Advanced Ocean Modelling: Using Open-Source Software

118 4 2.5D Vertical Slice Modelling4.6 Exercise 19: Ekman Pumping4.6.1 Theoretical BackgroundIt is obvious that an equilibrium distribution of sea-level elevation is only possible ifwind-induced flow divergence (convergence) in the surface Ekman layer is balancedby a flow convergence (divergence) in the ocean underneath. As a consequence ofthis, density surfaces in the ocean interior tend to be an amplified mirror image ofthe shape of the sea surface. The physical mechanism that converts flow divergencein the surface Ekman layer to vertical displacements of isopycnals is called Ekmanpumping. Coastal upwelling and downwelling of density interfaces (see previousexercise) are the signatures of Ekman pumping.4.6.2 AimDivergence of wind-driven flow in the surface Ekman layer is the principle agent tocreating deep-reaching geostrophic flows in the ocean. In a stratified fluid, however,dynamical adjustment of isopycnals in the ocean interior operates to reduce lateralpressure gradients such that large-scale geostrophic flows tend to become negligiblyweak below depths of 1,500–2,500 m. The aim of this exercise is to illustrate thisprinciple of baroclinic compensation using the wind-forced 2.5d vertical ocean-slicemodel.4.6.3 Task DescriptionThe model domain has a length of 500 km, resolved by a horizontal grid spacingof Δx = 5 km, and a depth of 500 m, resolved by a vertical grid spacing ofΔz = 20 m (Fig. 4.16). The unrealistically small depth has been chosen to allow forrelatively long numerical time steps. Initially, the ocean is at rest and void of lateraldensity variations. The surface mixed-layer is 200 m thick and has a density ofρ = 1,025 kg/m 3 . There is a density change at the base of this layer across which densitychanges by Δρ = 5 kg/m 3 . The associated stability frequency of this pycnoclineFig. 4.16 Initial configuration for Exercise 19