Advanced Ocean Modelling: Using Open-Source Software

5.8 Exercise 24: The Abyssal Circulation 149Fig. 5.18 Model domain for Exercise 24Lateral eddy viscosity and eddy diffusivity are set to a uniform value of A h =K h =1m 2 /s using no-slip conditions for flow parallel to coastlines. Vertical eddydiffusivities and eddy viscosities are diagnosed from Kochergin’s turbulence closurescheme. The bottom friction parameter is set to a value of r = 0.001. The beta-planeapproximation assumes a Coriolis parameter that varies with meridional distance yaccording to:f (y) = f o + β y (5.17)In this exercise, we use a reference Coriolis parameter of f o = 1 × 10 −4 s −1(mid-latitudes in Northern Hemisphere) and a meridional variation of the Coriolisparameter of β = 2.2 × 10 −11 s −1 m −1 . A total of 5,000 non-buoyant floats areinitiated at random locations of the model domain to trace the trajectories of waterparcels (see Sect. 3.16). In addition to this, Eulerian tracer concentration is usedto identify regions experiencing upwelling during the simulation. To this end, theinitial tracer concentration is set to zero in the upper 500 m of the water column andto values of unity below.Owing to the smallness of resultant vertical speeds and associated round-offerrors, predicted concentration fields in the author’s pilot experiments showedsome unwanted noisy patterns. To hide this, lateral eddy diffusivity used in theadvection-diffusion equation for tracer concentration is increased to 100 m 2 /s asa means of smoothing. This has no dynamical implications. The time step isset to Δt = 200 s using the rigid-lid approximation to eliminate fast propagatingsurface gravity waves. The pressure accuracy of the S.O.R. iteration is set toɛ =0.01Pa.