MOVEMENT G)E ,A SO~l)TE IN 

THE,J;,OTOMAC RIVER :ESTUARY 

AT WASHINGTON, D~C. 

AT LO,W INFLOW eONDITIO·N.S ( ' . . - ' 

Movement of a Solute in 

the Potomac River Estuary 

at Washington, D.C. 

at Low Inflow Conditions 

By James F. Wilson, Jr., Ernest D. Cobb, and 

Nobuhiro Yotsukura 

POTOMAC RIVER STUDIES 

GEOLOGICAL SURVEY CIRCULAR 529-B 

Washington J 969 
United States Department of the Interior 

WALTER J. HICKEL, Secretary 

Geological Survey 

William T. Pecora, Director 

Free on application to the U.S. Geological Survey, Washington, D.C. 20242 
CONTENTS 

Page Page 

Abstract----------------_--- __ --- ___ - 1 Presentation of data-Continued 

Introduction-- --- - - - - - -- __ -- ___ -- _- __ - 1 Stage and discharge records--------- 8 

Acknowledgments---- __ - ____ - __ --_____ 1 Average movement of dye mass-------- 9 

Description of the study reach _---- ___ - 1 Observed movement---------------- 9 

Field procedures ------------- _------- 3 Estimated movement--------------- 10 

Presentation of data------------------ 3 Characteristics of dispersion---------- 12 

Dye-distribution maps-------------- 3 Summary and conclusions------------- 14 

Aerial photographS---_------_---- __ - 8 References-------------------------- 14 

ILLUSTRATIONS 

Page 

Plate 1. Maps showing movement of soluble dye in the Potomac River estuarY------In pocket 

Figure 1. Map showing location of study reach- __________ -- __ -- ____ --- ___ -- __ --- ------ 2 

2. Diagrammatic sketch of fluorometer hookup in sampling boat ______ ------ ___ - 3 

3. Graph showing attenuation of peak concentration with time_---- __ ----_---- __ - 4 

4-6. Aerial photographs of: 

4. Dye cloud 1.9 hours after dye injection-------------------------------- 5 

5. Dye cloud 4.4 hours after dye injection-------------------------------- 6 

6. Dye cloud 6. 7 hours after dye injection-------------------------------- 7 

7-12. Graphs showing: 

7. Potomac River estuary water-surface elevations at GSA wharf, 

Alexandria, Va --------------------------------------------------- 8 

B. Nontidal discharge flowing into the Potomac River estuary-------------- 9 

9. Distribution of dye mass in the longitudinal direction - _---- _- ____ --- _-- 10 

10. Observed and estimated movement of dye-mass centroid with time------- 11 

11. Increase of variance and length of dye cloud with time------------------ 13 

12. Attenuation of peak dye mass with time------------------------------- 13 

TABLES 

Page 

Table 1. Computed recovery of the total dye mass at various stages of dilution_________ 12 

2. Product of peak dye mass,Mp'6 and dye cloud length, L, at various stages of 

dilution--------------------------------------------------------------- 14 

III 
IV CONTENTS 

SYMBOLS 

A Cross-sectional area of estuary 

Cp Observed peak dye concentration 

i Cross-section number 

L Dye- cloud length along the estuary 

N Total number of cross sections 

Mi Mass of dye per unit length of estuary 

At/ Mass of dye per unit length of estuary 

adjusted for dye loss 

Alp Peak of the dye-mass distribution 

Alp' Peak of the dye-mass distribution adjusted 

for dye loss 

QJ Total upstream inflow to the estuary 

Qo Total discharge through a selected estuary 

cross section 

M Change in storage above a selected estuary 

cross section 

t Time 

lit Increment of time 

V Average tidal velocity 

X Location of dye-mass centroid measured 

from the release point along the estuary 

centerline 

;0.X Increment of longitudinal distance 

Xi Distance measured along the estuary 

centerline from the release point 

f':u'(i Subreach length 

~ Summation 

~x Standard deviation, in the longitudinal 

direction, of the dye-mass distribution 
Potomac River Studies 

Movement of a Solute in the Potomac River Estuary at 

Washington, D. C., at Low Inflow Conditions 

By James F. Wilson, Jr., Ernest D. Cobb, and Nobuhiro Yotsukura 

ABSTRACT 

The movement of a solute, as represented by a soluble 

fluorescent dye, was observed in the Potomac River estuary at Washington, D.C. The average net rate of downstream movement of the solute centroid was less than 0.6 

