

. .;

.

.-I ^.;

~ 0.05 ..Q

0 1-1 p.. 0.025

- FLUID SIZE ⁵⁰¹²⁰

-- CRAIN SIZE

1,10 50 60 70 BO 90 LOO llO 120

Velocity (cm/sec)

- fLUIO SIZE ⁵⁰¹²¹

-- CRAIN SIZE

!JO 50 60 70 BO 90 100 110 120

Velocity (cm/sec)

- FLUID SIZE ⁵⁰¹²²

-- CllA IN SIZE

50 co ⁷⁰ ^BO ⁹⁰ ¹⁰⁰ ¹¹⁰ ¹²⁰

Velocity (cm/sec)

Figure 8.2.7.e Velocity probability density functions, location 1.20

130

:>.. 0.075 .µ

·r-1

·r-1 r-1

7a ^0.05

~ 0.025~

- FLUID SIZE

•• GflRIN SIZE

60 70 BO 90

Velocity (cm/sec)

100 110 120

Figure 8.2.7.f Velocity probability density function, location 0.75

SQ750

130

FLUID SIZE

o.75

GRAIN SIZE

o. 75

o.s

10 15

25 30

LAG M

25 30 35

LAG M.

SQIBI

ijQ 1.15 so 55 60

SQIBI

ijQ 1.15 50 55

Figure 8.2.8 Sample simple lag correlation coefficients of velocity fluctuation, location 1.80

determined by the probability density functions of lag time • at lag M.

Such a matrix becomes more nearly singular as the sampling becomes more irregular in time. The numerical inversion of a nearly singular matrix is plagued by numerical instability. The computed inverted matrix, if obtained at all, bears little or no resemblance to the inverse of the initial matrix. The velocimetry events obtained in this study are quite irregularly spaced in time. The resulting matrices of lag time probability density for both the fluid and the sediment grain

measurements in each data record are nearly singular. The computed true velocity auto-correlation functions were overwhelmingly dominated by the numerical errors and were physically meaningless.

The normalized power spectral estimate of the fluid velocity fluctuations and the relevant power spectral window function as computed for two of the data records are shown in Figure 8.2.9. The power spectral estimate is given by the solid line; the spectral window function is given by the dashed line. The mean sampling frequency is indicated with a plotting symbol. The results are presented for two of the data records with the most similiar time sampling characteristics.

The futility of the spectral computations is apparent. While the power spectral estimate generally decreases with increasing frequency, the expected error in the power spectral estimate is equal to the value of the estimate. There is no smoothing inherent in the direct

computation of the power spectral estimate. The spectral window function does indicate a lower bound on the frequency for which the computation of the power spectral estimate should be performed. For

101 100 ;,. ... ~ 10-1

.

N 0 Cl>

.,,

N ... E 0 ~ ;,. ... o..z

10-2 10-3 10-4 10-J

~

. SQi;O

l

101 r--r-' ·1 , '"I •--r-ir• ---YN(v)

I

^{' ' '} 1 ~ '1 /: ' , ' ' ' ' I I 0 ' ' ' 0 I I ' ' ' I I I \ I I I I\ I / I I ~ \I I I\ I I I I\ It I I \ t 11

1 1

f \ 11 I I \ •1 \ J ' 11 11 ' It 11 \ 11 \I I l " ' p I v ' 10 I ' '

.

' l t ,,

1 on ;,. >-.z 10-1 N 0 Q) .,, N~ 0 ~ ;,.

-

o..z

I c-2 1 o-a

-PN(l') ---YN(v) ' I \ I ' : , .. '

,.

I I 0 I I \ ~ \ I \ /J ~ : ·, : : 11 \I I 11 ,1 I ~ I t I I I t :\ I I I < ' ' I I I' •' ~ l\ I o 0 I ·, 1\ ~1 , , I °\ f \,,'\ f\ l :'\

~··'l'·I\''

,, ,, ,,,, ,{ i\ f\ I I \ I /,I,'~ ,, ' ... , I 0-2 10-1 100 101 Io< 10-2 10-1 100 JI Hz J1 Hz Figure 8.2.9 Sample fluid

velocity fluctuation

power

sp8ctral estimates

and power spectral

window

functions, location

1.20

101

50121 •' ,. 1\ I\ I I I \

~Ll

102

the presented data records, this lower bound is seen to be

approximately 0.02 Hz, which corresponds to roughly one-tenth of the total sampling period.

The results of the spectral calculations of the sediment grain velocity fluctuations are still less instructive. Figure 8.2.10 shows the power spectral estimate and the power spectral window function corresponding to the fluid results shown in Figure 8 .2. 9. No trend in the power spectral estimate is at all apparent. The mean sampling frequency of the sediment grain velocity in the data records shown is approximately 4 Hz. Thus, at best, only long-time fluctuations in sediment grain velocity can be considered. The expected error in the sediment grain velocity spectral calculations is greater than that of the fluid velocity spectral estimates due to the relatively smaller number of sediment grain velocity measurements.

The effects of the bias correction procedures on the computed mean and standard deviation of the fluid velocity are shown in Figure

8.2.11. The result of the Mc Laughlin-Tiederman ( 1973) correction is given in Figure 8.2.11.a. The trapezoidal bias correction suggested by Dimotakis (1976) was applied to give Figure 8.2.11.b. Figure 8.2.11.c illustrates the effect of the procedure developed by Mc Dougall (1980).

Little change in

u

results from any of the correction procedures. All of the bias corrections tend to

increase~

slightly. The

trapezoidal averaging correction yields a slightly larger change in

~

than the other correction procedures; however, no significant difference among the three correction procedures is apparent.

... ~ ·N u Q) fl) N...._ E u ~ ~ o..z

JOI -P14(v) ---YN ( v) JOO 10-2 10-s 10

,~ , : ' ' ' ' ' ' ^' ' ! : I~ '

..

