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138 6 Rotational Effectswhere Q x and Q y are components of a vector called volume transport that is yieldedfrom vertical integration of the lateral f ow over the entire water column. Volumetransport carries units of m 3 /s per unit width of the f ow. In recognition of HaraldSverdrup’s work (e.g., Sverdrup, 1947), oceanographers often express volumetransports in units of Sverdrups (Sv) with 1 Sv being equivalent to 1×10 6 m 3 /s. Thenet volume transport is composed of several contributions that compensate eachother in order to achieve a steady-state sea level. The details of this compensation isdiscussed in the following.6.8.3 A Simplifie Model of the Wind-driven CirculationA simplifie model of the wind-driven circulation can be constructed when consideringan ocean of uniform water depth h o being void of density stratificationLarge-scale oceanic f ows are associated with very small Rossby numbers. Thenonlinear terms can therefore be ignored. For simplicity, we also neglect horizontalmomentum diffusion. Accordingly, the vertically integrated momentum equations(6.1) and (6.2) can be written as:∂ Q x∂t∂ Q y∂t∂η− fQ y =−gh o∂x + τ xwind∂η+ fQ x =−gh o∂y + τ ywind− τ botxρ o− τ botyρ oIn a steady state, the latter equations turn into:∂η− fQ y =−gh o∂x + τ xwind − τxbot(6.41)ρ o∂η+ fQ x =−gh o∂y + τ ywind − τybot(6.42)ρ oThese are linear equations and each of the “forces” on the right-hand side can beattributed to a certain contribution to the net volume transport. To this end, volumetransport can be disintegrated into three individual components:Q x = Q ek,sxQ y = Q ek,sy+ Q geox+ Q geoy+ Q ek,bx+ Q ek,bywhere the firs term denotes the wind-driven component, the second term thegeostrophic component, and the last term the component attributed to bottomfriction.