Advanced Ocean Modelling: Using Open-Source Software

16 2 1D Models of Ekman Layerswhere (X, Y ) is the location of a float, and (u,v) is horizontal velocity at the depthhorizon of this float.2.3.2 ResultsThe wind-stress forcing imposed creates a lateral current in the ocean being strongestat the surface and decreasing rapidly with depth (Fig. 2.3). The surface current isdirected 45 ◦ to the right with respect to the wind direction in the Northern Hemisphere.The flow direction turns clockwise with increasing distance from the seasurface. The final shape is called the Ekman spiral. TheEkman-layer depth canbe defined as the depth at which the speed of the Ekman flow has decreased toexp (−π) ≈ 0.04 (4%) of its surface value. According to theory, this takes place ata depth of:δ E = π√2A z| f |(2.19)yielding 100 m for the setting of this exercises. This is in excellent agreement withthe simulation result. Note that some textbooks define the Ekman-layer depth withoutthe π multiplier.Fig. 2.3 Exercise 1. Structure of the surface Ekman layer (Northern Hemisphere). Small arrowsindicate lateral float displacements shown from the surface to a depth of 100 m at steps of 10 m.The thick arrow indicates the wind direction