Marine Ecosystem Dynamics Modeling Laboratory

Case 02. Wind-induced Waves over Slope Bottom Topography

Case 2.Wind-induced Waves over Slope Bottom Topography

1. Analytical Solution

Considering an idealized sloping-bottom circular lake with water depth given as

where is the radius of the lake and is the water depth at the center (Fig. 1).The governing equations shown in Case 1 are applied to this case and an analytical solution was derived by Birchfield and Hickie (BH) (1977). The solution was in the form of a complicated double series characterized by three waves: two for a gravity wave pair and one for a topographic wave. As an initial value problem, the waves are dominated by the first 4 radial modes in the first model day, but higher modes must be taken into account for a longer time period.


 Fig. 1: The illustration of an idealized, slopping-bottom, circular lake

2. Design of the Numerical Experiment

Unstructured triangular and structured rectangular grids used for FVCOM and POM/ECOM-si are similar to those shown in Case 1 except for a radius of 100 km and a maximum depth of 100 m. The analytical solution is derived with a lateral boundary condition at . This condition is allowed in the -coordinate transformation system used in FVCOM and POM/ECOM-si until a wet/dry treatment technique is incorporated. In order to make these models run for the case with this idealized sloping bottom, a depth of 0.5 m is added everywhere in , with an understanding that the numerical solution might lead to a bias of BH�s analytical solution for a long-time run. For this reason, the comparison of the models with the analytical solution is limited in the time scale of less than 1 day starting from the initial.

 

3. Results

In the first model day, both FVCOM and POM produce a reasonable simulation of the elevation composed of the first 4 radial modes of the analytical solution, although POM shows a small perturbation at the center at the first model hour and a biased maximum value away from the coast at the end of the 1st model day (Fig. 2).

Significant difference between FVCOM and POM occur after the 2nd model day. At the end of the 5th model day, for example, FVCOM with a horizontal resolution of 5 km shows a symmetridistribution of the elevation over the circular lake, with a maximum positive value on the right coast and a minimum negative value on the left coast (Fig. 3).


Fig. 2: Comparison of the spatial distributions of the surface elevation at the end of 1st hour and 1st day between analytical solution, FVCOM and POM. Horizontal resolution is 5 km for FVCOM and 2.5 km for POM.

Although POM with a horizontal resolution of 2.5 km also shows a similar pattern, multiple artificial eddies occur at the transition region from positive elevation to negative elevation and a series of small-scale perturbation structures of the elevation are detected along the coast on both sides of the wall.

This difference is clearly evident in model-computed transport. FVCOM shows a beautiful spiral circulation pattern along the coast and a double cell circulation in the interior, while POM-computed circulation is characterized by multiple eddies in the transition region of the elevation and significant divergence flow close to the coast.


Fig. 3: Comparison of the spatial distributions of the
surface elevation at the end of 5th day between FVCOM
and POM. Horizontal resolution is 5 km for FVCOM and
2.5 km for POM.

It is clear that eddies predicted by POM are numerical noises due to inaccurate fitting of the curvature coastline of the circular lake, since the size and strength of these eddies reduce as horizontal resolution increases. Again, theoretically these numerical noises could disappear as horizontal resolution increases to a certain level, but only at the sacrifice of impractical computational efficiency.

 
 

«PreviousNext» Posted on November 13, 2013