Advanced Ocean Modelling: Using Open-Source Software

116 4 2.5D Vertical Slice Modellingto the surface. The bottom Ekman layer is the result of geostrophic alongshore flowthat runs into the same direction as the wind. This geostrophic flow is magnified invicinity of the surface density front, created by the upwelling, where it attains speedsof 60 cm/s. Step-type representation of variable bathymetry obviously induces someartificial local disturbances, but this does not lead to numerical instabilities.Theory gives a frontal speed of c = √ (g ′ h 1 ) of 49 cm/s and an internal Rossbyradius of deformation R = c/ | f | of 4.8 km. Equation (4.18) suggests that the distanceof the density outcrop from the coast is a = 11.8 km after 5 days of simulation.Equation (4.19) suggests that the density interface outcrops at the surfaceafter 1.14 days. The model predictions are in good agreement with theory(see Fig. 4.14). The coastal sea level drops by 20 cm (not shown) as a consequenceof offshore Ekman drift. The magnification of the geostrophic flow in vicinity ofthe surface density front is caused by a steepening of the sea-level gradient in thisregion.Fig. 4.14 Exercise 18. Same as top panel of Fig. 4.13, but after 5 days of simulation. a is thedistance of the density outcrop from the coast. R is the frontal width4.5.5 Additional Exercise for the ReaderConsider a stronger density stratification by increasing the density change across thepycnocline to 5 kg/m 3 . Explore variations in the resultant upwelling dynamics andcompare the model prediction with theory.4.5.6 Results: Downwelling ScenarioThe wind-stress forcing creates onshore Ekman drift in the surface layer and offshoreEkman flow in the frictional bottom-boundary layer (Fig. 4.15). The onshoreflow pushes surface water against the coast and downward. As a consequence of theonshore Ekman transport in the surface layer, a geostrophic jet of 50 cm/s in speedand a width of 10 km establishes along the coast running into the same direction asthe wind. This alongshore geostrophic flow triggers net offshore drift in the bottom