Advanced Ocean Modelling: Using Open-Source Software

4.2 Exercise 16: Geostrophic Adjustment 103• Step structures of the sea floor are block-type obstacles for the vertically integratedcontinuity equation. This leads to a bias of the dynamics of gravity wavesvia partial reflection.These shortcoming, arising when using z-coordinate models, are unfortunate andcan only be avoided with the choice of other coordinate systems (such as sigmacoordinatemodels) or model types (such as layer models).4.2 Exercise 16: Geostrophic Adjustment4.2.1 AimThis exercise employs the 2.5d vertical ocean-slice model to study geostrophicadjustment of a surface density front of infinite length.4.2.2 Task DescriptionWe consider a model domain, 50 km in length and 500 m in depth, resolved by alateral grid spacing of Δx = 500 m and a vertical grid spacing of Δz = 10 m.Lateral boundaries are closed. An isolated surface layer of 10 km in width and 250 min thickness is initially placed in the centre of the model domain (Fig. 4.3). This layeris lighter compared with the ambient ocean in which the density is ρ = 1,028 kg/m 3 .The density anomaly of the surface layer is linearly adjusted from zero to a finalvalue of 0.1kg/m 3 over the first 6 hrs of the simulation. No further forcing is appliedafterward and the dynamics can evolve freely.Small uniform isotropic values of 1×10 −4 m 2 /s are used for both eddy diffusivityand eddy viscosity. The bottom friction parameter is set to r = 0.001. The totalsimulation time is 60 hrs with hourly data outputs. The time step is set to Δt = 5s.The model includes a freely moving sea surface. The pressure accuracy of the S.O.R.scheme is set to ɛ = 0.01 Pa. Two scenarios are considered. Rotational effects areignored in the first scenario by setting the Coriolis parameter to zero. The secondscenario uses a mid-latitude value of the Coriolis parameter of f = 1 × 10 −4 s −1(Northern Hemisphere).Fig. 4.3 Initial configuration for Exercise 16