Contents

144 6 Rotational EffectsFig. 6.14 Sketch of the structure of the meridional geostrophic f ow component v geoUsing typical values ( f = 1×10 −4 s −1 , δ ek =10 m, β = 2×10 −11 m −1 s −1 , andh o = 4000 m), we yield L ≈ 20 km.6.8.11 The Role of Lateral Momentum DiffusionBottom friction is irrelevant for the Sverdup regime that occupies most of thedomain. Therefore, the Sverdup relation is also valied in a stratifie ocean in whichthe f ow does not extend to the seafloo . In this case, the above geostrophic volumetransports represent the vertical integral of the baroclinic geostrophic f ow andthe vertical structure of this f ow is irrelevant for the resultant steady-state surfacepressure fieldIn our simplifie model, the western boundary current arises exclusively due tobottom friction and the model fails in the absence of near-bottom f ows. The use oflateral momentum diffusion instead of bottom friction in the governing equationsovercomes this problem and enables the analytical description of western boundarycurrents detached from the seafloo . The equations governing this problem are morecomplex and therefore not included in this book. The interested reader is referred tothe work by Munk (1950).6.9 Exercise 18: The Wind-Driven Circulation6.9.1 AimThe aim of this exercise is to reveal the wind-driven circulation of the ocean atmidlatitudes consisting of subtropical gyres and western boundary currents.6.9.2 Task DescriptionIn this exercise, we apply the shallow-water equations to study the wind-drivencirculation in a closed rectangular ocean basin of 1000 km in length and 500 km