Movement and Dispersion of 

Soluble Pollutants in the 

Northeast Cape Fear Estuary, 

North Carolina

GEOLOGICAL SURVEY WATER-SUPPLY PAPER 1873-E

Prepared in cooperation with the 

North Carolina Department of 

Heater and Air Resources
Movement and Dispersion of 

Soluble Pollutants in the 

Northeast Cape Fear Estuary, 

North Carolina

By E. F. HUBBARD and WILLIAM G. STAMPER

ENVIRONMENTAL QUALITY

GEOLOGICAL SURVEY WATER-SUPPLY PAPEP. 1873-E

Prepared in cooperation with the 

North Carolina Department of 

Plater and Air Resources

The flushing and dispersive characteristics 

of an essentially well-mixed estuary as 

defined by a flu ores cent-dye study

UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1972
UNITED STATES DEPARTMENT OF THE INTERIOR 

ROGERS C. B. MORTON, Secretary

GEOLOGICAL SURVEY 

V. E. McKelvey, Director

Library of Congress catalog-card No. 72-600007

For sale by the Superintendent of Documents, U.S. Government Printing Office

Washington, D.C. 20402 - Price 25 cents (paper cover)

Stock Number 2401-2142
CONTENTS

Page

Glossary _________-_________-___-_________.-__-_______ IV

Abstract _________________________________-_____ El

Introduction ____________________________________ 1

Objectives ____________________________________________ 4

Description of estuary and stream system _ ___ _. ______ 4

The dye study ________________________________________ 5

Data collection ________________________-____._______ 5

Data analysis __________________-_______.._________ 6

Results of the dye study _______________________ 11

Flow characteristics ___________________________ 20

Estimating fresh-water inflow _____________________._____ 20

Flushing time ________________________________ 21

Effect of tides _________________________________ 24

The scheduling of effluent releases ___________..______ 26

Summary __________________________________________ 29

References cited _____________________________ 31

ILLUSTRATIONS

Page

FIGURE 1. Index map showing location of cross sections 1-4 and gage

site _________________________________ E3 

2-3. Graphs showing fluctuation in dye concentration:

2. At a sampling point 200 feet from the left bank ir

cross section 1 _____________________ 7

3. At a sampling point 300 feet from the left bank ir

cross section 4 _________________.._______ 9

4-7. Graphs showing cumulative dye concentration versus time:

4. Section 1 _____________________.____ 11

5. Section 2 ___________________-______ 12

6. Section 3 __________________________ 12

7. Section 4 __________________________ 13 

8-11. Graphs showing lateral variation in daily maximum dye 

concentration:

8. Section 1 _________________.________ 14

9. Section 2 __________________________ 14

10. Section 3 __________________________ 14

11. Section 4 ______________________ ___ 15 

12-15. Graphs showing maximum concentration buildup versus 

rate of solute injection for selected fresh-water 

inflows:

12. Section 1 _______________..________ 16

m
iv CONTENTS

FIGURES 13-15. Graphs showing maximum concentration buildup 

versus rate of solute injection for selected 

fresh-water inflows:

Page

13. Section 2 _________________________ E16

14. Section 3 _______________________ ___ 17

15. Section 4 __________________________ 17 

16-20. Graphs showing:

16. Relation between flow measured at the gaging 

station, Northeast Cape Fear River at Chinquapin, and the fresh-water inflow to the Northeast Cape Fear Estuary _!_________________ 21

17. Low-flow frequency curves for the Northeast

Cape Fear Estuary _________________ 22

18. Cross-sectional area in the 12-mile reach above

the mouth of the Northeast Cape Fear Estuary. 22

19. Average flushing time for a solute injected into 

the Northeast Cape Fear River 6.5 miles up 

stream from the mouth ___________________ 23

20. Frequency curve of the maximum flushing time 

for the reach extending upstream on the Northeast Cape Fear River from the mouth to mile 

6.5 _____________________.________ 25 

21. Schematic diagram showing that the peak concentration 

of a solute released in the Northeast Cape Fear Estuary 

is located immediately above the mouth at each lowslack tide ____________________________ 29

GLOSSARY

The following definitions refer to technical terms as specifically used in this 

report.

Conservative solute. A dissolved substance of low degradability. 

Cubic feet per second (cfs). The rate of discharge of a stream whose channel is 1 square foot in cross-sectional area and whose average velocity

is 1 foot per second. 

Drainage area. The surface area at a certain point on a stream from which

runoff is drained by the stream system. 

Ebb tide. The outgoing tide, characterized by falling stage and downstream

flow. 

Flood tide. The incoming tide, characterized by rising stage and upstream

flow. 

Flushing time. The average time required for a particle of solute to travel

from a point of injection to the mouth of the estuary. 

Left bank. The streambank that is on the left when facing downstream

or seaward.
CONTENTS v

Low-flow frequency curve. A graph showing the magnitude and frequency 

of minimum flows for a period of given length. Frequency is usually 

expressed as the average interval, in years, between recurrences of an 

annual minimum flow equal to or less than that shown by the magnitude 

scale.

Micrograms per liter (,ug/l). A unit expressing the weight of a dissolved 

substance with respect to the solution volume. If it can be assumed that 

a liter of solution weighs 1 kilogram, results in micrograms per liter 

are equivalent to those in parts per billion.

Mileage figures. The distance along1 the center of the channel upstream 

from the mouth in statute miles.

Milligrams per liter (mg/1). A unit expressing the weight of a dissolved 

substance with respect to the solution volume. If it can be assumed that 

a liter of solution weighs 1 kilogram, results in milligrams per liter are 

equivalent to those in parts per million.

Recurrence interval. The average time, in years, within which an extreme 

event will be equaled or exceeded once. An example of an extreme event 

would be a drought or period of low streamflow.

Runoff. That part of precipitation that appears in streams.

Semidiurnal. A term which describes an event, or cycle, which occurs during half-day intervals. Since tidal cycles cover approximate intervals 

of one-half day, they are characterized as semidiurnal.

Solute. A substance which is dissolved in a liquid. Solute may be expressed 

as a concentration or as the total dry or! undiluted weight.

Stationing or station. As used in this report, the distance from the left 

bank to a sampling point in a cross section.

Tidal excursion. The distance a certain particle of water moves upstream 

or downstream during a tidal cycle with reference to some stationary 

point.
ENVIRONMENTAL QUALITY

MOVEMENT AND DISPERSION OF SOLUBLE POLLUTANTS

IN THE NORTHEAST CAPE FEAR ESTUARY,

NORTH CAROLINA

By E. F. HUBBARD and WILLIAM G. STAMPER

ABSTRACT

This report presents the results of a fluorescent-dye-tracing study to determine the concentrations of a pollutant that would be present in the Northeast 

Cape Fear Estuary at various rates of continuous waste injection and freshwater inflow.