mile per day. The movement of a solute is highly dependent on the nontidal inflow to the estuary. During the 

study, the average inflow was 900 cubic feet per seconda very low value, equaled or exceeded 98 percent of the 

time. Using a storage equation, the average movement of 

a solute was estimated for non tidal inflow of 3,100 and 

6,500 cubic feet per second; these inflows are equaled or 

exceeded 75 and 50 percent of the time, respectively. 

The study showed that tidal action was fairly efficient 

in dispersing the solute longitudinally. The solute, which 

was dumped 1,000 feet upstream from the 14th Street 

Bridge, was observed as far upstream as Roosevelt Island. 

A transient longitudinal dispersion coefficient at the end 

of 15 0 hours was determined to be 210 square feet per 

second. On the other hand, the lateral diffusion'was a slow 

process and the lateral distribution of the solute was far 

from unifonn at the end of 6Y2 days after the release. 

INTRODUCTION 

The purpose of this report is to describe 

the movement of a soluble material in the 

Potomac River estuary at Washington, D.C. 

In 1964, a time-of-travel study of a solute 

was made by the U.S. Geological Survey in the 

Potomac River from Cumberland, Md., to the 

upper end of the Potomac River estuary at 

Chain Bridge in Washington, D.C. {Wilson and 

Forrest, 1965 ). The Federal Water ·Pollution 

Control Administration in 1965 made a study 

of the movement and dispersion of a solute in 

the Potomac River estuary downstream from 

Washington, D.C. {Hetling and 0' Connell, 1966 ). 

The study reported herein is for a part of the 

estuary lying between these two study areas. 

ACKNOWLEDGMENTS 

The aerial photographs used in this report 

were provided by the U.S. Geological Survey 

project office, Phoenix, Ariz. The authors 

especially appreciate the help of M.A. Keenan, 

engineering aid, who reduced the basic data. 

DESCRIPTION OF THE STUDY REACH 

The physical characteristics of the study 

reach are well summarized by Durum and 

Langbein {1966, p. 1) as follows: 

"The tide in the Potomac River reaches 

just above Chain Bridge near the western 

limit of the District of Columbia. There is 

sharp contrast between the swift, turbulent, 

narrow river seen looking upstream from 

Chain Bridge and the gentle currents of the 

wide estuary just downstream at Georgetown. 

The quality of water in the estuary is ~a composite of the effects of the tide, the river discharge, and the waste disposal. 

"The estuary begins at about Chain Bridge 

and extends southeastward to the Chesapeake 

Bay at lat 38°. The estuary is several hundred 

feet in width at the head and broadens in its 

length of 117 miles to nearly 6 miles at its 

mouth. A channel with a minimum depth of 

24 feet is maintained in the estuary as far upstream as the upper end of the Washington 

Channel on the west side of Potomac Park 

in Washington. Except for the channel and 

depths of 80 feet at Chain Bridge and at The 

Three Sisters Islands, the estuary is re latively shallow; depths are predominantly less 

than 5 feet throughout most of the estuarine 

reach." 

