Determination of Mass 

Balance and Entrainment 

in the Stratified 

Duwamish River Estuary, 

King County, Washington

GEOLOGICAL SURVEY WATER-SUPPLY PAPER 1873-F

Prepared in cooperation with the 

Municipality of Metropolitan Seattle
Oetermination of Mass 

3alance and Entrainment 

: n the Stratified 

Duwamish River Estuary, 

King County, Washington

By J. D. STONER

ENVIRONMENTAL QUALITY

GEOLOGICAL SURVEY WATER-SUPPLY PAPER 1873-F

Prepared in cooperation with the 

Municipality of Metropolitan Seattle

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. 72-600253

For sale by the Superintendent of Documents, U.S. Government P-inting Office

Washington, D.C. 20402 - Price 30 cents (paper cover)

Stock Number 2401-00252
CONTENTS

Page

Abstract ________ Fl

Introduction _____ _ 1

Description of the estuary __ 3

Tides ______________________ 3

Salinity _____ 5

Methods and equipment _________ 7

Salinity and velocity studies _____ 8

Mass balance ________ 10

Entrainment velocity _____ _ 15

Summary and conclusions _____ ___ 16

Selected references ___________-_-__ 17

ILLUSTRATIONS

Page

FIGURE 1. Map of Duwamish River estuary ______________ F2

2. Longitudinal profile of the Duwamish River estuary __ 4

3. Graph showing cross-sectional area of the Duwamish

River estuary ________________________ 5

4. Generalized longitudinal diagram of part of the Duwamish River estuary, showing idealized conditions of 

water movement and entrainment _____________ 6

5. Diagrammatic cross section at 16th Avenue South

Bridge ______________________________ 8 

6-8. Graphs showing vertical salinity profiles at 16th Avenue 

South Bridge for maximum and minimum tide stages:

6. August 28-29, 1967 __________________ 9

7. September 6-7, 1967 __________________ 10

8. May 22-23, 1968 _____________________ 11 

9. Graph showing measured flow rates for upper and bottorr 

layers, and for total cross-sectional area, at 16tl 

Avenue South Bridge _____________________ 13

in
ENVIRONMENTAL QUALITY

DETERMINATION OF MASS BALANCE AND

ENTRAINMENT IN THE STRATIFIED DUWAMISH RI^ER

ESTUARY, KING COUNTY, WASHINGTON

By J. D. STONER

ABSTRACT

During a study of the effects of waste-water input on the stratified 

Duwamish River estuary, intensive water-velocity and salinity measurements 

were made in both the lower salt wedge and the upper fresher water layer 

for tidal-cycle periods. The net movement of water and salt mass past a 

cross section during a tidal cycle was determined from integration of the 

measured rates of movement of water and salt past the section. The net 

volume of water that moved downstream past the section during the cycle 

agreed with the volume of fresh-water inflow at the head of the e?tuary 

within (1) 3.8 and 7.2 percent, respectively, for two studies made during 

periods of maximum and minimum tidal-prism thickness and identical inflow 

rates of 312 cfs (cubic feet per second), and (2) 15 percent for one study 

made during a period of average tidal-prism thickness and an inflow rate 

of 1,280 cfs. For the three studies, the difference between salt mass transported upstream and downstream during the cycles ranged from 0.8 to 19 

percent of the respective mean salt-mass transport. Water was entrained 

from the salt-water wedge into the overlying layer of mixed fresh and salt 

water at tidal-cycle-average rates of 30 and 69 cfs per million square feet 

of interface for the inflow rates of 312 cfs, and 99 cfs per million square 

feet of interface for an inflow rate of 1,280 cfs. At a constant inflov rate, 

the rate of entrainment of salt-wedge water in the Duwamish River estuary 

more than doubled for a doubling of tidal-prism thickness. It also doubled 

for a quadrupling of inflow rate at about constant tidal-prism thickness.

INTRODUCTION

A comprehensive investigation of the Duwamish River estuary 

is being made by the U.S. Geological Survey in cooperation with 

the Municipality of Metropolitan Seattle (Metro) to evaluate the 

changes that take place in the estuary as a result of changes in

Fl
F2 ENVIRONMENTAL QUALITY

the quantity and type of waste being discharged irto the estuary. 