Rhodamine WT dye was introduced into the estuary at a constant rate over 

a 24.8-hour period (two tidal cycles) at a point 6.4 miles upstream from the 

mouth in Wilmington, N.C., and concentrations were monitored at several 

selected sections in the tide-affected part of the river for 17 days. Th Q range 

between high and low tide in this reach of the estuary averages about 3.5 

feet, and there is usually strong flow in both directions.

Results of the dye study indicate that if a pollutant were injected at a 

rate of 100 pounds per day under the conditions of relatively low inflow 

existing- at the time, concentrations would ultimately build up to 20 micrograms of dye per liter of water 1,000 feet downstream. The flushing time 

during the study is estimated to be 17 days. These results are extrapolated 

to include periods of lower or higher inflow. For example, at average intervals 

of 10 years, it is estimated that inflow is so low that 100 days are required 

for a pollutant to travel the 6.4 miles from the point of waste release to the 

mouth of the river. Under these conditions it is expected that 1,000 feet 

downstream from the point of waste discharge, daily maximum concentrations will average about 130 micrograms per liter for each 100 pounds of 

pollutant injected per day.

Results of a continuous discharge measurement of flow made by current 

meter during a complete tidal cycle are presented as a part of this report. 

Data from this measurement and other evidence indicate that net upstream 

flow in the estuary is possible over a period of several days.

INTRODUCTION

Increasingly, attention is centered on an important natural 

resource of North Carolina, the estuaries of its rivers. These 

tidal reaches have tremendous potential for recreation, waste disposal, navigation, and water supply. In addition to these direct 

uses by man, biologists stress the dependence of many plants and

El
E2 ENVIRONMENTAL QUALITY

animals on an estuarine environment during all or a pp.rt of their 

life cycle. For good management of this resource, information is 

needed on the mechanics of flow in the estuaries.

The lower part of the Northeast Cape Fear River is an example 

of an estuary that many industries presently use. This use is 

expected to increase rapidly in the near future, especially for 

waste disposal. Owing to the varied flow patterns of an estuary, 

which alternately has upstream and downstream flow, waste disposal can pose complex problems. The concentration of a waste 

injected into an estuary may dissipate in three ways: (1) natural 

purification or assimilation can occur, (2) tidal and freshwater inflow tend to dilute it, and (3) seaward migration caused 

by fresh-water inflow and dispersion eventually flush the waste 

into the ocean. Pollution can reach dangerous levels if the buildup 

in waste concentration exceeds the capacity of the estuary to 

reduce it. If the estuaries are to be protected from undue pollution and used for the benefit of the public, a thorough knowledge 

of the system is essential. (For discussions on dispersion models, 

see Harleman, 1966, and Sayre, 1968.)

The Nuclear Energy Division of the General Electric Co. recently constructed and placed into production a plant located between U.S. Highway 117 and the Northeast Cape Fear River 

about 6 miles north of Wilmington near Wrightsboro, N.C. Effluent from this plant is being introduced into the river.

Because of the complex flow in the Northeast Cape Fear Estuary, a special investigation was conducted to determine the dispersive and assimilative characteristics of the reach into which 

the General Electric Co. is discharging wastes. The U.S. Geological Survey, at the request of and in cooperation with the North 

Carolina Department of Water and Air Resources, made the study. 

The General Electric Co., in addition to making a finardal contribution to the North Carolina Department of Water and Air 

Resources, furnished a pier and recording instruments for a gaging station to record river stage and velocity and direction of 

flow on the river near the point at which the waste? are being 

discharged. (See location map, fig. 1.)

We thank the participants in this project not onbr for their 

efforts but also for the willingness with which they performed 

them. Special thanks are given to James F. Bailey, Nobuhiro 

Yotsukura, and Frederick A. Kilpatrick, hydraulic engineers of 

the Geological Survey, who assisted in the initial reconnaissance, 

the data collection and reduction, the analyses of data, and the 

review of this report.
POLLUTANTS, NORTHEAST CAPE FEAR ESTUARY, N.C, E3

78°00' 77"55'

34°20' -

34° 15' -j

FIGURE 1. Index map showing cross sections 1-4 and gage site.

466-113 O - 72 - 2
E4 ENVIRONMENTAL QUALITY

OBJECTIVES

The objectives of this study were to:

1. Understand the flow and dispersive characteristics of the 

Northeast Cape Fear Estuary and determine how they affect 

the flushing1 of soluble wastes.

2. Develop methods permitting- the prediction of buildup in concentrations to occur at selected points within th?. estuary 

when a conservative solute (dissolved substance of low 

degradability) is discharged to the system. 

The authors' objectives were accomplished by injecting a fluorescent dye and tracing- its movement and dispersion in the 

estuary as it was expelled from the system and by measuringtidal velocity, direction, and volume of flow. This experiment, for 

the most part, took place in October 1969, and the results are 

included in this report. (For other recent reports on estuarine 

dye studies, see Williams, 1967, and Beverage and Swecker, 1969.) 

It was anticipated at the beginning of the study that waste 

concentrations might reach undesirably high levels dur'ng certain 

periods of low fresh-water inflow and that it might be necessary 

to schedule waste releases to make optimum use of tl^ flushing 

effects of ebb tides and higher inflows and to minimize the upstream migration of the wastes. Scheduling release^ requires 

current data on the direction and velocity of flow in ths estuary. 

The General Electric Co. constructed a pier on which the Geological Survey installed a deflection-vane and a stilling well. The company provided instruments which record direction of flow, vane 

deflection, and stage. These instruments are arranged so that 

relative velocity and direction of flow, as well as stage, can be 

monitored and recorded at the river or in the General Electric 

plant.

DESCRIPTION OF ESTUARY AND STREAM SYSTEM

The Northeast Cape Fear River heads in Wayne County, N.C., 

and flows south through Duplin, Fender and New Hanover Counties, and at Wilmington flows into the Cape Fear River which 

empties into the ocean about 30 miles south of Wilmington. The 

gage site, also the point of dye injection, is on General Electric 

Co. property at mile 6.4 above the mouth of the Northeast Cape 

Fear River. The drainage area at the gage is 1,700 sq mi (square 

miles) and at the mouth is 1,740 sq mi.

Much of the analysis in this report concerns the reach of the 

river from the mouth upstream for about 12 miles. This is the 

area usually affected by the discharge of solutes in the vicinity of 

the gaging station.
POLLUTANTS, NORTHEAST CAPE FEAR ESTUARY, N.C. E5

The tidal effect in the Northeast Cape Fear River extends about 

20 or 30 miles above the mouth. The tidal range is 3.4 feet at the 

gaging station, compared to the tidal range of 4.5 feet in the ocean 

near the mouth of the Cape Fear River. The characteristic diurnal 

cycle of tides (a high high, a low low, a low high, and a high low 

tide) is approximately 24 hours and 50 minutes.