1 
2 MOVFMEN'T OF A SOLUTE IN THE POTOMAC RIVER ESTUARY AT WASHINGTON, D.C. • AT LOW INFLOW CONDITIONS 

/1 

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FAIRFAX CO 

VIRGINIA 

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21._ _ __._ _ __,_? ____ 21...1 ___ ----l.,j ____ GL-1 ___ ......~f M.ILES 

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MARYLAND 

1. Chain 

·2. Key 

3. Roo seve 1 t 

4. Memorial 

s. 14th Street 

6. Wilson 

V/J 

Study· reach' 

Streamflow • 

Gages 

A 

• Tidal stage 

A Anacostia ~aval Air Stat~on 

B General Services Administ'ration 

wharf (Alexandria) 

C Memorial Bridge 

D u.s. Coast ~nd Geodetic Survey 

(Washington Channel) 

Figure 1. -Location of study reach. 
i' PRESENTATION· OF DATA 3 

The study reach, shown in figure 1, included 

that part of the reach described above which 

lies between Key Bridge (3.3 miles below 

Chain Bridge) and Broad Creek (3.5 miles below Woodrow Wilson Memorial Bridge). 

FIELD PROCEDURES 

On August 3, 1965, at 0700 e.s.t., 200 pounds 

of rhodamine B dye (30 percent solution) was 

injected into the Potomac River estuary at 

midstream, 1, 000 feet upstream from the 14th · 

Street Bridge in Washington, D.C. The dye 

was released during slack tide. 

Shortly after the dye was released sampling 

was star!ed. Dye concentrations were monitored continuously by use of a flow-through 

setup on the Turner Model 111 fluorometer 

mounted in a 17-foot boat. (See fig. 2.) The 

river water was pumped from the intake, located about 1 foot below the water surface, 

through the fluorometer by a t-horsepower 

pump, and fluorometer readings were re-

_corded on a continuous strip chart. Periodic 

Intake 

! 

Gasoline-powered 

generator 

Plan view of boat 

Figure 2, -Diagrammatic sketch of fluorometer hookup in 

sampling boat. 

grab samples were obtained along with the 

continuous monitoring to provide a means of 

calibrating the chart record. Water temperatures were recorded periodically to determine 

corrections to the fluorometer readings. 

The above sampling system was used 

throughout the test period with the exception 

of one afternoon on August 6, when the fluorometer was temporarily out of service due to a 

broken cuvette. A set or grab_ samples was 

collected in lieu of the flow-through data during this period. 

The location of the boat at any time was determined by the use of a Doppler navigator 

which was 'mounted on the bow of the boat. The 

navigator measured the distance that the boat 

had traveled from a selected location by 

sensing the Doppler effect of sound waves reflected off the streambed. Supplemental observations of buoys, bridges, and other welldefined landmarks were recorded and used to 

check the navigator. 

A total of seven sets of surface-sampling 

data were collected in the study. Each set of 

data consisted of traverses along several 

cross sections and at least one traverse along 

a longitudinal axis of the channel. Each set of 

surface samples required successively longer 

sampling periods owing to the ever-lengthening dye cloud. Sampling periods varied from 

30 minutes for the first set of data to 4.5 

hours for the last set. Each set :represents 

an average spat-ial distribution of concentration at the middle of the sampling period. 

Each sampling period was ti~ed near a slack 

tide so that the extreme positions taken by the 

dye mass could be determined. The dye was 

traced until 1230 e.s.t., August 9. 

PRESENTATION OF DATA 

DYE-DISTRIBUTION MAPS 

The observed patterns of dye distribution 

are illustrated in the seven maps shown in 

chronological order, plate 1. Lines of equal 

concentration were drawn by observing the 

concentrations along a set of traverse lines 

and by assuming that the variation of concentration was uniform and continuous in the 

areas not sampled. 

A bypass flow through the Tidal Basin and 

the Washington Channel is worthy of special 

mention. The_ movement of dye into this 
4 MOVEMENT OF A SOLUTE IN THE POTOMAC RIVER ESTU.AlW AT WASHINGTON, D.C., AT LOW INFLOW CONDITIONS 

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100 

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TIME (t) 1 IN HOURS AFTER DOSING 

1. Map number refers to map on plate 1. 

2, Values of Cp arc not adjusted 

for dye loss. 