The purpose of this phase of the study is to develop a better 

understanding of the rate that the saline water (salt-water 

wedge) flowing into the estuary from Elliott Bay entrains into 

the river water containing the Renton Treatment Plant effluent. 

The part of the estuary under study extends from the mouth of 

the estuary at Elliott Bay to Renton Junction, approximately 13.1 

river miles upstream (fig. 1). Prior to 1969 several sewage out122°20' 122°15'

47"35'

47°30'

Spokane 

Street Bridge

16th Avenue South Bridge

CITY__LIMITSJ

Turning

X*Jf'<£,%

0 1/2 1

I I I I I

2 MILES

'Study Area 

WASHINGTON

Foster Bridge 

KING COUNTY

Renton Junction! 

(gaging station)

FIGURE 1. Duwamish River estuary and data-collection sites.
ENTRAINMENT, DUWAMISH RIVER ESTUARY, WASHINGTON F3

falls existed in the study reacfy since then Metro's interceptor 

sewer has eliminated all except a few minor waste-water outfalls, 

and the only sizable sewage discharge to the study reach is the 

treated effluent from Metro's Renton Treatment Plant (fig. 1). A 

major objective of the comprehensive investigation is to determine the effects of this treated effluent on the estuary.

Other phases of the comprehensive investigation of the estuary, 

but beyond the scope of this report, include estuary ecology and 

the physical, chemical, and biochemical characteristics of the 

fresh and saline water. (See "Selected References.")

DESCRIPTION OP THE ESTUARY

The bottom of the estuary channel ranges from about 5 feet 

above MLLW (mean lower low water; see "Tides") at Renton 

Junction, 13.1 miles above the mouth of the estuary, to 38 feet 

below MLLW at Spokane Street Bridge, 1.2 miles above the mouth 

(fig. 2). The estuary channel downstream from the turning basin 

(fig. 1), which is 6.1 miles above the mouth, is dredged in stairstep fashion, being progressively deeper downstream. The tuning 

basin is the upstream limit of navigation for all but small boats.

The cross-sectional area of the estuary channel decreases upstream approximately exponentially (fig. 3). Cross-sectional areas 

in the reach from Renton Junction to East Marginal Way Bridge, 

7.8 miles above the mouth, are generally less than 1,000 square 

feet, whereas cross-sectional areas in the widest reach of the 

lower part of the estuary exceed 30,000 square feet.

The estuary is divided near the mouth into the East and West 

Waterways. The East Waterway is closed to upstream navigation 

by pilings set at the southeast end of Harbor Island. Flow measurements have shown that about 80 percent of the flow passes through 

the West Waterway.

TIDES

The tides in the Duwamish River estuary are semidiurnal, 

with marked inequalities in the successive high- or low-water 

stages. This diurnal inequality necessitates the designation of a 

higher high water (HHW), a higher low water (HLW), a lower 

high water (LHW), and a lower low water (LLW) during each 

complete tidal cycle of about 25 hours. The datum plane for tide 

height in the Duwamish River estuary is mean lower low water 

(MLLW) at a tide reference station about 1 mile northesst of 

the estuary mouth; this station is maintained by the U.S. Environmental Science Services Administration. Mean lower low
F4 ENVIRONMENTAL QUALITY

-

-4-> 'So 

§

U31VAA MO"I U3MO1 NV3W 

MO"I3a QNV 3AO9V 133d Nl 'NOI1VA313
ENTRAINMENT, DUWAMISH RIVER ESTUARY, WASHINGTON F5 

100,000

100

10,000 20,000 30,000 40,000 50,000 60,000 

DISTANCE, IN FEET UPSTREAM FROM THE MOUTH

70,000

FIGURE 3. Cross-sectional area of the Duwamish River estuary at 7.2 feet 

above mean lower low water.

water is the average of the lower low-water levels. Mean tide 

stage is 6.6 feet above MLLW, and maximum and minimum 

recorded stages are 14.7 feet above MLLW and 4.6 feet below 

MLLW, respectively. These data were obtained from the U.S. 

