Willem Botes: WAMTechnology cc

Willem Botes: WAMTechnology ccwww.wamsys.co.za

A Milnerton Estuary Study (Diep River), during 2004 was used as an example.

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A demonstration of estuary mouth dynamics, estuary hydrodynamics and the concepts of numerical modelling applied to an estuary with a simple

geometry.

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The inlet of the Milnerton Estuary…….

The estuary inlet is the significant element for the controlling of the hydrodynamic behaviour of an estuary

Sea

Inlet

Estuary‘throat’



The inlet of the Milnerton Estuary…….

The inlet of the Milnerton estuary consists of a meandering channel, varying during river floods and extreme tidal events.

The flow (velocity) in the inlet is a function of the water levels in the estuary and in the sea with external inflows (river flows) superimposed on it. When the estuary mouth closes, the mouth disappears and a ‘bar’ is formed (highest level of the sand bar is the sill).


Sea

Beach

Estuary


The inlet processes at the Milnerton Estuary…….

Tidal flows ………. Inflows (flood flows) ….


Sea

Beach

Estuary


The inlet processes at the Milnerton Estuary…….Sediment transport into the estuary during inflows (flood flows) ….

Flood ‘shoal’ is formed in the estuary


Sea

Beach

Estuary


The inlet processes at the Milnerton Estuary…….

Tidal flows ………. Outflows (ebb flows) ….

…….. along the shoreline …….


Sea

Beach

Estuary


The inlet processes at the Milnerton Estuary…….Sediment transport from the estuary during out flows (ebb flows) ….

Ebb ‘shoal’ is formed in the sea



Milnerton estuary …….

Sediment sources ….

Milnerton inlet to estuary

Littoral TransportThe process of sediment moving along a coastline. This process has two components: LONGSHORE TRANSPORT and ONSHORE OFFSHORE TRANSPORT.

Longshore TransportThe transport of sediment in water parallel to the shoreline.

Onshore-Offshore TransportThe up and down movement of sediment roughly perpendicular to a shoreline because of wave action

Fluvial TransportFrom the Diep River catchment.

Stormwater runoff




“Water supply” to the estuary ….

Tidal flows

Potsdam WWTW

Diep River



The hydrodynamic flushing of the estuary ….

The exchange of water in an estuary, is generally referred to as the term Tidal Prism:

Volume of water that flows into a tidal channel and out again during a complete tide, excluding any upland discharges

The volume of water present between mean low and mean high tide.

O’Brien (1931) provided a relationship between the Tidal Prism and the cross-sectional area of the inlet (using data from numerous estuaries), which provide a ‘ball-park’ answer to the stability/non-stability of an estuary inlet.



The hydrodynamic flushing of the estuary ….

O’Brien (1936): Tidal Prism vs cross-sectional area data …….

Ref: USACE(2002)O'Briens Tidal Prism-inlet area relationship

1E+0 1E+1 1E+2 1E+3 1E+4 1E+51E+5

1E+6

1E+7

1E+8

1E+9

1E+10

Inlet cross-sectional area (sq.m)

Tidal prism (cub.m)

> 90% of stable tidal inlets

Milnerton


The functioning of an estuary …….

The saline conditions in Milnerton estuary ….

Historically, the Milnerton estuary was closed during dry summer months and open during the wet winter months, resulting in hyper saline conditions during the summer months and a gradual decreasing salinity profile from the mouth to the Otto du Plessis bridge during the wet winter period.

1974 (Grindley, et.al., 1974)

0 500 1,000 1,500 2,000 2,500 3,0000

20

40

60

80

100

Distance from mouth (m)

Salinity (ppt)

Winter (Open mouth) Summer (Closed mouth)

Average sea salinity

Summer conditions (Closed mouth)

Winter conditions (Open mouth)

On 28 May 2004 a typical ‘historical’ winter condition was measured when the Diep River flow was > 3 cumec together with other inflows (eg. from WWTW’s)


The response of an estuary during tidal variations

Consider a length section and an inflowing tide

Gravity induced flows into the estuary due to water level differences

Mixing of saline sea water with fresh water in the estuary takes place

Sea

EstuaryEstuary mouth

Rising tide



The response of an estuary during tidal variations

Consider a length section and an outflowing tide

Gravity induced flows out of the estuary due to water level differences

Mixing of saline sea water with fresh water in the estuary takes place

Sea

EstuaryEstuary mouth

Out flowing tide


The volumetric properties can now be determined for any section length (x =1 to n)

2. Determine cross-sectional areas

1. “Box” the estuary (Depth and length)


Estuary modeling: Hydro-geometric description of an estuary

-1

0

+1

+

2

Wate

r le

vel (m

to M

SL) Mouth (0)

t

o

End of tidal reach (Length)

X(1)

X(2)

X(….)

X(n)

Cross-sectional area



The numerical solution

For a relative narrow estuary, the velocity and acceleration components in the transverse and vertical directions will be insignificant, compared to the components in longitudinal section, and the motion of the flow can be assumed as 1-dimensional.

The hydrodynamic equation for motion at time t, choosing the x-axis in the upstream direction is:

h/ x = 1/gA Q/ t - |Q|Q/(C2.A2.R) + 2bQ/(gA2). h/ t + Wx/(gR)

The equation for continuity of flow is:

Q/ x = -b h/ t

Where:h = water level (m)x = distance (positive upstream) (m)Q = Flow (m3/s)g = Gravitation (m/s2)A = Cross-sectional area (m2)b = stream width (m)t = time (s)C = Chezy coefficient for frictionR = Hydraulic radius (A/P) (m)P = Wetted circumference (m)

and:Wx = Wind factor = w cos w = Wind shear stress = rair.CDV2

air = density of air (kg/m3)CD = Drag coefficient = 0.5 V 10-3

V = Wind velocity (m/s) = Angle between wind direction and estuary alignment.



The numerical solution

The differential equations ( h/ x = ….. And Q/ x = …..) can be transformed to finite difference equations for numerical computations by replacing the differential quotients by finite difference quotients, for example ……..

h/ x = (hx+x – hx)/x at time t

and …

h/ t = (ht+Dt – ht)/t at distance x

According to the following forward difference approach …..

xn xn+1

h(x) h/ x

hn

hn+1


xx/2x

X=1 X=2X=m

t

t

t/2

t=1

t=1

t=n

Initial conditions (Start)

Boundary Condition (Tide)


The numerical solution continued

Thus, replacing all differential components by difference quotients in terms of a horizontal distance interval (x) and a time interval (t), finite difference equations for momentum and the continuity of flow can be defined, which can be solved numerically by elimination (explicitly) or by iteration (implicitly)…The approach to solve the equation can best be illustrated with a ‘Computational grid’, describing

the spatial (x) and temporal (t) schematization, solving the equations explicitly…. ………. the unknown value of Q and h at a certain time level are calculated, using the known values of Q and h

at the previous time level.

Q Q Q Q Q Q Q Q Q Q Q

h h h h h h h h h h h








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Willem Botes: WAMTechnology cc