The Northeast Cape Fear Estuary is essentially well-mixed; 

that is, there is practically no vertical stratification of fre?h and 

salt water within the system, except possibly during large floods. 

This condition usually applies to estuaries in which the volume 

of water due to tidal flow is several orders of magnitude greater 

than the volume of fresh-water inflow.

THE DYE STUDY

The dye study, designed to simulate the waste discharge from 

the industrial facility into the Northeast Cape Fear Estuary, was 

accomplished by injecting Rhodamine WT dye solution into the 

estuary at a constant rate from the gaging station pier and monitoring the movement and dispersion of the resulting dye cloud 

by collecting samples at selected points in the study reach. (For 

discussions of fluorescent-dye-tracing techniques, see Wilson. 

1968, and Pritchard and Carpenter, 1960.) The assumption was 

made that this dye would be as conservative (see glossary) as 

the waste material it simulated. In other words, the dye would 

resist destruction or alteration by chemical, photo-chemical, biological, or other processes to the same degree as waste materials 

and would not be absorbed or adsorbed by bed materials and 

substances in the water.

During the study fresh-water inflow was estimated to be 400 

cfs, moderately low for this estuary. Tides were somewhat above 

normal, probably because of a tropical storm which moved north 

off the coast during the first few days of the study. These factors, 

relatively low fresh-water inflow and higher than average tides, 

provided ideal conditions for the study. Because both factors tend 

to retard the flushing action of an estuary (Wilder and Hubbard, 

1968), the results of the investigation are particularly applicable 

to times when pollution buildup may reach critical values.

DATA COLLECTION

Before injecting the dye, the authors needed to find the approximate tidal excursion: the distances the dye cloud would move upstream and downstream during one tidal cycle. These distances 

were determined by the authors observing the movement of floats 

placed in the estuary when flow conditions were similar to those
EG ENVIRONMENTAL QUALITY

predicted for the injection period. The estimated upstream and 

downstream tidal excursions were 2.9 and 5.0 miles from the 

injection point, respectively.

Four cross sections were established at strategic locations along 

the estuary. Sampling sections 1 and 4 which, respectively, were 

the farthest upstream and downstream, were located near the 

ends of the tidal excursion zone noted above, at river miles 9.3 

and 1.4. The locations of the sections and the gage are shown in 

the following table.

Distance above Distance from gage and

mouth dye-injection point

(miles) (miles)

Section 1 _________________ 9.3 2.9

Gage ___________________ 6.4 

Section 2 _________________ 6.2 C.2

Section 3 _________________ 4.4 2.0

Section 4 _________________ 1.4 £.0

One hundred thirty pounds of Rhodamine WT dye in a 6.25 percent solution with water was used in the study. Dye injection 

began at 2:00 a.m. e.d.t. on October 14, 1969, the tirie of highslack tide at the injection point, and continued for two complete 

tidal cycles, which ended at 3:00 a.m. on October 15.

During the first two tidal cycles after the dye injection began, 

six to 10 surface samples and two bottom samples at selected stations in each cross section were collected at about 15-minute 

intervals. These sampling intervals were gradually lergthened as 

the concentration versus time curves became flatter. (See fig. 2.) 

The number of sampling stations within each cross section were 

reduced as lateral mixing became more complete. After the first 

week of the study, a schedule was developed so that representative 

samples were collected from each cross section at tim°.s of maximum concentration. Sampling was continued through Oct. 30, 

1969, when the maximum concentration measured in any cross 

section was less than 0.25 /*g/l, below the level of significance 

for this analysis; therefore, collection of data was corcluded.

DATA ANALYSIS

The dye study was designed to simulate the injection and movement of a conservative soluble substance within the estuary for an 

indefinite length of time. The experiment could duplicate this 

situation exactly by the dye's being injected until the flushing 

process stabilized and daily maximum concentrations measured in 

the estuary reached a constant value for the prevailing inflow and 

tidal conditions. It is prohibitively expensive, however, to inject 

dye for the 15 or more days required to build up concentrations to 

this steady value. The method of superposition, therefore, is
LITER PER MICROGRAMS IN CONCENTRATION, DYE 

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E8 ENVIRONMENTAL QUALITY

applied to the observed short-term data to compute tlie concentration that would result from long-term injection of a solute. 

Theoretical application of this method, which has been known for 

some time (Bailey and others, 1966), was recently described by 

Yotsukura (1968).

Understanding the superposition procedure to estimate the 

buildup in dye concentrations requires considering the effect of 

a solute being injected into the river. During the dye study, it was 

observed that the dye quickly dispersed into a reach of the estuary 

approximately 6 miles long at low tide. This cloud of dye moved 

back and forth in the estuary in response to the ebb and flow of 

the tide. Consequently, if the dye concentration was monitored at 

a given point, the concentration would rise, reach a peak, and 

then diminish as the dye cloud moved past. Then during the 

reverse tide when the cloud recrossed the monitoring point, it 

would cause another rise, peak, and diminution. The dye-cloud 

movement produces two peaks of concentration for each tidal 

cycle unless the dye disperses so uniformly throughout the reach 

that no peak concentration is discernible. If the concentration is 

monitored near either end of the reach in which the dye cloud is 

moving, only one peak is observed during each tidal cycle because 

the dye cloud arrives at the end of the reach, causing s.n increase 

in concentration; remains there during slack tide; and leaves 

when the tide reverses, causing a decrease in concentration.

The superposition procedure, by which concentration buildup 

is estimated, used the data from samples collected in the estuary. 

The dye concentrations of these samples were determined, and 

graphs of concentration versus time were plotted for selected 

sampling points. Examples are shown in figures 2 and 3. For simplicity, figures 2 and 3 depict the dye concentrations at sections 

1 and 4. Because these sections are near the upstream and downstream ends of the reach affected by the dye cloud, there is only 

one peak in concentration per tidal cycle of 12.4 hour?-. Had the 

concentrations at sections 2 or 3 been shown, there would be 

two peaks per tidal cycle, as explained above.

These peaks maintain a nearly constant relation with the rise 

and fall of the tides. For example at section 4, which is near the 

mouth of the Northeast Cape Fear, the peak in concentration 

occurs approximately at low slack tide, when the dye cloud is 

as far downstream as it will travel during that tidal cycle. The 

concentrations at section 4, the most downstream sampling section, therefore, are at the maximum for that tidal cycle. This relation between the low slack tide and maximum concentration at
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section 4 is maintained as long as the solute remains in the estuary. Likewise a fixed relation between the tidal movement and the 

fluctuation in dye concentration exists at any other point in the 

reach. The effects of tidal motion on a solute are discussed in 

greater detail later in this report.