50 

Fig\U'e 3, -Attenuation of peak concentration with time, 

Map \ 

1\ 

\ 

Map 7\ 

100 200 
PRESENTATION OF DATA 5 

Figure 4. -Aerial photograph of dye cloud 1. 9 hours after dye injection. 
6 MOVEMENT OF A SOLUTE IN THE POTOMAC RIVER ESTUARY AT WASHINGTON, D.C., AT LOW INFLOW CONDITIONS 

Figure 5, -Aerial photograph of dye cloud 4, 4 hours after dye injection. 
PRESFNT A TION OF DATA 7 

Figure 6. -Aerial photograph of dye cloud 6. 7 hours after dye injection. 
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8 MOVEMENT OF A SOLUTE IN THE POTOMAC RIVER ESTUARY AT WASHINGTON, D. C., AT LOW INFLOW CONDITIONS 

channel was visually noticeable during the 

first ebb tide, and the exchange between the 

main channel and the bypass must have continued for a number of subsequent tidal periods. Other than by aerial photographs, the 

movement of this portion of the dye was not 

monitored until the last day and was excluded 

from the .computations. According to the mass 

recovery computations for the main channel, 

this bypass dye was relatively small in quantity. On the other hand, the isolated dye itself 

remained relatively undispersed for a considerable period of time apparently because 

of low flow velocities in the bypass channel, 

map 7, plate 1. 

A plot of the observed peak dye concentration, Cp, from the dye-distribution maps against 

elapsed time is shown in figure 3. The points 

line up well on a straight line which has a 

slope of -1.6. The attenuation of peak concentration with time is indicative of the combined effect of the dilution capacity of the 

estuary and the dye loss; therefore, the slope 

of the relationship should not be construed as 

a constant characteristic of this estuary. 

AERIAL PHOTOGRAPHS 

A number of aerial photographs of the dye 

cloud, both in color and in black and white, 

were taken during the early stages of the experiment. Although quantitative evaluation of 

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the photographs is outside the scope of this 

report, three selected examples are shown in 

figures 4-6. The white images of the dye cloud 

against darker water are the result of using 

an orange sharp- cut filter on the camera with 

ordinary black and white film. 

Photographs are limited, of course, to periods of daylight and to the time span during 

which the dye cloud is visible; in the present 

study the dye cloud was only visible on the 

first day. The obvious general value of aerial 

photographs is that they provide instantaneous 

synoptic views of the dye cloud and reveal 

fine structure of the cloud not shown by surface sampling. The general shapes of the dye 

cloud determined by surface sampling in maps 

1 and 2, plate 1, compare favorably with the 

shapes revealed in the three photographs, 

figures 4-6. 

STAGE AND DISCHARGE RECORDS 

Records of stage were obtained at the GSA 

(General Services Administration) wharf in 

Alexandria, Va., and at the Anacostia Naval Air 

Station. (See fig. 1.) The difference in watersurface elevations between the two gages was 

always less than 0.2 foot, and the time lag between peak stages at these two gages was about 

10 minutes. The record of stage variation obtained at the GSA wharf is shown in figure 7. 

0 Refers to time corresponding 

to the map numbers on plate 1 

1\ 

\ A A '\ 

l ' 

\ \ 

v v D ·~ \, 

f 

7 8 g 

TIME, DAY IN AUGUST 1965 

Figure 7. -Potomac River estuary water-surface elevations at GSA wharf, Alexandria, Va. 
AVERAGE MOVEMENT OF DYE MASS 9 

1200 

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TIME1 DAY IN AUGUST 1965 

Figure 8. -Nontidal discharge flowing into the Potomac River estuary. Hydrograph is for the gaging station 1 Potomac River n:ear 

Washington. D. C. 1 2 1/4 miles upstream from Chain Bridge. 

Nontidal discharge in the Potomac River 

above Chain Bridge, together with minor discharges from Rock Creek, Fourmile Run, 

and the Anacostia River, constitute the net inflow to the estuary. The discharge hydrograph 

for the gage, Potomac River near Washington, 

D.C., is shown in figure 8. 