I <' 1 I\ t : : v ' ' I ' ' ' 0 I I I '' <I I I '' 0 I

'' '' •'

"

•'

" " "

"

,,

I \j 11 ~ 1 ... ·1 ~ :

T-' '1 '"'I

1 SQl20 " •"'I " I

'"i 1 ~

.!\,

~

.~ ,, .}, \'l ~ '

{ : I : f 0 0 I ,' ~ ; ! :

i

I ' ' ' ' ' ' ' '

i

! :\ : I \ 11 '

i

! !\ ' ! I I 11 I I I : : } : : : :: : : ,1 11 q l ~ : , I 11 It I \1' '• ~: : -~.LLJ._.i:...._,

--'-'-'-L..' I. I 102 101 10-1 100 v Hz

JOI

t~~~-:;>TTr---,--.--,.-,-.-.-,..,.,--~-,-.,...,,,...;:..r---r-r-.-,.~"'"'"r~.,--,_,.~-

E , , , I "" F I ' ' • J "" - PN(y) I I ''i'"'i ''I·

---YN(V)

SQ.121 I- JOO I- ...

-

>-z 10-1 1- NU Q) fl) ... NE u ,.... ...

I- J 0-2 ~ I- I o-s 1- 10-Y 10-3

I I ' I I I ' I I I ' I : ' ' t I I l ' : ' : ' ' ' ^I ' I I ' I ' .I' 10-2

I :: " " " " :: '' '' : ~I i}

i

"'

/ )

I ~

I A 11 I, '• 11

~ ^!

,, ,, 11 t1 1, 11 ,, ., 11 I I I\ ~ 1 l ii' t t} I: ~ I :1: :' : 1 I\ I 1 I\ I\ ~ '1 : ~ : : : : I I I I I I I It ~ I : : : : ~ .' t : : ~ : t : ~ 11 ! : : : : I {}: t u : : :,• ;; t; ~ u \ : :: ~ 11 :: I :r II: ~: :: I -~, f ~1• t , , ; 10-1 I oo v Hz

!· l .

, ' 'r

1

iol l " ' I l ' ' ': '' '' ,, " " " l ; " " " '' '' I \ ' 1 }

!l

1, ' 1, ' ,, '' \I ',

,. "

' l. '"' 101

l.. ~t

/'\

' ' ' '. ' ' ' 11· I

-

- -

- - - -

- 102

Figure 8.2.10 Sample

grain

velocity fluctuation

power

spectral estimates

and power

spectral window functions, location

1.20

100 • y=6.00 cm x y=4.00 cm

+

y=2. 70 cm £ y=l.80 cm x y=l.20 cm 901-Cl y=O. 75 cm

IJ

p 'O <I> .µ u <I> 70 1-1 1-1 0 u _{s::: p} 60 60

9 • y=6.00 cm x y=4.00 cm

+

y=2. 70 cm £ y=l.80 cm x y=l.20 cm Cl y=O. 75 cm ... 8 IJ. u

/ j

<I> Ill -... fj ...

ll~ ">

7 + 'O

~ +/ 2J .

a u IA <I> 1-1 1-1 0 )( u i::: ::> 6 70 60 90 100 Corrected

U

(cm/sec)

6 7 6 Corrected

J'UFz'

(cm/sec) Figure 8.2.11.a Comparison of uncorrected and corrected fluid velocity mean and standard deviation, Mc Laughlin-Tiederman procedure

1

60 70 60 90 100 5v1 I I I I I I 1 I I J I ! I I t I I I J I I I I I I I I I I I I I I I 5 6 7 6 Corrected

U

(cm/sec) Corrected

~

(cm/sec) Figure 8.2.11.b Comparison of uncorrected and corrected fluid velocity mean and standard deviation, Dimotakis procedure

soV1 I I I I I I I If I I I I I I I I I I I I I I It I! I I I I I I I I I I A JI 1 I I It I I I I 50 60 70 60 90 100 Corrected U (cm/sec)

5v., , , , , , , , 1 , , , , , , , , , 1 , , , , , , , , , 1 , , , , 5 6 7 6 Coirected

.llJ7I

(cm/sec) Figure 8.2.11.c Comparison of uncorrected and corrected fluid velocity mean and standard deviation, Mc Dougall procedure

The Mc Laughlin-Tiederman and the Dimotakis procedures procedures were also used to compute corrected velocity probability density

functions. The results for one of the data records from each location are shown in Figure 8.2.12. The corrected velocity probability density functions are only very slightly broadened. Again, the two correction procedures are very similiar and have only minor effect compared to the uncorrected velocity distribution.

8.3 Representative sediment grain inter-arrival time records

Associated with each velocimetry data record is a sediment grain inter-arrival time data record. As discussed in Chapter 3, sediment transport rate is inversely related to the sediment grain inter-arrival time. The fluctuations in grain inter-arrival times give a measure of the small time-scale fluctuations in the sediment transport rate. The inter-arrival time data records corresponding to each of the previously given velocimetry data records are shown in Figures 8.3.1 through

8.3.6. The inter-arrival times for all detected the sediment grains, size class 4 G, are connected with a solid line; those sediment grains which generated good velocimetry signals, size class 9, are indicated witb plotting symbols. Note that the inter-arrival time values for size class 9 are not plotted; only the occurrence of a valid

velocimetry measurement at a given time is implied.

The time variability in sediment grain inter-arrival time at any one of the measurement locations is readily apparent from the figures.

Also, the occurrence of a valid velocimetry data does not seem to be obviously correlated with long inter-arrival times.

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Dalam dokumen John List for numerous discussions on the analysis and physical interpretation of the data (Halaman 104-140)