The method of superposition is a technique for adding concentrations observed on succeeding tidal cycles, after a short-term 

injection of a solute, to approximate the concentration that would 

result from a long-term injection. Consider the concentration 

versus time curves illustrated in figures 2 and 3. The amplitude 

of these curves increased sharply during the dye injection period 

of two tidal cycles and then gradually decreased as th? dye was 

dispersed and flushed from the system. Had the injection continued for another two tidal cycles, the concentratior resulting 

only from the dye injected during second two cycles would follow 

the same curve as that for the first injection for two cycles, but 

the time would be delayed by 24.8 hours. Thus, the concentration 

observed at a given time after an injection for two tidal cycles 

plus the concentration observed 24.8 hours earlier would be 

equal to the concentration that would result at that s^me given 

time after (or during) an injection for four tidal cycles. If the 

injection were continued for the more than 3 days required for 

another two tidal cycles (six tidal cycles in all), the concentrations on the third day would be equal to the superposition of the 

concentration curves for the first, second, and third days. If the 

injection were continued for many days, the concentration of any 

peak would equal the sum of the peak concentrations resulting 

from a two-cycle injection taken at the same time in every other 

tidal cycle. Because the injection was for two tidal cycles, it is 

necessary to sum only the peak concentration for every other 

cycle. If the injection were for one tidal cycle, every p?ak would 

have to be added to obtain an estimate of concentration buildup.

For this study it was decided to inject dye for two tidal cycles 

because of the asymmetry of the tides in this region. During a 

two-tidal cycle period there is a high-high, a low-low, a low-high, 

and a high-low tide. A determination of the response of the dye 

cloud to this asymmetry was necessary to estimate tVn. concentration buildup accurately. In other words, it would make some 

difference in ultimate concentration whether the solute were injected through just the high-high or the low-high cycle. By 

injecting through both it was possible for the authors to choose 

the combination of peaks that would add up to the Irrgest dye 

concentration. This summation was done, as is illustrated in
POLLUTANTS, NORTHEAST CAPE FEAR ESTUARY, N.C. Ell

figure 3, and the value obtained is referred to hereafter as the 

daily maximum concentration.

One way to understand this computational procedure is to consider that, if there were an injection of dye for many days, the 

first incremental concentration would represent dye injected that 

day; the second incremental concentration would represent dye 

injected the day before. The third would represent dye injected 

3 days before, and so on until the concentrations build to a steady 

level. Under flow conditions similar to those during the dye 

study, this plateau concentration would be reached after about 

17 days.

RESULTS OF THE DYE STUDY

Dye concentrations were added for sampling stations in each 

section. Dye was injected at the rate of 125 pounds per day. Dyeconcentration data were divided by 125 so that the units were 

micrograms per liter for each pound of solute injected per day. 

Figures 4-7 illustrate the sum of incremental concentrations in

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0.07

0.06

0.05

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14 16 18 20 22 24 

OCTOBER 1969

26 28 30 1 3 

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FIGURE 4. Cumulative dye concentration versus time, in days, at a sampling 

point 200 feet from the left bank in cross section 1.

466-113 O - 72 - 3
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CUMULATIVE DYE CONCENTRATION, IN MICROGRAMS PER LITER

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Concentration buildup caused by an 

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14 16 18 20 22 24 

OCTOBER 1969

26 28 30 1 3 

NOV

FIGURE 7. Cumulative dye concentration versus time, in days, at a sampling point 300 feet from the left bank in cross section 4.

these units, as described above. These curves represent the buildup in daily maximum concentrations at the indicated sampling 

station if there were continuous injection of a solute. Th Q. horizontal line which these curves approach asymptotically is the 

maximum concentration buildup possible for the conditions during the dye study.

Figures 8-11 show the lateral distribution of daily mrximum 

dye concentrations hereafter referred to as unit concentrations, 

because they represent the maximum daily concentrations that 

would result from an injection rate of 1 pound per day. The 

cumulative dye-concentration computations illustrated in figure 3 

were done for all sampling stations in each cross section. These 

unit concentrations can be multiplied by the amount of any solute, 

in pounds per day injected, to determine the daily mrximum 

buildup of that solute, at any point. For example, suppose it were 

necessary to determine the daily maximum concentration at a 

point 500 feet from the left bank in section 3 after long-term 

injection of phosphate at a rate of 3,000 pounds per day, when a 

fresh-water inflow of 400 cfs exists. Figure 10 shows that the unit 

concentration is 0.17 Mg/1. Multiplying 0.17 by 3,000, we obtain 

a maximum daily concentration of 510 /*g/l of phosphate. This
E14 ENVIRONMENTAL QUALITY

0.14

0.12

5 o ca

0.10

Concentration buildup caured by an 

injection rate of 1 pound per day

100 200 300 400 

DISTANCE FROM LEFT BANK, IN FEET

507 600

FIGURE 8. Lateral variation in maximum dye-concentration buildup for 

sampling stations in section 1, 9.4 miles above mouth.

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0.18

0.16

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0.12

Concentration buildup caused by an 

injection rate of 1 pound per day

100 200 300 400

DISTANCE FROM LEFT BANK, IN FEET

500 600

FIGURE 9. Lateral variation in maximum dye-concentration buildup for 

sampling stations in section 2, 6.2 miles above mouth.

0.16

Concentration buildup caused by ai 

injection rate of 1 pound per day

0.12

200 300 400 

DISTANCE FROM LEFT BANK, IN FEET

FIGURE 10. Lateral variation in maximum dye-concentration buildup for 

sampling stations in section 3, 4.4 miles above moutl .
POLLUTANTS, NORTHEAST CAPE FEAR ESTUARY, N.C. E15

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Concentration buildup caused by an 

injection rate of 1 pound per day

100 200 300 400 

DISTANCE FROM LEFT BANK, IN FEET

500 600

FIGURE 11. Lateral variation in maximum dye-concentration buildup for 

sampling stations in section 4, 1.4 miles above mouth.

value applies only for flow conditions similar to those that prevailed during the study.

To eliminate the need for making the computation described 

above, we calculated pollutant concentrations at each cross section 

for different rates of injection by using the maximum buildup factors for each section. The resulting curves, the solid lines in figures 12-15, are based on the estimated average fresh-water runoff of the entire basin (to the mouth) which occurred during the 

dye-injection study. To increase the versatility of these curves, 

we extrapolated them to cover various rates of fresh-water inflow which are shown as the dashed lines in figures 12-15. This 

resulting family of curves was extrapolated from this single dye 

study by the authors assuming that concentration buildup is inversely proportional to fresh-water inflow to the estuary. While 

this simplifies the complexities involved, and other dye studies at 

different rates of fresh-water inflow are necessary to test the 

assumption, we consider the extrapolated curves useful approximations. (For a discussion on the linearity of the response of 

flushing time to inflow, see Carpenter, 1960.)