AVERAGE MOVEMENT OF DYE MASS 

OBSERVED MOVEMENT 

Time of travel in an upland stream without 

tidal action usually is defined as the time taken 

by the centroid of a dye mass to travel from 

one specified point to another downstream point 

in a reach, the centroid representing an average 

location for all dye particles. In an estuary, 

however, such time of travel is not so defined, 

because a dye mass subjected to tidal action 

may pass specified points several times. Accordingly, "average movement of dye" refers 

to distance traveled instead of time. The· 

measurement of the dye-mass centroid is most 

meaningful if it is measured at both slack periods of tidal cycles so that a series of extreme 

upstream and downstream positions of the dye 

mass can be defined along the river axis. In 

this study, mass centroids from dye-distribution maps 1, 3, 4, and 7, plate 1, represent the 

approximate extremes at the end of ebb tides, 

whereas those from maps 2, 5, and 6 represent 

the approximate extremes at the ends of flood 

tides. 

The following procedure was used to compute 

the location of the dye-mass centroids: 

1. On a given map, 10 to 20 cross sections 

were marked off to sufficiently define the distribution of the dye. The intervals between 

cross sections were not necessarily uniform, 

b ec a use of the shapes of the cone entr at ion isolines. The cross sections were assigned numbers, i=1, 2, ... , N (N is the total number of 

cross sections). Areas or concentrations to 

the east of a line between Hains Point and Giesboro Point were not included in cross sections 

located at the mouth of the Anacostia River. 

Similar deletions were made for the larger 

bays, such as the mouth of Hunting Creek. 

2. For each cross section, i, observed dye 

concentrations (assumed to be uniform vertically) and water depths were plotted against 

width. The cross section was then divided into about 20 subsections of uniform width. 

3. For each subsection, the product of subwidth, depth, and average dye concentration was 

determined. The sum of these products, Mi. 

represents the total mass of dye per unit length 

of subreach associated with the tth cross 

section. The distribution of the dye mass along 

the estuary is shown in figure 9. It is noted 

that the ordinate M/ is obtained by uniformly 

adjusting M; for the measured dye loss, so that 

the area under the curve remains the s arne for 

all maps. 
10 MOVEMENT OF A SOLUTE IN THE POTOMAC RIVER ESTUARY AT WASHINGTON. D.C. 1 AT LOW INFLOW CONDITIONS 

1-

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u.. 

UJ 

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\/Map 2 

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52 

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-10 0 10 20 30 40 50 

RIVER DISTANCE (Xi), IN THOUSANDS OF FEET FROM 

DYE-INJECTION SITE 

Map number refers to map on plate 1 

Figure 9. -Distribution of dye mass in the longitudinal direction. 

4. For each cross section, i, Mt was multiplied by the sub reach length,, !:Xi, associated 

with that cross section, where Mt is equal to 

one-half the distance between the two adjacent 

cross sections, i +1 and i -1. The sum of the 

products represents the total mass of dye observed for this sampling period. 

5. The dye-mass centroid location, X, was 

computed as the first moment of the distribution of M1 in the longitudinal direction. The 

moment arm, x1

, was the estuary centerline 

distance from the dye-injection site. Values 

for x1 were designated as positive in the downstream, or seaward, direction and negative in 

the upstream direction. In equation form, the 

dye-mass centroid is defined as 

X 

N 

'f-Mt MtXt 

i=l 

N 

'f-Mt Mt 

i=l 

(1) 

The mass-centroid positions for maps 2-7 

(pl. 1) are plotted in figure 10. It may be seen 

that by the end of an ebb tide on August 9 the 

centroid had traveled a net downstream distance of 19,400 feet, or 3. 7 miles .. Considering 

the period between the time of release, 0700 

e.s.t., August 3, and the end of measurement, 

123~ e.s.t., August 9, the average velocity of 

net downstream motion is less than 0.6 mile 

per day-a very slow movement in comparison 

with that in most upland streams. Also apparent 

is the fact that the mass centroids measured 

at the end of ebb tides and flood tides form two 

separate envelopes within which the to-and-fro 

motion of the dye-mass centroid is restricted. 

