Improvement 2.Multiple Choices of Open Boundary Treatment Methods of FVCOM

Improvement 2.Multiple Choices of Open Boundary Treatment Methods of FVCOM

FVCOM was originally coded with two choices for open boundaries: 1) user specified sea levels and 2) gravity wave radiation condition for sea elevation. Some experiments have shown that the gravity wave radiation condition can guarantee the numerical stability of the model but might cause the decrease of the sea level due to the wave reflection (Chapman 1985). To provide users more options on open boundary treatments. We have added more choices. In the updated FVCOM code, five types of open boundary conditions (OBCs) of elevation were added. In each case, two types of the velocity treatment (linear and nonlinear) were included.

To check the code, we have run different types of the open boundary conditions for a freshwater discharge case on an idealized shelf. A brief summary is posted here to provide users some information about the performance of these methods.

1. Open Boundary Conditions

a. The Elevation

Type 1:	Active (ASL) Specified at OBC. For example, tidal forcing (amplitudes and phases)
Type 2:	Clamped (ASL-CLP) (Beardsley and Haidvogel, 1981)
Type 3:	Implicit Gravity Wave Radiation (GWI) (Chapman, 1985)
Type 4:	Partial Clamped (Blumberg and Kantha, 1985)
Type 5:	Explicit Orlanski Radiation (ORE) (Orlanski, 1976 and Chapman,1985)

b. The Velocity

In each of OBC for the elevation, the velocity in the mesh with one side on the OB, can be determined by two methods: 1) calculated directly using the linear momentum equations and 2) determined by a fully nonlinear momentum equations.

In the second method, the vertically integrated flux at open boundaries is first calculated based on the mass conservation from the continuity equation, and then a 2-D external velocity is calculated using the fully nonlinear momentum equations. The perturbation velocity after subtracting the 2-D velocity is determined by the linear momentum equations. In order to calculate the flux at the open boundary, ghost cells are added at the open boundary in which the velocity is specified as the same value and direction in the open boundary cell.

Fig. 1: Unstructured triangular grids used for OBCs case tests. Horizontal resolution is 20 km.

2. Design of A Testing Case

All OBCs are tested for an idealized case of the freshwater river plume over a simple geometric continental shelf shown in Fig. 1 and Fig. 2. The computational domain is characterized with a semi-enclosed rectangular basin with a length of 800 km, a width of 400 km and one OB downstream (600 km away from the freshwater source). The water depth is 10 m at the coast and increased to 100 m over a distance of 100 km.

The horizontal resolution is 20 km and 10 sigma-levels are chosen in the vertical.

Freshwater discharge at the point source was specified 1000 m³/s. The water was specified uniformly in the vertical. The background salinity was specified as a constant value of 30 PSU.

3. Results

ASL_CLP-nonlinear: No significant reflection was found in the first 10 days. When the plume reaches the OB, the reflection causes the current flow along the OB. The interior solution seems to be influenced little from the OB in a time scale of 50 days. This is consistent with Chapman (1985) finding.

GWI-nonlinear: Velocity and salinity look good, but the sea level in the entire domain significantly decayed with time. At 50th day, the sea level dropped more than 0.5 m. This boundary condition is not recommended for freshwater discharge cases.

BKI-nonlinear: The sea level variation is the same as ASL-CLP, and velocity was similar to GWI and better than ASL-CLP. The salinity is similar to ASL-CLP and GWI.

ORI-nonlinear: Velocity and salinity are similar to BKI, but the sea level decays with time. However, the decay rate was much smaller than GWI.

In this simple case, no significant differences were found for choices of linear and nonlinear approaches for the calculation of the velocity at the open boundary cell. However, we do find a significant difference in the estuarine application when an open boundary was specified in the area with the intertidal zone.

4. Animations:

Fig. 2: The illustration of an idealized, straight-coastline continental shelf used for OBCs case tests.

Fig. 3: Comparison of the spatial distributions of the water elevation at the end of the 10th model day. (a) CLP: ASL_CLP-nonlinear result; (b) GWI: GWI-nonlinear result; (c) BKI: BKI-nonlinear result; (d) ORI: ORI-nonlinear result. Click here for animation
Fig. 4: Comparison of the spatial distributions of the surface salinity at the end of the 10th model day. (a) CLP: ASL_CLP-nonlinear result; (b) GWI: GWI-nonlinear result; (c) BKI: BKI-nonlinear result; (d) ORI: ORI-nonlinear result. Click here for animation
Fig. 5: Comparison of the spatial distributions of the surface velocity at the end of the 10th day. (a) CLP: ASL_CLP-nonlinear result; (b) GWI: GWI-nonlinear result; (c) BKI: BKI-nonlinear result; (d) ORI: ORI-nonlinear result. Click here for animation --------------------------------------------------------------------------------------------------------------------- Changsheng Chen, Jianhua Qi, 08/27/2004

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