To illustrate the use of figures 12-15, we can estimate tl N « daily 

maximum concentration at section 2 if a solute were introduced 

into the estuary near the gage at a rate of 1,000 pounds per day 

when the fresh-water inflow was 200 cfs. Enter figure 13 on the 

bottom scale and locate the intersection with the 200-cfs curve. 

The maximum concentration is then read on the left-hand scale 

opposite this point, which is 400 Mg/1 for this example. This procedure may be used with any curves in figures 12-15. The resulting estimate represents the highest possible concentratior at the 

section during the daily maximum.

Figures 12-15 may be represented by a simple equation. The 

equation, like the curves it represents, is more precise for fresh-
E16 ENVIRONMENTAL QUALITY

- ^ "^ 80Q_cls _ 

0 200 400 600 800 1000 1200 1400 1600 1800 2000 

AMOUNT OF SOLUTE, IN POUNDS PER DAY

FIGURE 12. Maximum concentration buildup versus rate of solute injection for selected fresh-water inflows at section 1.

Z 800 -

g 700 h

0 200 400 600 800 1000 1200 1400 1600 1800 2COO 

AMOUNT OF SOLUTE, IN POUNDS PER DAY

FIGURE 13. Maximum concentration buildup versus rate of solute injection for selected fresh-water inflows at section 2.
MAXIMUM DAILY CONCENTRATION, IN MICROGRAMS PER LITER MAXIM

I 
E18 ENVIRONMENTAL QUALITY

water inflows near the 400 cfs experienced during the study than 

for other inflow rates. The general equation is:

Ct = Kt xL/Q (1)

where

C{ is the estimated maximum daily concentration, in micrograms per liter of a solute at sections 1-4, and i designates

the section number; 

Ki is a constant of proportionality for each cross section

(#! = 46, #2 = 80, #3 = 72, and #4 = 63) ; 

L is the average daily load of the solute being injected into

the estuary, in pounds; and 

Q is the average fresh-water inflow, in cubic feet per second,

to the estuary during the designated period.

For example, if one wished to calculate the maximum daily concentration at section 1 if 10,000 pounds of fluoride were injected 

daily during a period in which fresh-water inflow averaged about 

1,000 cfs, these figures could be used in the equation as follows:

d = 46 X 10,000/1,000 = 460 vg/l

This value would represent the concentration of fluoride in the 

water at section 1 resulting from the injection of 10,000 pounds 

of fluoride per day in the vicinity of the gaging station. To obtain 

the total concentration at this point, one would have to add any 

background concentration already in the water from either natural or man-made sources.

Another application of the superposition method to the present 

data is the estimation of transient concentrations because of a 

varied daily load. This capability might be needed if the daily 

load of injected solute varied so greatly that an average value 

used in equation 1 would not give a representative answer. Here 

the computation is performed by summing up daily maximum 

concentrations which are linearly related to daily lo°ds, or, in 

equation form:

Cl = [0.047 (Lf.0 ) + 0.023 (L^) +0.011 (Lf_2 ) +0.007 (Lf_8 ) 

+ 0.005 (L,_4 )+ 0.003 (L*_5 )+ 0.003 (Lf_e ) +O.C02 (L,_7 ) 

+ 0.002 (Lf_ 8 )+ 0.002 (L,_9 )+ 0.002 (L,_10 ) +O.C02 (L«_u) 

+ 0.001 (L*_12 ) + 0.001 (L*_13 )+ 0.001 (L*_14 )+ 0.001 (Lf_ 16 )

+ 0.001 <L«_16 ) + 0.001 (L,_17 )] (2)
POLLUTANTS, NORTHEAST CAPE FEAR ESTUARY, N.C. E19

C2 = [0.060 (L,_0 )+ 0.038 (L^) +0.026 (L,_2 ) +0.018 (Lt_3 ) 

+ 0.013 (L,_4 )+ 0.010 (Lt_ 5 )+ 0.008 (L,_6 ) +0.006 (£,_7 ) 

+ 0.005 (L,_8 ) +0.004 (L,_9 ) +0.003 (L,_10 ) +0.003 (Lt_ n ) 

+ 0.002 (L,_i2 ) + 0.001 (L,_13 )+ 0.001 (L,_ 14 ) +0.001 (L,_15 )

+ 0.001 (Lt_ 16 )]^? (3)

C3 = [0.027 (L,_0 ) +0.042 (L^) +0.025 (L,_2 ) +0.018 (L,_3 ) 

+ 0.012 (L,_4 ) +0.010 (L,_B ) +0.009 (Lt_ 6 ) +0.008 (L,_7 ) 

+ 0.007 (L,_8 ) +0.006 (L(_ 9 ) +0.005 (L,_10 ) +0.004 (Lt_ u ) 

+ 0.003 (L,_,,) +0.002 (L,_13 ) +0.001 (L,_14 ) +0.001 (L,_1B )]

4 = [0.004 (L,_0 ) +0.006(Lt_ 1 ) +0.027 (L,_2 ) +0.015(L,_ 3 ) 

+ 0.010 (Lf_ 4 ) + 0.008 (Lt_B ) +0.006 (L(_ 6 ) + 0.005 (L(_ 7 ) 

+ 0.004 (Lt_ 8 ) + 0.003 (L( _ 9 ) +0.003 (Lt_ 10 ) + 0.002 (L(_n) 

+ 0.002 (L,_12 ) + 0.001 (L,_13 ) +0.001 (L,_14 ) +0.001 (Lt_ 15 ) ]

where

Ci, C2 , C3 , C4 are the estimated daily maximum concenti'ations

at ^ days after the start of loading, in micrograms per liter,

at cross sections 1, 2, 3, and 4, respectively. 

Lt_ 0 is the load of solute, in pounds, being injected on the day

for which d_4 is estimated, Lf^ is the load injected on the

preceding day, L,_2 is that injected 2 days before, and so on. 

Q is the average fresh-water inflow, in cubic feet per second,

for the period being considered.

These equations were developed from the data collected during 

the dye study and give the same concentration as does equation 1 

when all values are summed. The unit concentrations shovm for 

each day, however, are values taken from a smoothed curve and 

do not precisely agree with the concentration observed during the 

study. The curves were smoothed so that the equations would 

represent the response of the estuary to the injection of a solute 

and not include the short-term effects of any anomalous tidal 

movements that occurred during the study.