Environmental Science Services Administration (1967, p. 174).

SALINITY

Circulation of water within a stratified estuary comprises a net 

upstream movement of water within a lowermost salt-water 

wedge and a net downstream movement of fresher water in the 

layer overriding the wedge (fig. 4) (Pritchard, 1955). The saline 

wedge water, which has its source in Elliott Bay, oscillates upstream and downstream with the tide. During periods of low 

fresh-water inflow and high tide stage the salt-water wedge has 

extended upstream as far as the Foster Bridge, 10.2 miles above 

the mouth. At fresh-water inflow greater than 1,000 cfs (cubic 

feet per second) the salt-water wedge does not extend upstream 

beyond East Marginal Way Bridge regardless of tide bright 

(Stoner, 1967).
F6 ENVIRONMENTAL QUALITY

<H OJ

° S

.j O) S >

<a o

a g

S

'-3

ZT3
ENTRAINMENT, DUWAMISH RIVER ESTUARY, WASHINGTON F7

Saline water from the wedge is entrained in the overriding 

layer of fresher water at the interface between the two. Theve is 

little or no downward movement of water from the upper layer 

into the salt-water wedge; studies using fluorescent dye have 

shown that downward mixing in the stratified estuary is negligible 

(Santos and Stoner, 1972). Also, at any given time and location 

along the estuary, the salinity concentration at a given depth is 

nearly the same from one side of the channel to the other.

METHODS AND EQUIPMENT

The determination of the distribution of fresh water (and its 

contained pollutants) by the concurrent measurement of velocity 

and salinity profiles at many flow sections is impractical even in 

a small estuary like the Duwamish. Therefore, the approach in 

this study utilizes net changes in discharge and salinity over 

specific tidal cycles in a reach of the estuary where bourdary 

conditions and inflow and outflow can be closely defined. Three 

salinity-velocity studies at a selected cross section in the estuary 

were made to determine whether the mass balance for water and 

salt could be calculated from field measurements. If mass balance, 

particularly in the case of water volume, could be closely approximated from field data, then a fairly valid rate of entrainment of 

saline water into the upper layer could be determined.

The 16th Avenue South Bridge, 4.8 miles upstream from the 

estuary mouth, was chosen as the site for the salinity-veT ocity 

studies. Velocities were measured with current meters fron the 

bridge, while direction of flow was measured with a vane attached 

to a pointer which was free to pivot about the cable from which 

the current meter was suspended. Velocity and direction of flow 

were measured simultaneously always at two verticals in the 

main channel, and at an additional vertical on each side of the 

channel only during periods of maximum velocity. Velocity and 

direction of flow were measured just below the water surface 

and at every tenth of the depth to the channel bottom. The angle 

of direction of flow was measured relative to the bridge.

Salinity and temperature were measured with an electrodeless 

induction salinometer. Because the salinity is laterally uniform, 

it and temperature were measured only at midstream. These 

parameters were measured just below the surface and at every 

1.5 feet of depth. Measurements were made from a small boat 

in order to facilitate the handling of the salinometer cable. Velocity, flow direction, salinity, and temperature were measured 

every half hour, except at the side verticals where flow velocity
F8 ENVIRONMENTAL QUALITY

and direction were measured at hourly intervals during the periods of higher velocity. All the field studies were continued for a 

minimum of 26 hours to insure the obtaining of data during a 

complete tidal cycle.

Prior to any fieldwork, a water-stage recorder was installed on 

a fender at the 16th Avenue South Bridge. The rtage recorder 

established the changes in tide stage, which were used to calculate changes in cross-sectional area. Before the initial study, 

the channel cross section at the site was measured accurately and 

plotted with the depth scale referenced to MLLW (fig. 5).

,_ 30

III 

III

" 20

£ 10

°500 O

< -J

O UJ 

E §

5 -J

in LLJ 

5 -30

100 200 300 400 

DISTANCE FROM LEFT BANK, IN FEET

500 550

FIGURE 5. Diagrammatic cross section at 16th Avenue South Bridge. 

Shaded areas are bridge piers.

