Advanced Ocean Modelling: Using Open-Source Software

120 4 2.5D Vertical Slice ModellingFig. 4.18 Illustration for implementation of lateral boundary conditions. Vertical arrows indicatethe grid columns in which values of vertical velocity and of the nonhydrostatic part of dynamicpressure q are set to zerovalues of vertical eddy viscosity and diffusivity. The bottom friction parameter isset to r = 0.001. The total simulation time is 50 days with half daily data outputs.The pressure accuracy for the S.O.R. iteration is set to ɛ = 10 −3 Pa. The time stepis chosen at Δt = 90 s, using the free-surface version of the model.4.6.4 Results: Scenario 1The wind stress imposed (see Fig. 4.17a) creates a surface Ekman layer in the ocean.Details of the vertical structure of this Ekman layer are not revolved by the relativelycoarse vertical grid spacing of 20 m chosen. Nevertheless, the model capturesthe resultant net horizontal movement, the so-called Ekman-layer transport. IntheNorthern Hemisphere, Ekman-layer transport in the surface ocean is directed 90 ◦ tothe right with respect to the wind direction. Its magnitude varies with the magnitudeof the wind stress. Consequently, the wind-stress forcing of Scenario 1 creates alateral divergence of surface Ekman-layer transports. With ignorance of flows belowthe surface Ekman layer, this divergence would result in a drop of the sea surface atarateof:w ek = 1ρ o f∂τ windy∂x(4.24)called Ekman-pumping velocity. In this exercise, the Ekman-pumping velocityattains a maximum value in the middle of the model domain of about 6 × 10 −3 mm/sor 50 cm per day. The sea surface, however, does not drop at this rate, given that flowdivergence in the surface Ekman layer is partially compensated by a convergenceof lateral flow in the ocean underneath. Instead, the sea level rapidly approachesa steady state, accompanied by a steady-state geostrophic flow in the surface layer.As a consequence of this, the Ekman-pumping velocity translates now to the verticaldisplacement speed of the pycnocline caused by lateral flow divergence in the oceaninterior. Accordingly, we can anticipate that the shape of the sea level mirrors thehorizontal distribution of the Ekman-pumping velocity; that is,η ∝ w ek = 1ρ o f∂τ windy∂xτ o=−π sin (π x/L) (4.25)ρ o fL