ESTIMATED MOVEMENT 

The average movement of the centroid of a 

solute in the estuary was estimated using the 

following equation of continuity, 

(2} 

where 

Qo is the flow through a cross section, 

QJ is the total nontidal inflow to the estuary, 

and 

6S is the change of storage upstream from 

the cross section during the time increment, 6.t. 

QI is always positive, whereas t:S is defined as 

positive if the stage is rising with time and negative if it is falling with time. Qo is positive 

if the flow is downstream and negative if the 

flow is upstream. 

Two other equations required to estimate the 

water mov.ement are 

(3) 

and 

M=V6.t, (4) 
AVERAGE MOVEMENT OF DYE MASS 11 

10 

9 

8 

4 

Map 

0 

Q

1 of observed conditions 

(Average, 900 cfs) 

10 20 

Q1 = 3,100 cfs 

EXPLANATION 

• Observed 

~ Estimated 

30 40 50 

DISTANCE FROM DYE-INJECTION SITE, IN THOUSANDS OF FEET 

Map number refers to mdp on plate 1 

Figure 10,-Qbserved and estimated movement of dye-mass centroid with time, 

where 

V is the average tidal velocity, 

A is the cross-sectional area of" flow, and 

t::X is the distance of travel -during the time 

interval, /::;t. 

The signs of V and t::X are the same as Qo; that 

is, they are positive if the flow is downstream 

and negative if the flow is upstream. 

Most of the inflow Q/ came from the nontidal 

Potomac River discharge. A small adjustment 

was made to include minor discharges from 

otherstreams. Forthestudyperiod, QI ranged 
12 MOVEMENT OF A SOLUTE IN THE POTOMAC RIVER ESTUARY AT WASHINGTON, D.C., AT LOW INFLOW CONDITIONS 

from 700 to 1, 200 cfs, averaging approximately 

900 cfs (cubic feet per second). (See fig. 8.) 

This is considered to be very low flow, being 

equaled or exceeded 98 percent of the time 

during the 28-year period, 1931 through 1958. 

The change in storage, 6S, was determined 

from the surface area of water in the estuary 

and from the change in stage. The surface area 

was determined from U.S. Geological Survey 

topographic maps. It was assumed that this 

area did not change significantly in the range 

of stage normally resulting from tides. The 

change of stage was determined from the stage 

record obtained at the Anacostia Naval Air 

Station. The water surface for the area under 

study was assumed to rise and fall as a horizontal plane. No corrections were made for the 

small slope in the water surface. 

A time increment, /::,.t, of 15 minutes was used 

in the computations. The starting cross section 

was at the dye-injection site, and Qo at that 

section was computed from equation 2 for the 

first 15-minute period. The average tidal velocity, V, and distance of travel, M, during the 

first 15-minute period were computed from 

equations 3 and 4, respectively. The second 

cross section was then located at a distance 

of M, computed from equation 4, from the 

initial location, and Qo, v, and M were computed in similar fashion for the second 15-

minute increment. The procedure was repeated 

for successive 15-minute time increments for 

the total time period of interest-approximately 6t days. 

Results of the computations are plotted in 

figure 10 to compare with the observed movement of the dye. The agreement is generally 

satisfactory. The fact that most of the observed 

points lie outside of the estimated curve suggests that the dye cloud was traveling faster 

than the average water particles, probably because of the lack of complete lateral mixing 

throughout the entire sampling period. 

The results of the first set of computations 

were encouraging enough that the computations 

were extended to two hypothetical cases, also 

shown in figure 10. Values of QJ of 3,100 and 

6, 500 cfs were used in these computations. 

The discharges of 3,100 and 6,500 cfs at the 

Potomac River gage upstream from Chain 

Bridge are expected to be equaled or exceeded, 

respectively 75 and 50 percent of the time. 

According to past records, the range of stage 

variation in the estuary is nearly independent 

of QJ if QJ is less than 40,000 cfs. Therefore, 

the M data used in the observed computations 

were assumed to be applicable for the two hypothetical cases. The computations indicate 

that the downstream movement is very closely 

related to QJ; the rate of increase in the movement is slightly less than the rate of increase 

in QJ for the computed range. 