SALINITY AND VELOCITY STUDIES

The initial salinity-velocity study was made on .August 28-29, 

1967, when tidal exchange was small and the rate of fresh-water 

inflow was low. The tidal exchange was indicated by the tidalprism thickness (sum of the high tides minus the sum of the 

low tides over a tidal cycle), which was 10.2 feet. Minimum tidalprism thickness in the Duwamish River estuary during the year 

is about 9.5 feet, whereas the maximums range from 18 to 21 

feet. Average fresh-water inflow during the 2-day period was 

312 cfs, which is in the low-inflow range for the estuary.

The vertical salinity profiles taken during the study showed 

that the salt-water wedge was fairly well developed even during 

this period of low tidal exchange and fresh-water inf ow. Vertical 

salinity profiles, at times of maximum and minimum tide stage,
ENTRAINMENT, DUWAMISH RIVER ESTUARY, WASHINGTON F9

are shown in figure 6. The depth to the interface between the 

salt wedge and the upper layer was determined for each of the 

one-half-hourly measurements, by inspection of the respective 

vertical salinity, temperature, and velocity profiles. The top of the 

wedge was generally delineated at the depth where the rate of 

change in the salinity profile (measuring upward) became greater 

than about 1 ppt (parts per thousand) per 3 feet of depth. (See 

fig. 6 for example.) The salinity concentration at the interface 

varied slightly and the average was 24.5 ppt. The salinity of the 

wedge water remained fairly constant during this study (fig. 

6) and averaged about 27.5 ppt.

10

20

30

Lower high water

I I

Lower low water '

I I I I I I I

20

30

Higher high water

I I I I I

Salt wedge

Higher low water

I I I I I

10 20 30 40 0 10 20 

SALINITY, IN PARTS PERTHOUSAND

30 40

FIGURE 6. Vertical salinity profiles at 16th Avenue South Bridge for 

maximum and minimum tide stages, August 28-29, 1967.

The second salinity-velocity study was made during September 

6-7, 1967. The average fresh-water inflow during the study was 

312 cfs, the same as that of the initial study; the significant difference in conditions between the studies was the tidal exchange. 

The tidal-prism thickness of 20.6 feet was near maximum and
F10 ENVIRONMENTAL QUALITY

was 10.4 feet thicker than the tidal prism during the initial study. 

Vertical salinity profiles (fig. 7) show that the wedge was reasonably well developed. The average salinity at the interface for 

this study was 23.0 ppt, and the mean salt-wedge salinity was 25.8 

ppt.

The third salinity-velocity study was made on May 22-23, 1968. 

The tidal exchange was 14.7 feet, which was near the mean 15.2 

feet, and the fresh-water inflow was 1,280 cfs. Definition of the 

salt-water wedge and interface throughout this study was very 

good (fig. 8). The average salinity was 24.1 ppt at the interface 

and 26.9 ppt in the salt wedge.

MASS BALANCE

The principle of continuity, or mass conservation, requires that, 

at the steady state, net mass advected upstream of a given point 

in the estuary must equal the net mass advected downstream of 

the point. The principle holds for either water mass or salt mass.

10

,- 30 LUI

0

<

LL

tr

D

CO

O

I IS 10

Higher high water Lower low water

20 -

30

Lower high water Higher low water

I I

10 20 30 40 0 10 20 

SALINITY, IN PARTS PER THOUSAND

30 40

FIGURE 7. Vertical salinity profiles at 16th Avenue South Bridge for 

maximum and minimum tide stages, September 6-7, 1967.
ENTRATNMENT, DUWAMISH RIVER ESTUARY, WASHINGTON Fll

10

Lower low water

I I I I I

I T

Lower high water

I I I I I

I

CL

0 10

20

30

i I

Higher low water

J__I

1 I

Higher high water

I I I I

10 20 30 40 0 10 20 

SALINITY, IN PARTS PER THOUSAND

30 40

FIGURE 8. Vertical salinity profiles at 16th Avenue South Bridge for 

maximum and minimum tide stages, May 22-23, 1968.

