# Case 05. The thermal boundary layer on steep slope bottom

The -errors in POM and ECOM-si have been examined both theoretically and numerically by Mellor et al. (1994) and Chen and Beardsley (1995). Mellor et al. pointed out that these errors in POM could retain at a certain level if sufficient high horizontal and vertical resolutions are used. Chen and Beardsley found that at a fixed location over a sloping bottom -errors in ECOM-si increases with water depth. Since the buoyancy velocity error caused by the -transformation always opposes the velocity in the thermal boundary layer on the bottom of the slope, this error can be suppressed if the vertical resolution is high enough to resolve the thermal current near the bottom. The experiments shown here are focused on the influence of the horizontal resolution used in FVCOM and POM on the thermal boundary layer on steep topography. POM uses the simplified temperature bottom condition of , while FVCOM uses the completed exact temperature bottom condition. To compare FVCOM with POM, we ran FVCOM for the two separate cases: one with the same bottom boundary condition as POM and the other with the exact condition.
where is the surface water temperature given as 15o C, is the bottom water temperature given as 6oC, and H is the maximum water depth specified as 300 m.
There are no physical reasons supporting an asymmetric distribution of the current across the lake for POM, since the numerical grids are composed of squares which are symmetrically distributed around the circular lake, and also the mixing coefficient is the same everywhere. The fact that the asymmetric pattern of the currents mainly occur near the surface around the coast implies that POM has a limitation when applied to a very shallow region. This is probably due to the time-and space-smoothing program used in the code and also to the limitation in geometric fitting.
Also, when the pressure gradient forcing moves the water in the interior into the boundary layer, the thermal diffusion tends to reduce it density and hence cause it to upwell along the slope.
Our numerical experiments imply that both POM and FVCOM could resolve the structure of the thermal boundary layer over the sloping bottom topography at a certain horizontal resolution. In spite of it, FVCOM utilizes unstructured grids which provide more flexibility to increase the local horizontal resolution at the shelf break. Also, the POM-predicted currents are not symmetrically distributed in the shallow water close to the coast, even when the horizontal resolution is increased. This issue needs to be fixed when applying POM to a very shallow water region. It should be pointed out here that the model results shown above are all based on the bottom boundary of . This simplification may lead to an overestimation of the vertical mixing and hence horizontal and vertical velocities over the steep slope bottom like shelf break. For a given horizontal resolution of 2.25 km, the currents at the 10th model day predicted by FVCOM with an exact no flux normal to the slope are about one order of magnitude weaker than those described above (Chen et al., 2004). These results suggest that an inaccurate use of the bottom boundary condition of temperature exaggerates vertical mixing and thus overestimates both along-isobath and vertical velocities within the thermal boundary layer over the slope. |