Willem Botes: WAMTechnology cc A Milnerton Estuary Study (Diep River), during 2004 was used as an example. Click to continue A demonstration of estuary mouth dynamics, estuary hydrodynamics and the concepts of numerical modelling applied to an estuary with a simple geometry.

Click to continue 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

Click to continue 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 Click to continue The inlet processes at the Milnerton Estuary……. Tidal flows ………. Inflows (flood flows) ….

Sea Beach Estuary Click to continue 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 Click to continue The inlet processes at the Milnerton Estuary……. Tidal flows ………. Outflows (ebb flows) …. …….. along the shoreline …….

Sea Beach Estuary Click to continue The inlet processes at the Milnerton Estuary……. Sediment transport from the estuary during out flows (ebb flows) …. Ebb shoal is formed in the sea

Click to continue Milnerton estuary ……. Sediment sources …. Milnerton inlet to estuary Littoral Transport The process of sediment moving along a coastline. This process has two components: LONGSHORE TRANSPORT and ONSHORE OFFSHORE TRANSPORT. Longshore Transport The transport of sediment in water parallel to the shoreline. Onshore-Offshore Transport The up and down movement of sediment roughly perpendicular to a shoreline because of wave action Fluvial Transport From the Diep River catchment. Stormwater runoff

Click to continue Milnerton estuary ……. Water supply to the estuary …. Tidal flows Potsdam WWTW Diep River

Click to continue Milnerton estuary ……. 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. OBrien (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.

Click to continue Milnerton estuary ……. The hydrodynamic flushing of the estuary …. OBrien (1936): Tidal Prism vs cross-sectional area data ……. > 90% of stable tidal inlets Milnerton

Click to continue 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. 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 WWTWs)

Click to continue 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 SeaEstuaryEstuary mouth Rising tide

Click to continue 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 SeaEstuaryEstuary 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) Click to continue Estuary modeling: Hydro-geometric description of an estuary Water level (m to MSL) Mouth (0) to End of tidal reach (Length) X(1) X(2) X(….) X(n) Cross-sectional area

Click to continue 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/(C 2.A 2.R) + 2bQ/(gA 2 ). h/ t + W x /( 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 friction R = Hydraulic radius (A/P) (m) P = Wetted circumference (m) and: W x = Wind factor = w cos w = Wind shear stress = r air.C D V 2 air = density of air (kg/m 3 ) C D = Drag coefficient = 0.5 V V = Wind velocity (m/s) = Angle between wind direction and estuary alignment.

Click to continue 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 = (h x+ x – h x )/ x at time t and … h/ t = (h t+Dt – h t )/ t at distance x According to the following forward difference approach ….. xnxn x n+1 h(x) h/ x hnhn h n+1

x x/2 x X=1X=2 X=m t t t/2 t=1 t=n Initial conditions (Start) Boundary Condition (Tide) Click to continue 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. QQQQQQQQ QQQ hh hh hhhh hhh hh hh hhhh hhh QQQQQQQQ QQQ hh hh hhhh hhh QQQQQQQQ QQQ hh hh hhhh hhh QQQQQQQQ QQQ