Flushing Time or Turnover Time

1) Time required to replace the Volume of the basin V by the Volume Influx Vin

R Vout

Vin

x

z

t = V / Vin

t is obtained in seconds [ m3 / m3/s]

Vout = Vin + RVout Sout = Vin Sin

Water Budget:Salt Budget:

Knudsen’s RelationsKnudsen’s Relations

2) Time required to replace the fresh water volume in the estuary by the river discharge

RV

t f Volume of fresh water in the system (m3)River discharge (m3/s)

R

x

z

Flushing Time or Turnover Time

3) Same as 2) but using the concept of freshwater fraction to determine Vf

Define oceanic salinity as σ and salinity at any part of the estuary as S

The freshwater fraction f is given by:

Sf

If f = 0, all salty water; if f = 1, all fresh water

RVf

t

VfdVfVf

average freshwater fraction

Could use salinity between head and mouth to get f

4) Flushing by Tides (Tidal Prism Method)

Tides bring oceanic water into the estuary during flood.

The volume of this oceanic water Vp is equal to the difference betweenhigh hw and low hl water multiplied times the surface area A of the estuary;

Vp = (hw – hl ) A

Assume:- no variations of depth along the estuary short estuary- over a full tidal cycle, Vp is entirely mixed with VR

- entire volume of mixed water is removed from estuary during ebb- on the next flood the process is repeated with seawater of S = σ entering the estuaryWater going in has oceanic salinity; water going out has mixed S = Š

zVR

Vp

x

hw

hl

Volume offresh water

Volume oftidal prism

S = 0 S = σ

Flushing by Tides (Cont.)

VR

Vp

x

hw

hl

Volume offresh water

Volume oftidal prism

S = 0 S = σ

z

The average Š of the mixed water at high tide can be obtained from salt balance:

Rp

p

Rp

p

Rpp

VV

V

VV

VS

SVVV

or

If Vp >> VR , then Š σ

If VR >> Vp , then Š 0

The mean fresh water fraction is:Rp

R

Rp

p

VVV

VV

VSSf

11

which includes River and Tidal effects

Flushing by Tides (Cont.)

RpT VV

TVt

Flushing time by the tidal prism

Taking our definition 3):

RpRRp

R

RT VV

TVTV

VVV

VTVVf

RVf

t

T is the tidal period, i.e., the characteristic

period of tidal exchange

It would take a lot of T scales to flush the system if V >> Vp + VR

Drawbacks:-complete mixing from head to mouth of waters entering estuary;this shortens tT relative to real tT

-no atmospheric forcing-water coming in is of oceanic salinity, which is usually not the case

tT should be < t [t as derived from (1), (2) or (3)]

Flushing Rates

Flushing rate F - rate at which the total volume of the estuary is exchanged

fR

tV

F

FT should be > F

and the Flushing rate due to tidal prism FT

T

VV

tV

F Rp

TT

RpT VV

TVt

R

Vft

Flushing Rates in Sections (or segments)

Modify tidal prism method by dividing the estuary into segments over whichmixing takes place, rather than assume that there is complete mixing over the length of the estuary during each tidal cycle.

Let, Pi = intertidal volume for segment i (or tidal prism + VR) Vi = low water volume Vi

Pi

At the landward end:Vi = V0 -- low tide volumePi = P0 = VR -- over a tidal cycle; provided by the river discharge

The length of each segment is determined by the tidal excursion:

dttUXT

0

0 sin 00 cos

2t

TU

TU0

For the succeeding segments, assume that the high tide volume of the landward section is the low tide volume of the seaward section.

This implies that the tidal excursion decreases landward or that the channel gets narrower.

VnVn -1

Pn -1

11 nnn PVV

Flushing Rates in Sections (or segments)

1

10

1

0011

2100223

100112

001

n

mmR

n

mmnnn PVVPVPVV

PPPVPVV

PPVPVV

PVV

Therefore,

Flushing Rates in Sections (or segments)

If the water within each segment is completely mixed at high tide, the proportion of water removed on ebb tide will be given by the ratio between intertidal volume and the high tide volume of the segment, or exchange ratioof segment ‘n’ rn:

nn

nn PV

Pr

Modified Tidal Prism

High Tide VolumeVnVn -1

Pn -1

nn r

Tt

nn

nn

RpRpT rP

PVVV

Vand

VVTV

t1

Using:

Volume of basin / (tidal prism + fresh water volume)or High Tide Volume / Modified Tidal Prism

If Vn = 0 (as in a tidal flat) rn = 1

Flushing Rates in Sections (or segments)

Accumulated freshwater in each volume segment:

n

RR

nnfn r

VTV

rT

RtV

Finally, nn

fn fV

VS 1

Reference on Residence Time:

Sheldon, J.E. and M. Alber (2002), A comparison of residence time calculations using simple compartment

models of the Altamaha River Estuary, Georgia. Estuaries, 25:1304-1317.

Refer to to Tomczac’s page for more information on Flushing Times .

Anabela Pacheco de Oliveira

5) Residence time: time required for water or material elements found initially at certain locations of a basin to exit the basin.

Tejo Estuary, Portugal

Residence Times (hours)(following particles with a numerical model)

from particle tracking in numerical models

TAMPA BAY, FLORIDATAMPA BAY, FLORIDA

From Lucas (2010)

entrance

exit

“age”

“residence tim

e”

“transit time”

embaymentboundary

Fig. 10.3. Schematic of an aquatic water body with two openings, one through which water parcels, scalar constituents, and/or particles enter and one through which they exit. The total time it takes a particle to pass through the embayment is the “transit time”, which is the sum of water or particle “age” (the time since entering) and “residence time” (the time a parcel will remain in the embayment). Average transit time may be considered equivalent to “turnover time” or “flushing time” (Bolin and Rodhe 1973; Sheldon and Alber 2006). “Age” and “residence time” are measured relative to an arbitrary time “ t” and particle location within the water body (Monsen et al. 2002).

time “t”

Banas and Hickey (2005)

Willapa Bay, WA

Flushing time in Mururoa Atoll Lagoona coral island in Polynesia previously used for nuclear tests, determined from a numerical model

The model takes into account tides and wind-driven water movement and includes flow over the coral reef as well as through the access channel. The figure on the left shows the circulation in the form of streamlines along which the water circulates. The zero streamline separates anti-clockwise circulation near the channel from clockwise circulation in the lagoon. Notice that most of the lagoon circulation is closed, so exchange with the ocean can only occur through turbulent diffusion across streamlines.The figure on the right shows the water residence time or flushing time in days. Most of the lagoon is flushed within less than 100 days, but there is a less well flushed region in the east where the flushing time exceeds 140 days.

bathymetry

© 2000 M. Tomczak

4) Consider these relationships a step further in terms of theEquivalent Downstream Transport represented by Qd

RS = 0

x

z

f = 1 f = 0.5 f

Qd = R Qd = 2R Qd = R / f

R

R

Qd is a fictitious quantity;it could be measured under unusual circumstances.

It is an expression in terms of the advective and diffusive effects

Flushing time α Qd / R = 1 / f

It measures the combined effects of advection and diffusion in removing a pollutant in an estuary, compared to advection only

The greater Qd (small f ), the longer the flushing time