Advanced Ocean Modelling: Using Open-Source Software

30 3 Basics of Nonhydrostatic ModellingThe vertically integrated horizontal velocity can then be calculated from:u r+1sum,k = ∑ i(u r+1i,kΔz) (3.30)Slight variations of the thickness of the water column owing to sea-level elevationsare ignored here. Finally, the surface value of dynamic pressure can be adjustedvia:Δq r+10,k= q r+10,k− q0,k n =−dt/Δx ( u r+1sum,k − )ur+1 sum,k−1(3.31)The S.O.R. iteration is repeated until the solution has converged to an almoststeady value; that is,∣ Δqr+1i,k− Δqi,kr ∣ 500 iterations of the S.O.R. scheme for each time step of the