Because the estuary is of the salt-water wedge type and essentially a two-layer system, it may be assumed that net upstream 

advection occurs in the bottom layer and net downstream advection 

occurs in the upper layer. The following mathematical statements 

show the net salt- and water-mass balance at a cross section:

and

where

(1)

(2)

Sb = net salt mass advected in the bottom layer, 

Su =net salt mass advected in the upper layer, 

Qb = net water mass advected in the bottom layer, 

Qu = net water mass advected in the upper layer, and 

Qf = fresh-water inflow.
F12 ENVIRONMENTAL QUALITY

All transports (advections) are defined positive downstream wise 

at the cross section. Qf is always nonnegative.

To approximate steady-state conditions in the Duwamish River 

estuary, a time period over approximately one tidal cycle was 

chosen. A tidal cycle is short enough to allow field measurements 

and, also, flow, stage, and other conditions in the estuary at the 

beginning and ending of the cycle may agree closely enough to 

reasonably approximate a steady-state condition. The boundary 

condition that required satisfaction is that the water elevations 

within the estuary at the beginning of the study period (a tidal 

cycle) were equal to the water elevations at the end of the period. 

When this boundary condition is satisfied, water-mass balance is 

achieved. As for salt-mass balance, the boundary condition is that 

the salinity at every point in the reach is equal at the beginning 

and at the end of the study period. It is difficult to ascertain this 

condition in the estuary, thus salt-mass balance as observed may 

not be as exact as in the mathematical expression, equation 1.

The analysis of the water-mass balance was developed as follows : The computed flow rates for the three studies were plotted 

against time as in figure 9. A quasi-steady-state period, T, was 

chosen using the boundary conditions stated previously for each 

of the three studies. The areas under the upper-layer, bottomlayer, and total-flow curves were then planimete^ed over the 

period T to determine the total volume of water that moved 

through each of the layers and through the section. Fresh-water 

inflow to the system was determined from the relation between 

recorded stage and discharge at Renton Junction (fig. 1). In addition to this inflow, 35 cfs was added to account for the discharge 

from the Renton Treatment Plant and minor ur gaged inflow 

between the stage-recorder site and the cross section where 

salinity and velocity were measured.

The following table shows the values calculated from the field 

studies for the water-mass balance.

Date

Aug. 28-29 

Sept. 6-7, 

May 22-23,

s

, 1967 ___ 

1967 _____ 

1968 ___

Quasiiteady-state 

period, T 

(thousands 

of sec)

85.0 

83.4 

84.0

Bottomlayer 

outflow,

-11.5 

-21.7 

-15.1

Upperlayer 

outflow, 

Qu

Millions

39.9 

47.7 

139

Total 

net 

outflow, 

Qt

of cubic feet

28.4 

27.0 

124

Freshwater 

inflow, 

Qt

26.5 

26.0 

108

Percentage 

error, 

(Qt-Q/)100

Qt

7.2 

3.8 

15

The negative quantities calculated for Qb show that net watermass movement in the bottom layer is, in fact, in the upstream
6000 

4000 

2000 -

O-2000 -

o

-4000

I 1 I 

Total area

o

CO

o 

o

z

§

O

_l 

u. 

u. 

O

2000 

0 

-2000 

^

1 1 1 1 1 I 

x^ >v Upper (overriding) layer

1 1 l 1 1 1

-

4000

2000

0

-2000

-4000

Bottom (salt-water wedge) layer

1600 2000 2400 0400 0800 

TIME, IN HOURS

1200 1600 2000

FIGURE 9. Measured flow rates for upper and bottom layers, and for total 

cross-sectional area, at 16th Avenue South Bridge, from 160C hours 

August 28 to 1900 hours August 29, 1967. Negative flow rates indicate 

upstream flow. The vertical bars represent the times of equal tide, height 

used to define the period analyzed.

direction. Conversely, the positive quantities for Qu ind: cate a 

downstream direction for net water-mass movement in the upper 

layer. These calculations from field measurements serve to prove 

that water circulation within the estuary closely approximates 

that described on page F5, and in figure 4.