Equations 2-5 would have application for a process where 

wastes for perhaps a week would be released in 1 or 2 days. These 

four equations, like equation 1, are more precise for fresh-inflow 

around 400 cfs than for other rates of inflow and must be added 

to the background concentration to obtain the total concentration.
E20 ENVIRONMENTAL QUALITY

FLOW CHARACTERISTICS

The amount of fresh-water inflow primarily determines the 

rate at which a solute is flushed from the estuary. Tides cause 

tremendous volumes of water to flow back and forth past any 

given point in the estuary. If there is no fresh-water inflow, however, net flow is zero when averaged over many dayr. The net 

downstream movement of a particle of water primarily depends, 

in the long run, on fresh-water inflow.

The dye injected during this study was quickly dispersed by 

turbulent diifusion resulting from tidal movements. A reach 

extending approximately 12 miles above the mouth of the estuary 

contained the dye cloud. A solute discharged into the estuary near 

the gaging station would also be dispersed into this rerch during 

equivalent inflow and tidal conditions. During periods of higher 

tides and lower inflow, the aifected reach would probably extend 

a few miles farther upstream. Conversely, during periods of 

lower tides and higher inflows the aifected reach would not 

extend as far as 12 miles upstream. Eifective use of the curves 

developed in the preceding section, particularly those in figures 

12-15, requires some data on fresh-water flow into the estuary.

ESTIMATING FRESH-WATER INFLOW

Figure 16 illustrates a method of estimating the fresh-water 

inflow to the estuary, upstream from the mouth, by using the flow 

measured at the gaging station on the Northeast Cape Fear 

River at Chinquapin, about 78 river miles upstream. This graph 

is based on flow records collected at Chinquapin and at stations 

on three downstream tributaries. This curve provides a reliable 

approximation of the total fresh-water inflow only during stable 

low-flow recessions. Since such conditions usually occur only 

when inflow is less than approximately 1,000 cfs, the curve is not 

extended to higher flows. Under these conditions of low flow, pollution problems are most critical. It is preferable to apply the 

curve on an average-flow basis, that is, flow at the Chinquapin 

station averaged over a period of several days and the derived 

fresh-water inflow taken as the average during the corresponding 

time period.

The low-flow frequency curves in figure 17 give the expected 

inflow regime in the estuary at both continuous and partialrecord gaging stations in the Northeast Cape Fear River basin. 

These curves may be used to estimate the recurrence intervals of 

annual minimum flows less than the indicated values. At average
POLLUTANTS, NORTHEAST CAPE FEAR ESTUARY, N.C. E21

1000

100

10

I I I I

10 100 

FLOW AT CHINQUAPIN, IN CUBIC FEET PER SECOND

1000

FIGURE 16. Relation between flow measured at the gaging station, Northeast Cape Fear River at Chinquapin, and the fresh-water inflow to the 

Northeast Cape Fear Estuary.

intervals of 10 years, for example, the annual minimum flow, 

averaged over 7 days, is less than about 15 cfs, as the dashed line 

in figure 17 indicates.

FLUSHING TIME

As noted earlier, the maximum concentration buildup is assumed to be inversely proportional to fresh-water inflow. Freshwater inflow is important because it controls the rate ai which 

wastes are flushed from the estuary. The rate of flushing is expressed in traveltime of a solute (the center of the mass) from 

its point of injection to the mouth of the estuary.

For this analysis, average traveltimes are computed from the 

gage to the mouth for various rates of fresh-water inflow. Crosssectional areas were computed at many points through the reach. 

Figure 18 shows both the variation and the trend of these crosssectional areas. Volumes for each 1-mile part of the reach were
E22 ENVIRONMENTAL QUALITY

500

100

- 10

I I I

1.01 1.1 1.3 1.5 2 345 10 20 30 40 50 100 

RECURRENCE INTERVAL, IN YEARS

FIGURE 17. Low-flow frequency curves for the Northeast Cape Fear

Estuary.

40

z QJ 30

V) <

V) <f>

O D

20

10

468 

MILEAGE ABOVE MOUTH

10 12

FIGURE 18. Cross-sectional area in the 12-mile reach above the mouth of 

the Northeast Cape Fear Estuary.
POLLUTANTS, NORTHEAST CAPE FEAR ESTUARY, N.C. E23

determined from these areas. Mean velocities for each of these 

subreaches were then computed for various values of fresh -water 

inflow using the simple flow equation :

(6)

where

F = mean velocity, in feet per second through the subreach 

Q = inflow, in cubic feet per second 

A = area, in square feet.

Dividing the length of each subreach by the mean velocities 

gave net traveltimes, which are based on fresh-water inflow, disregarding tidal effects. Figure 19 shows the average flushing time 

versus inflow for the GV^-mile reach from the gage to the mouth. 

This curve can be used to estimate the average time necessary for 

a solute to travel through this reach of the estuary under various 

conditions of inflow. Because the flushing times obtained from

500

100

10

10 100 1000 

FRESH-WATER INFLOW, IN CUBIC FEET PER SECOND

10,000

FIGURE 19. Average flushing time for a solute injected into the Northeast 

Cape Fear River about 6.5 miles upstream from the mouth.
E24 ENVIRONMENTAL QUALITY

the graph are average values, only one-half of the dispersed solute 

would move past the mouth of the Northeast Cape Fear in the 

indicated time.

Figure 17, the frequency of occurrence of low inflows, and figure 19, the average flushing time as a function of inflow, may be 

combined for one to estimate the time period required for the 

estuary to flush for any given recurrence interval. This relation 

between flushing time and recurrence interval was developed by 

the authors first selecting flushing times of 30, 60, 90, and 120 

days and then determining the corresponding fresh-water inflows, 

using figure 19. The recurrence interval was then determined for 

each particular inflow for the designated period, in days, by using 

the appropriate curve in figure 17. Figure 20 gives the resulting 

relation of flushing time versus recurrence interval. One can 

estimate the probability of an average flushing time for any 

magnitude occurring as the annual maximum.

For example, assume that it is necessary to determine how 

often a solute being discharged into the estuary near the gage 

will be retained in the river for longer than 75 days. The frequency of occurrence may be estimated by entering figure 20 on 

the left-hand scale at 75 days, proceeding horizontally to the 

curve, and then vertically to the bottom scale, as the dashed line 

illustrates. This procedure gives a result of about 5 years. Thus, 

the maximum flushing time would exceed 75 days rt average 

intervals of 5 years.

EFFECT OP TIDES

Fresh-water inflow is the prime force in the lon^r-term net 

movement of solutes within the Northeast Cape Fear Estuary. 

In the short run, however, the effects of fresh-water inflow, except 

during major floods, are insignificant when compared with tidal 

flows. In the estuary there are strong tides, flood and ebb, which 

result in large volumes of water moving upstream and downstream past the gage during each tidal cycle.

On October 22-23, 1969, a continuous measurement of discharge was made at the gaging station for one complete tidal 

cycle. The results of this measurement illustrate the effects of 

tide. During the first ebb tide of the day, a total of 220 million 

cubic feet of water passed the gaging station. On the following 

flood tide 310 million cubic feet was measured at the gage. During 

these periods, the volume of fresh-water inflow to tV?. estuary 

is estimated to be only 11 and 10 million cubic feet, respectively. 