CHARACTERISTICS OF DISPERSION 

The seven dye-distribution maps, plate 1, 

show a complex but steadily progressing pattern of dye dispersion in the study reach. Two 

general features are immediately noticeable. 

One is that even after 150 hours of diffusion, 

the cross-channel distribution of dye concentration was far from being uniform. The other 

feature is that the dye cloud stayed closer to 

the left bank than the right throughout the study. 

This appears to be a persisting effect of an 

early drifting of the dye. The dye mass, initially poured at the middle of the stream, remained almost stationary for about 2 hours 

after the release. During the ensuing period 

of the first flood tide, the dye mass was rapidly 

elongated between the 14th Street and Memorial 

Bridges. (See figs. 4 and 5.) At the same time, 

for some undetermined reason, the main part 

of the dye drifted toward the left bank. 

The recovery of dye mass for each map of 

plate 1, which was computed in step 4 (p. 10) 

of the centroid determination, is tabulated in 

table 1. The values given in table 1 for maps 

Table I.-Computed recovery of the total dye mass at 

various stages of dilution 

Map No. 

(pl. 1) 

2----------------------

3----------------------

4----------------------

5-~--------------------

6---------------------- 7 _____________________ _ 

Computed 

recovery 

(percent) 

105 

138 

121 

68 

47 

32 

numbered 2-4 (pl. 1) reflect the inadequacy of 

the dye-cloud sampling in the early stages of 

the study. 

From the viewpoint of considering movement 

of dissolved substances introduced as a point 

source, the progress of the longitudinal dispersion is probably the most important because 
CHARACTERISTICS OF DISPERSION 

13 

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ln 

~ 

40 ji 

::::> 

~ z 

30 :i 

1-

~ w 

....J 

20 g 

g 

u 

1 0 

0 1 

10 100 1000 0 200 1+"00 bOO 

TIME (t), IN THOUSANDS OF SECONDS TIME (t), IN THOUSANDS OF SECONDS 

Map number refers to map on plate 1. 

Figure 11. -Increase of variance and length of dye cloud with time. 

of its predominant role in the total dilution. As 

a primary measure of this dispersion, the 

longitudinal length of the dye cloud may be 

plotted against time. A more stable parameter, 

however, is the variances of the longitudinal 

mass distribution. The variance,o/, was computed by the formula 

N 

"LM; (X-X;i !::X; 

(f_ 2 i=l X ~~~-----------

N 

"LM;M; 

i=l 

A plot of D"iagainst time is presented in figure 11. At large dispersion times, cx2 was increasing almost linearly with the square of 

time, t. Consequently, the longitudinal dispersion coefficient, defined as one-half of the rate 

of increase of ax 2 with t. had not attained a constant value. A transient value of 210 sq ft per 

sec (square feet per second) was o.btained by 

observing that the rate of increase of 0:"t 2 with 

time between maps 6 and 7 (pl. 1) was about 

420 sq ft per sec. In figure 11. the longitudinal 

cloud length and the standard deviation. D"x, are 

also plotted against time to demonstrate the 

consistent relation between the total length 

and ~ax. 

The peak of the dye-mass distribution, Mp', 

is plotted against time in figure 12. Again, 

the ordinate Mp' is the adjusted value for dye 

loss (table 1) rather than the observed Mp. It 

may be seen that, at large dispersion times, 

Mp'is about inversely linear with time. This 

is to be expected from the principle of the 

Vl 500 

Vl 

~ 

1-W 

~tu u.. 

3 w 200 

~~ 'i'g 

'-J 

Vl X lQf) VlZ 

~8 ...J W...J 

>--

0 Ol 50 :>.£~ 

iti~ a.. Vl 01-

w~ 

I-<( 

VlO.. 

:::> 20 -:>U.. 

~0 

Vl 

Vl 

0 

1-

1-

f--

1-

f--

I--

I1-

I I I I II I I I I I I 

- C Map 2 

"' -

Map 30 

~~ Map 5 

'~ -

- Map 6 -

-

""' -

Map R -

I I I I II I I I I I I 

...J 10 20 50 100 200 500 1000 

TIME (t), IN THOUSANDS OF SECONDS 

Map number refers to map on plate 1. 

