ESTUARY TEST CASE

Suspended Sediment Test in an Estuary

This test case provides a fundamental check of the ability of a model to represent 1) mixing processes typical of estuarine conditions, 2) resuspension, advection, and deposition for suspended-sediment transport, 3) temporal dynamics of upper bed layer, and 4) interaction of suspended-sediment and the bed.

Domain

The domain is a long, narrow rectangular channel.

Model Parameter	Variable	Value
Length (east-west)	$l$	100000 m
Width (north-south)	$w$	1000 m
Depth	$h$	10 m at western end, decreasing linearly to 5 at eastern end
Temperature	$T$	$10^{o}C$

Bottom Sediment

Single grain size on bottom:

Model Parameter	Variable	Value
Size	$D_{50}$	0.15 mm
Density	$\rho _{s}$	$2650\,kg/m^{3}$
Settling Velocity	$w_{s}$	0.50 mm/s
Critical shear stress	$\tau _{c}$	$0.05\,N/m^{2}$
Porosity	$\phi$	0.90
Bed thickness	$bed\_thick$	1mm

Forcing

No Coriolis
No wind
No heating/cooling

Initial Conditions

Salinity distribution from west end = 35 to east end = 0. (Vertically well mixed)

Boundary Conditions

North and south sides = walls with no fluxes, no friction
Bottom roughness $K_{s}\,=\,0.15\,m\,(Z_{o}\,=\,K_{s}/30\,=\,0.005\,m)$
Sediment flux calculated by model
Surface = free surface, no fluxes

Flow, Western end, tidal
$q_{west}\,=\,4000\,m^{3}/s*sin(\omega t)-q_{east}$,br> $\omega \,=\,2\pi /T$
T = 12 * 3600 seconds
t = model time step, seconds

Flow, Eastern end, constant riverine (varying depth)
$q_{east}\,=\,400\,m^{3}/s$
Salinity, western end
Radiation condition with nudging, $t_{nudge}\,=\,3\,hours$
Salinity at eastern end = 0

Output (ASCII files suitable for plotting)

At t = 10 days (20 tidal cycles):
Tidally averaged velocity field (average over last 2 tidal cycles)
Bed profile
Tidal-mean suspended sediment field

Physical Constants

Gravitational acceleration $g\,=\,9.81m/s^{2}$
Von Karman's constant $\kappa \,=\,0.41$
Dynamic viscosity (and minimum diffusivity) $\nu =1e-6\,m^{2}/s$

Note: If a model incorporates physical constants that differ from these, and/or automatically calculates some values specified here, please specify the values used.

Results

Figure 1. Initial salinity distribution for estuary simulations.

Model was initialized with a constant longitudinal salinity field as shown in Figure 1. Simulations were the calculated for 20 tidal cycles (10 days), after which time a quasi-steady state had been reached. Figure 2 shows the resulting salinity fields for 4 different closure methods near the end of 20 tidal cycles. The 4 different closures are: MY25, Generic Length Scale (GLS) as KKL, GLS as KE, and GLS as KW88. The MY25 closure is computed based on the classical scheme of Mellor/Yamada (1982), and the GLS closures are computed with the method of Umlauf and Burchard (2002 submitted). The main difference is in the length scale limitations. For the MY25 method, the length scale is only limited in the calculation of the stability functions, whereas for the GLS method the length scale is limited in the production, wall proximity function, and the stability functions.

The MY25 closure does not develop a well defined surface mixed layer as with the closures computed with the GLS method. This is most likely due to the length scale limitation and the buoyancy parameter (E3 = 1.8). As discussed by Burchard (2001), a value of c3 ~ 2.5 (E3 ~ 5.0) provides a more realistic simulation of a wind induced surface mixed layer test experiment.

Figure 2. Initial salinity distribution for estuary simulations.

Suspended sediment results (figure 3) are very dependent on the bottom stresses and vertical mixing processes. For these simulations, a thin layer of sediment was placed on the bed at time = 10 days. Sediment parameters were selected to allow rapid erosion. Upstream riverine flow will transport the sediment downstream and the estuarine circulation creates a turbidity maximum at the limit of salt intrusion. For the MY25 closure, this limit is near x = 35 km, while for the KE and KW simulations, a near bottom turbidity maximum is located near x = 50 km. For the KKL simulation, the turbidity maximum is further upstream, near x = 60 km.

Figure 3. Suspended sediment concentration distribution after 9.9 days for the estuary simulations.