In this case, the component of flow due to fresh-water inflow was
c < 

5 t? 

<*3 O 

ST. 3 

i-O

b

DAYS IN TIME, FLUSHING 

oo CTI 01 *. co ro 

O O O O O O 

I I 

'sxNvxmioa xsvanxaoN aavo ava^ 'Aavnxsa 
E26 ENVIRONMENTAL QUALITY

only 5 percent during the ebb tide and 3 percent on the flood tide.

The discharge measurement was made while tides, which were 

higher than average, effectively raised the water surface and 

caused water to be backed up or stored in the estuary. For this 

reason the volume of the flood tide was larger than that of the 

ebb tide. The difference in these volumes represents the water 

stored in the estuary upstream from the gaging station during 

this particular tidal cycle. Such net upstream flow may occur for 

a few tidal cycles as a result of high tidal levels. Averaged over 

a longer period of time, however, net flow will be downstream and 

will equal the fresh-water inflow.

Because the peak concentration of a solute injected into the 

Northeast Cape Fear Estuary moves back and forth past a given 

point in the estuary in fixed relation to the tidal cycle, it may be 

desirable to schedule any program of sampling to obtain data on 

the maximum concentration rather than on some lower value. The 

following table shows the relation between the events that occur 

on the Northeast Cape Fear tidal cycle. This table can be used 

to schedule sampling so that the maximum concentration of a 

substance is monitored.

Elapsed time Time range 

(hours) Event and location (hours)

0 _ High tide at gage ____ ___ __ - - 

.3________ Peak concentration at section 1 ____________ ±1.0

I.9_______ High slack tide at gage __________-____- ± .5

2.9_ ______ Peak concentration at section 2 __________ ±1.0

4.1 _ _____ Peak concentration at section 3 ____ _ ±1.0

6.4________ Peak concentration at section 4 _____________ ±2.0

6.8________ Low tide at gage ________________ ± .5

7.8_________ Low slack tide at gage ____________ __ - ± .5

8.8_______ Peak concentration at section 3 ______________ ±1.0

10.7_______ Peak concentration at section 2 _____________ ±1.0

II.4_______ High tide at Wilmington _________________ ±1.0

12.4_______ High tide at gage ______________________ ±1.0

Although the table is based on the time of high tide at the 

gaging station, it can be placed in terms of some other tidal event 

by transposing the figures. In using the table one should allow 

for the time range shown in the right-hand column, all or part 

of which may result from variations in the typical tidal pattern 

due to high fresh-water inflow, wind effects, or other factors.

THE SCHEDULING OF EFFLUENT RELEASES

An interesting question raised during this project w^s whether 

or not the scheduling of waste releases would help reduce the 

concentration of wastes or their persistence in the estuary. If 

wastes were released in the vicinity of the gaging station at high 

slack tide, would they be carried out of the Northeast Cape Fear
POLLUTANTS, NORTHEAST CAPE FEAR ESTUARY, N.C. E27

on the following ebb tide and not return to cause a buildup of 

waste concentration in the estuary? The answer to this question 

is a qualified no. The following three factors, observed during 

the dye study or inferred from the data, show that the scheduling 

of waste releases would not preclude the buildup of waste concentrations within the estuary:

1. Ordinarily, a solute released on high slack tide will not reach 

the mouth of the Northeast Cape Fear and will be returned 

on the following flood tide. The point to which the center 

of mass of the solute will be returned, under moderate and 

low inflow conditions, will be only a short distance below 

the point of release. Short-term tidal conditions may cause 

this distance to vary considerably and will, on occasion, 

cause the center of mass to return to a point upstream from 

the point of release. Figure 3 indicates that the higher concentrations near the center of mass of the dye cloud would 

not reach section 4, located 1.4 miles upstream frcm the 

mouth of the Northeast Cape Fear River, before two tidal 

cycles (more than 24 hours) had elapsed.

2. The flow in the estuary becomes swift and turbulent during 

each tidal phase and causes rather rapid dispersion, as indicated by the reduction of dye concentration with time, as 

shown in figures 2 and 3. Instead of moving from the estuary as a discrete slug, a solute mixes rather quickly into a 

part of the system and is gradually removed by the combined flushing action of fresh-water inflow and dispersion.

3. Although a solute that has been moved beyond the mouth of 

the Northeast Cape Fear by ebb tide is subject to further 

dispersion in the Cape Fear River, part of the solute may 

return to the Northeast Cape Fear on the following flood 

tide. The fraction of the solute which will reenter the Northeast Cape Fear River depends on the flow in the Cape Fear. 

The lower the Cape Fear flow, the more solute will reenter 

the Northeast Cape Fear.

In spite of these factors, scheduling of releases may be profitable to limit the upstream buildup of solute. If minimizing the upstream concentrations of solute in the estuary becomes desirable, 

the gaging station may be used to schedule releases. If a solute 

were released on high slack tide, the upstream migration of this 

solute would not be completely eliminated, but it would H significantly reduced. Releasing the solute all at once, however, would 

cause the maximum concentrations in the downstream part of the
E28 ENVIRONMENTAL QUALITY

estuary to be higher than they would be in continuous release.

Conversely, if solute is released at low slack tide, the mass 

center of the contaminant will be moved first upstream, increasing the effective distance that the solute must move to h? flushed 

from the estuary. Average retention time in the estusry therefore is longer. The time of low-slack tide is least desirable to 

release a solute. Periods of high inflow might not last long enough 

to flush the estuary before periods of low inflow returned.

A solute released in a tributary to the estuary would primarily 

be introduced into the estuary during the lower part of the tidal 

cycle because water from the estuary would be backed up into 

the tributary at high tide so that the solute would be stored in 

the tributary or in the surrounding marsh. As noted previously, 

a solute released into the estuary during the lower phase of the 

tidal cycle would tend to cause a greater upstream migration of 

the solute and a longer retention time, which might possibly lead 

to a higher buildup in concentrations.

As previously indicated, the peak concentration of a solute will 

pass a point in the reach in a fixed relation to the tidal cycle. For 

example, the peak concentration of a solute released at the gage 

on high slack tide will pass cross section 3 on the outgoing ebb 

tide and again on the incoming flood tide. This process will 

continue on subsequent tides until the solute is flushed from the 

estuary.

During the flushing of the dye cloud from the estuary, samples 

were taken at about 1-mile intervals along the center of the 

channel during low-slack tide. This sampling was begun in the 

Cape Fear Estuary several miles downstream from Wilmington 

and ended several miles upstream from section 1 in the Northeast 

Cape Fear River. These data show that the peak dye concentration at low-slack tide occurs near cross section 4, which is near 

the mouth at mile 1.4.