The measured values verify the requirement that, under steadystate conditions, the volume of fresh water entering the estuary 

must equal the net volume of mixed (fresh plus saline) water 

moving downstream past the measuring section. Inasmuch as the 

algebraic sum of Qu and Q6 equals the net water mass moved
F14 ENVIRONMENTAL QUALITY 

downstream past the section (Qt ), or

Qt (3) 

then, substituting from equation 2,

Q/-Q* (4)

The measured values for net water-mass movement past the 

measuring section, Qt, were all greater than the fresh-water inflow, Qf. However, the differences between the measured Qt and 

the actual Qf were not so large as to invalidate the use of results 

of these measurements as reasonable estimates of water-mass 

balance within the estuary.

Salt-mass balance within the estuary was calculated in much 

the same manner as the water-mass balance. That is, the measured values of net water-mass movement, Qu and Q6 , and the 

measured mean values of salinity in the upper and lower layers, 

CM and Cft, were used to develop values for the net weight of salt 

moved past the measuring section during the study periods. Because the salinity of the inflowing river water is essentially zero, 

combining equations 1 and 2 yields

(0) - (Q6 ) (C6 ) + (Q.) (C.) 

or

Sb +Su = Q (5)

where S6 = (Q&) (C6 ) and SU =(QU )(CU ). Because the salt-mass 

movement is dependent upon the measured water-mass movement, any errors in salinity would be superimposed upon the 

errors in the water-mass balance. Also, as previously stated 

(p. F12), the relative volumes of the upper and bottom layers 

might be different at the beginning and end of the study periods. 

Therefore, the salt-mass balance was not expected to be as accurate as the water-mass balance. Salt-mass balance was determined from integration of plotted curves of the rates of salt 

movement in the upper and lower layers during the study periods. 

The resulting transport of salt at the section are rhown in the 

following table.

Salt transport Salt transport

Quasi-steady- in the upper in the bottom Difference Percentage

Date state period, T layer. Su layer, Si, (millions of error of (thousands of sec) = pounds) Su and Si, 

Millions of pounds

Aug. 28-29, 1967 __ 85.0 106 -117 11 9.9

Sept. 6-7, 1967 ___ 83.4 236 238 2 .8

Aug. 22-23, 1968 __ 84.0 92 -111 19 19
ENTRAINMENT, DUWAMISH RIVER ESTUARY, WASHINGTON F15

The percentage differences in the table were determined by comparing the difference values to the average of the corresponding 

products, QU CU and QzA, inasmuch as there was no way of knowing which of those products more closely approximated the actual 

salt transport. The negative quantities of Sb in the table indicate 

upstream transport of salt mass in the wedge.

The magnitude of the percentage error in salt-mass balance 

corresponds reasonably well with the magnitude of the percentage 

error in water-mass balance.

ENTRAINMENT VELOCITY

Because of the reasonable balance of salt and water masses 

that were determined from the field measurements, it can be 

assumed that the volume of wedge water that is entrainel into 

the upper layer during the quasi-steady-state period is equal to 

the water mass that is moved upstream in the bottom layer during 

that period. The rate of entrainment obviously is not constant 

throughout the period, but definition of instantaneous ertrainment rates by using these data is not feasible. However, the 

average rate of upstream water-mass movement of the bottom 

layer can be used with reasonable confidence to compute an average rate of entrainment of salt-wedge water during a tidal-cycle 

study period.

For the computation of the entrainment velocity, two assumptions were made. The first, which was reinforced by field data, 

was that at fresh-water inflow rate of 312 cfs the mean location 

of the toe (upstream end) of the salt wedge would be at East 

Marginal Way Bridge, and at fresh-water inflow of 1,280 cfs the 

mean location of the toe would be at Boeing Bridge (fig. 1). The 

second assumption was that wedge water was entrained through 

the interface at the same rate throughout the extent of the interface upstream from 16th Avenue South Bridge.