Figure 12. -Attenuation of peak dye mass with time. 
14 MOVEMENT OF A SOLUTE IN THE POTOMAC RIVER ESTUARY AT WASHINGTON, D.C., AT LOW INFLOW CONDITIONS 

Table 2.--Product of peak dye mass, Mp~ and dye cloud 

length, L, at mrious stages of dilution 

Map No. .Mp'· L in 

(pl. 1) 106 ppb X CU ft 

2 _______________________ _ 

3------------------------ 4------------------------ 5 _______________________ _ 

6------------------------ 7 _______________________ _ 

2~ 102 

1~966 

2,453 

2~ 153 

2~841 

1,944 

continuity of dye mass which may be crudely 

expressed by the constancy of the product of 

the cloud length and Mp' (table 2). If the cloud 

length of (Jx varies linearly with time, Mp' 

should be inversely linear with time. 

The above dispersion parameters are not 

applicable for the prediction of dispersion at 

other flow conditions in this estuary because 

a correlation of the dispersion parameters 

with the hydraulic variables is not available 

from just one test. 

SUMMARY AND CONCLUSIONS 

The surface-sampling data and its analysis 

produced useful information on the movement 

of a solute in the upper end of the Potomac 

River estuary at Washington~ D.C. Quantitative analysis of the rate of movement and the 

dispersion characteristics was based on the 

distribution of dye mass rather than dye concentration. The analysis was reduced to a onedimensional approach. However, this should 

not obscure the fact that the dye movement in 

the estuary was essentially a two-dimensional 

phenomenon throughout the study period. 

Several conclusions derived from the study 

are itemized as follows: 

1. The centroid of the dye mass injected 

near the 14th Street Bridge traveled downstream at a net daily rate of less than 0.6 mile 

for the 6-day period. Nontidal discharge at 

Chain Bridge varied from 700 to 1,200 cfs in 

this period~ averaging 900 cfs. 

2. The above rate of net movement~ defined 

daily at a fixed phase of the tidal cycle~ is 

primarily controlled by the nontidal discharge 

flowing into the estuary. However~ during each 

tidal cycle~ the centroid of a solute mass 

moves approximately with the average tidal 

velocity of water, which changes direction approximately every 6 hours. 

3. Tidal actions are fairly efficient means 

of diluting the dye in the longitudinal direction; the rate of increase of the longitudinal 

variance was almost proportional to the 

square of elapsed time. A transient longitudinal dispersion coefficient at the end of 150 

hours was 210 sq ft per sec. However, the 

lateral diffusion was far from complete even 

after the 6t-day test period. 

4. At low inflow to the estuary, the dye 

disperses upstream to a point where the inflow to the estuary is sufficient to prevent 

further upstream movement; in this study no 

dye was observed above Key Bridge. As the 

inflow to the estuary increases, the upstream 

distance which the dye would be expected to 

move would decrease. Of importance is that 

a contaminant dumped at a downstream point 

can move some distance upstream and pollute 

upstream as well as downstream areas. Increased inflow to the estuary would be expected to decrease this effect. 

REFERENCES 

Durum~ W. H.~ and Langbein, W. B., 1966; Water 

quality of the Potomac River estuary at 

Washington~ D.C.: U.S. Geol. Survey Circ. 

529-A, 9 p. 

Hetling~ L. J ·~ and O'Connell, R. L., 1966, A 

study of tidal dispersion in the Potomac 

River: Water Resources Research, v. 2, 

no. 4, p. 825-841. 

Wilson, J. F., and Forrest, W. E., 1965~ Poto-

,mac River time-of-travel measurements: 

.Lamont Geol. Observatory Symposium on 

Diffusion in Oceans and Fresh Waters, 

Palisades, N.Y., 1964~ Proc.~ p. 1-18. 

* U. S. GOVERNMENT PRINTING OFFICE: 1969 0- 351-826