Both the center of mass and the peak concentration of the 

solute will oscillate in response to the tidal flows within the estuary. As fresh-water inflow and dispersion act on the solute, the 

center of mass will translate seaward. This net movement is the 

flushing process. The peak concentration does not make any net 

seaward progress, however, but remains within the Northeast 

Cape Fear because that part of the solute cloud that moves into 

the Cape Fear during the ebb tide becomes more diluted than 

that which remains in the Northeast Cape Fear. When the tide 

changes and the cloud is starting to move back upstream again, 

the maximum concentration is in the Northeast Cape Fear just
POLLUTANTS, NORTHEAST CAPE FEAR ESTUARY, N.C. E29

above the mouth. Since this condition occurs on every tidal cycle, 

the geometry and dynamics of the system position the peak concentration to keep it in phase with tidal movement. This process 

is illustrated in figure 21.

 Position of solute at low slack 

tide. Darkness indicates 

relative concentration

Solute that has entered Cape 

Fear River is greatly diluted

FIGURE 21. Schematic diagram showing that the peak concentration of a solute released in the Northeast Cape Fear 

Estuary is located immediately above the mouth at each 

low-slack tide.

SUMMARY

Data from the dye experiment were used to predict the maximum buildup in concentration of a soluble contaminant introduced into the Northeast Cape Fear Estuary at any given rate. 

The values of buildup represent the highest concentration that
E30 ENVIRONMENTAL QUALITY

would occur during a day. Also curves were developed for the 

point of maximum concentration in each cross section. The study 

was conducted under conditions of below-average fresh-water 

inflow and above-normal high tides. The concentrations measured 

would be lower during normal conditions. On the other hand, 

since much lower inflow rates do occur, correspondingly higher 

concentrations of contaminants can be expected. Since inflow 

rates to the estuary vary widely, the results are expanded to provide a basis for estimating the buildup for different inflow conditions. Other curves are presented to give the reader a concept of 

the average flushing time of the estuary as related to fresh-water 

inflow, the probability of occurrence of low flows, and the probability of occurrence of flushing times of various durations.

These relations may be applied, with appropriate safety factors, 

to any waste release in the estuary near the gaging station. In 

fact it is probably feasible to infer the consequences of pollution 

from outfalls at sites other than the injection site of this study 

by shifting the results of the dye experiment either upstream or 

downstream. Shifting the outfall downstream probably will reduce buildup because shorter net traveltime is required to move 

the solutes into the Cape Fear River. On the other hand, shifting 

the outfall upstream would probably increase the amount of 

buildup because of a longer net traveltime.

If problems are anticipated from the continuous introduction 

of a certain quantity of industrial wastes into the estuary, a release shedule could be developed which would lessen upstream 

migration of the pollutant. Releases only at high slack tide, or for 

a short period thereafter, would significantly reduce concentrations upstream from the point of injection. The pollutant would 

be flushed from the estuary more quickly because of the initial 

downstream displacement of the solute cloud.

Discharge measurements during the tidal cycle measured 

showed upstream flow exceeded downstream flow. A pollutant 

released on the high-slack tide preceding the measurements 

would make no net downstream progress during the cycle. 

This phenomenon was observed during a period of only moderately low fresh-water inflow. During periods of extremely low 

fresh-water inflow, furthermore, the net movement of water in 

the estuary could be upstream for several days, particularly if 

higher-than-normal tidal levels prevailed.

The Northeast Cape Fear quickly disperses a solute both vertically and horizontally. Little difference was noticed between dye 

concentrations of samples collected at the surface and those col-
POLLUTANTS, NORTHEAST CAPE FEAR ESTUARY, N.C. E31

lected near the bottom during the dye study. Figures 8-11 show 

that no really significant difference in concentration buildup can 

be detected at any of the sampling cross sections with the exception of section 2 which is only about 1,000 feet from the point 

of injection. The high velocities and resulting turbulence of water 

associated with the tidal movement cause this rapid dispersion. 

Pollutants released into the Northeast Cape Fear Estuary do 

not tend to remain in a discrete, highly concentrated mass, but 

rather quickly disperse into a tremendous volume of water. For 

this reason during moderate flow conditions, tidal flow will not 

immediately carry a solute injected in the vicinity of the gaging 

station out of the Northeast Cape Fear. It will instead be dispersed to form a cloud several miles long which will gradually 

decrease in concentration as the forces of dispersion and the 

effects of fresh-water inflow remove it from the estuary.

REFERENCES CITED

Bailey, T. E., McCullough, C. A., Gunnerson, C. G., 1966, Mixing and dispersion studies in San Francisco Bay: Jour. Sanitary Eng. Div., Proceedings of the Am. Soc. of Civil Eng., p. 23-45.

Beverage, J. P., and Swecker, M. N., 1969, Estuarine studies in Upper Grays 

Harbor Washington: U.S. Geol. Survey Water-Supply Paper 1873-B, 

p. B1-B90.

Carpenter, J. H., I960, The Chesapeake Bay Institute study of the Baltimore Harbor: The Maryland-Delaware Water and Sewage Asscc., Proceedings of the 33d Annual Conf., Chesapeake Bay Institute, Johns 

Hopkins University, p. 62-78.

Harleman, D. R. F., 1966, Pollution in estuaries, in Ippen, A. T., ed., Estuary and coastline hydrodynamics: New York, McGraw-Hill, chap. 14, 

p. 630-647.

Pritchard, D. W., and Carpenter, J. H., 1960, Measurement of turbul°nt diffusion in estuarine and inshore waters: Internat. Assoc. of Sci. Hydrol. 

Bull. 20, p. 37-50.

Sayre, W. W., 1968, Dispersion of mass in open-channel flow: Colorado State 

University Hydraulics Papers.

Wilder, H. B., and Hubbard, E. F., 1968, Interim report on sea-wrter encroachment in the Cape Fear River estuary, North Carolina: U.S. Geol. 

Survey open-file report, 35 p.

Williams, J. R., 1967, Movement and dispersion of fluorescent dye in the 

Duwamish River estuary, Washington: U.S. Geol. Survey Prof. Paper 

575-B, p. B245-B249.

Wilson, J. F., Jr., 1968, Fluorometric procedures for dye tracing: Techniques 

of Water-Resources Investigations of the U.S. Geol. Survey, Book 3, 

Chap. A12, 31 p.

Yotsukura, Nobuhiro, 1968, (Discussion of "Longitudinal mixing in natural 

streams," by E. L. Thackston and P. A. Krenkel: Jour. San. Eng., v. 93, 

no. SA5, Oct. 1967) : Jour. San. Eng., v. 94, no. SA3, p. 568-571.

U.S. GOVERNMENT PRINTING OFFICE: 1972 O 466-113