The area of the interface is dependent upon its depth within 

the channel the interface varies in width and length as it rises 

and declines in response to the tides. These variations were assumed to be uniform throughout the tidal cycle and the average 

position of the interface was used to calculate its area. For example, the average stage during the first study was 7.2 feet above 

MLLW and the average interface depth was 6 feet. The calculated 

interface area between East Marginal Way Bridge anc1 16th 

Avenue South Bridge at that stage and depth was 4.5 million 

square feet. Water in the bottom layer moved upstream during 

the study period at an average rate of 135 cfs. The entrainment
F16 ENVIRONMENTAL QUALITY

across the interface is:

135 cfs

4.5Xl06 ft2

= 30xlO-6 cfsperft2 . (6)

The resulting entrainment velocity (E) has the dimensions, cfs 

per square foot, which reduce to feet per second (ft per sec). The 

following table shows the parameters determined for each of the 

salinity-velocity studies:

Date

Aug. 28-29. 1967 __ 

Sept. 6-7, 1967 ____

May 22-23, 1968 ____

Freshwater 

inflow 

(cfs)

312 

312

1,280

Bottomlayer-flow 

upstream 

(cfs)

135 

260

180

Quasi-steadystate period 

(thousands 

of sec)

85.0 

83.4

84.0

Area of 

interface 

(thousands 

of sq ft )

4,500 

3,794

1,827

Entrainment 

velocity, E 

(millionths of 

a cfs per sq ft)

30 

69

99

Even though the first two studies were done at essentially the 

same fresh-water inflow, the calculated E for the second study 

is approximately twice that of the first study. This is due primarily to the differences in the tidal exchange during the two 

studies. The study of August 1967 was done during1 a period of 

minimum tidal exchange and the study of September 1967 during 

a period of maximum tidal exchange. Apparently, the greater 

inflow and outflow in the study reach, produced by the larger 

tidal exchange, induced a more rapid upward movement of the 

wedge water. The study of May 1968 was done during a period 

of average tidal exchange; however, the fresh-water inflow was 

considerably larger and, as expected, the calculated E was greater.

SUMMARY AND CONCLUSIONS

Water mass and salt mass computed from field measurements 

on the stratified Duwamish River estuary have been shown to 

balance over selected quasi-steady-state periods (tidal cycles). The 

quasi-steady-state period is the period during which the water 

volume in a reach of the estuary is the same at the beginning as 

at the end of the period. Entrainment velocities for the movement 

of wedge water into the overriding upper layer have been calculated from mass-balance data.

The entrainment velocity for mixing of water from the saltwater wedge upward into the layer of fresher water was found 

to vary with fresh-water inflow and tidal-prism tl ickness. The 

range of the entrainment velocity was from 30X10-6 cfs per sq 

ft to 99X10~6 cfs per sq ft between the salt-water wedge and the
ENTRAINMENT, DUWAMISH RIVER ESTUARY, WASHINGTON FIT

overlying layer at fresh-water-inflow rates of 312 cfs and 1,280 

cfs, respectively. At a constant inflow rate of 312 cfs, the ertrainment velocity increased from 30X1Q-6 to 69xlO~6 cfs per sq ft, 

for an increase in tidal-prism thickness from 10.2 to 20.6 feet.

The concept and values of the entrainment velocity developed 

here for the Duwamish River estuary are expected to greatly aid 

further quantitative studies of flow patterns and mixing in this 

estuary. The same approach should prove helpful also in studies 

of other stratified estuaries.

SELECTED REFERENCES

Fischer, H. B., 1968, Methods for predicting dispersion coefficients in natural

streams, with applications to the lower reaches of the Green and

Duwamish Rivers, Washington: U.S. Geol. Survey Prof. Paper 582-A,

27 p. 

Isaac, G. W., Farris, G. D., and Gibbs, C. V., 1964, Special Duwamish River

studies: Municipality of Metropolitan Seattle, Water Quality Series 1,

37 p. 

Pritchard, D. W., 1955, Estuarine circulation patterns: Am. Soc. Civil Eng.

Proc., v. 81, separate 717, 11 p. 

Santos, J. F., and Stoner, J. D., 1972, Physical, chemical, and biological

aspects of the Duwamish River estuary, King County, Washington:

U.S. Geol. Survey Water-Supply Paper 1873-C, 74 p. 

Stoner, J. D., 1967, Prediction of salt-water intrusion in the Duwamish River

estuary, King County, Washington, in Geological Survey researcl , 1967:

U.S. Geol. Survey Prof. Paper 575-D, p. D253-D255. 

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