Advanced Ocean Modelling: Using Open-Source Software

4.6 Exercise 19: Ekman Pumping 119is N ≈ 0.05 s −1 . Below the pycnocline, density increases linearly with depth characterisedby a stability frequency of N ≈ 8 × 10 −3 s −1 . The Coriolis parameter isset to a constant value of f =1× 10 −4 s −1 (Northern Hemisphere). Variation of theCoriolis parameter with geographical latitude is ignored.The model is forced by prescription of wind stress acting in the y-directionand thus normal to the model slice. Three different wind forcings are considered(Fig. 4.17). The structure of the wind-stress forcing is:τ windy = τ o cos (π x/L) + τ 1 (4.23)where L is the horizontal extent of the model domain. The first scenario usesτ o = −0.1 Pa and τ 1 = 0, the second scenario τ o = +0.1 Pa and τ 1 = 0, and the thirdscenario τ o = +0.05 Pa and τ 1 = +0.05 Pa. In each case, the wind field is graduallyadjusted from zero to its final values during the initial 2 days of simulation to avoidunwanted initial disturbances in the form of gravity waves and inertial oscillations.The wind-stress forcing is such that surface Ekman transports are free of lateraldivergence at lateral boundaries. This implies that the sea-level elevation, thedynamic pressure part q and vertical velocity should remain at zero values at theseboundaries. This is consistent with choice of zero-gradient conditions for u, which,in turn, specify the indices of boundary grid cells (see Fig. 4.18). Zero-gradientlateral boundary conditions are used for the remainder variables; that is, the velocitycomponent normal to the model slice v and density.Uniform values of A h = K h =50m 2 /s are used for horizontal diffusivity and viscosity.The Kochergin turbulence scheme of previous exercises is used to calculateFig. 4.17 Three different steady wind-stress forcings for Exercise 19