COHSTREX 2006 Numerical Modeling and Simulation

During the past year, we have focused on completing the set-up and early runs with the SUNTANS code. A major effort was aimed at grid generation; also the advection algorithm was changed to an Eulerian-Lagrangian method to facilitate the significant wetting and drying of the coastline during the large Snohomish tidal range.

Background and setup
The bathymetry data used in the numerical model is a combination of data measured by Finlayson in 2000, the field measurement data obtained by our team last year in the river channel and mouth, and the field measurement data by Fram (2002), which gives an estimated bottom slope for Snohomish River upstream from the bridge.

In order to capture the interaction between the river and the tide, the computational domain is chosen as shown in Figure 22 to include the Snohomish River Estuary, 30 kilometers of Snohomish River in the east, Possession Sound in the west, and Port Susan (a closed-end bay connected to Possession Sound). Whidbey Basin, another basin connected to Possession Sound, is not in the model. Steamboat Slough as a tributary of the Snohomish River is modeled.

Figure 22. Simulation domain and boundaries.

In addition to the closed boundaries for coastlines and river banks, there are three open boundaries, two forced with tides [at the junction of Possession Sound and Whidbey Basin, and at the junction of Possession Sound and Main Puget Sound Basin] and one with Snohomish River flow. Studies by Fram (2002) showed that the salt wedge goes up to 13 km upstream from the river mouth. Because the gage data at USGS Gage Station (Snohomish River at Snohomish), located 20 km from the river mouth, shows significant tidal influence, the grid is extended to 30 km upriver where the next USGS gage station (Snohomish River near Monroe) shows no tide influence.

An unstructured grid of 36,000 horizontal cells has been generated with GAMBIT. This grid has 600m resolution for Puget Sound and 80m resolution for the river channels. Cells with 20m resolution are used at the focus site [Jetty Island]. This grid is sufficient for capturing the main flow conditions, but not for resolving fine coherent structure detail. It has been found efficient and useful in the initial testing.

We have a grid that has been further refined at the focus site (Figure 23). It has 300m resolution for Puget Sound, 80m resolution for the river and 1m resolution for the coherent structures. It consists of 100,000 horizontal cells. We are currently working on improving the quality of this grid for production computations.

Figure 23. The focus site on the fine grid.

Observations and studies on the circulation in Puget Sound (Gustafson et al 2000; Stout et al 2001; and Lavell et al 1988) have shown that Possession Sound, Port Susan and Whidbey Basin act like a closed basin and that the depth in entire area varies at the same pace (in phase). Thus, fluxes through a specific cross section can be estimated via volume conservation and forcing done with the expected tidal values. The results are in agreement with the predictions from Lavelle's model.

There are three river flows, viz., the Skagit River, the Snohomish River and Stillaguamish River [but the latter is a minor contributor and is ignored]. The discharge rates of the rivers are found in USGS databases and a few other documents. The Skagit River is not modeled, but its freshwater inflow enters our computational domain through the north tidally-forced boundary, and then goes out through the south boundary. The water from the Snohomish River comes in through the river inlet and flows out through the south boundary.

The saline water in the sound is slightly stratified, with the typical salinity of 27 psu or so near the top (Gustafson, 2000). In our simulation, we assume that the flows in and out of the tidally forced boundaries are saline water of 30 psu, and the river inflow is 0 psu. The simulation starts from quiescent conditions at HHW. As Fram (2002) found that the salt wedge travels up 10km from the river mouth at HHW, we setup the initial conditions with a linear horizontal salinity gradient changing from 30psu to 0psu at that location. Water downstream of that is saline and upstream of that is fresh.

Simulation results
Multiple test runs have been performed to improve the boundary conditions and drag coefficients. The following results from the recent runs are an illustration of the simulations. These runs are hydrostatic without a turbulence mixing model. However, they have modeled the nonlinear advection of momentum under wetting and drying conditions. The predicted free surface height matches the real tide pattern reasonably well in most of the deeper Possession Sound areas. The prediction near Jetty Island shows a lag at low low water, which is reasonable. It has underestimated the amplitude of the ebb a bit. Further upstream at the USGS Gaging Station there is a similar underestimation of the ebb. River slope and bottom drag are being investigated as possible causes of this behavior.

Figure 24 shows velocity fields near the free surface at low low water and on a strong flood tide. The model is able to capture a number of observed features of the real flow: (a) the significant drying that happens at low low water, when only the deepest part of the bypass to the north of Jetty Island stays wet; (b) flow is strong during ebb; (c) at high high water, the currents are very slow.

Figure 24(a). Velocity field at LLW on July 20th.

Figure 24(b). Velocity field during strong flooding.

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