Physical Oceanography: An Overview
2.8 The Wind.Driven Oceanic Circulation
3a Principles of Ocean Physics
Fig. 2.19 Rotation and attenuation of near-surface velocity vector with depth through the surface Ekman layer of the ocean. Wind direction is indicated by topmost vane. [From Ekman, V. W., Ark. f. Mat., Astron. och Fysik (1905).]
so that the locai yelocity vector of the oceanic current rotates continuously to the right with depth, while decaying exponentially with a scale of order 10 to 20 m. Figure 2.19 illustrates Ekman's original diagram of the behavior of the current velocity vector, a representation called a hodograph. If the wind drift current is integrated over all depths, it is found that the net trans- port of water is at 90" to the direction of wind stress, and is t o the right of it in the Northern Hemisphere and to the left in the Southern Hemisphere.
This volume flow rate per unit horizontal distance is termed Ekman trans- port, with units of square meters per second. On the equatorward flanks of
the easterly trade winds, the right-angle forcing moves surface water poleward away from the equatorial region and results in cold, subsurface water flow- ing upward to replace the missing surface water, a process called equatorial up welling.
Ekman transport represents the first step in the formation of the major subtropical and subpolar oceanic gyres as well as the equatorial current sys- tems. In a typical ocean basin (Fig. 2.20), both the southeasterly trade winds and the mid-latitude westerlies force surface water toward the gyre interior because of Ekman transport. The surface convergence causes an accumula- tion there of warmer, lighter water, and results in a small elevation (of order 1 m or less) of the surface above the equipotential. It also causes a much larger deepening of the thermocline, which is found down to depths of several
Fig. 2.20 Convergence of surface water toward the interior of the North Atlantic Gyre under the influence of Ekman transport. Both trade winds and westerlies con- tribute to accumulation and deepening of the warm water pool.
hundred meters in the western Sargasso Sea, for example. Thus Ekman in- flow into the subtropic convergence region (i.e., the interior of the gyre) results in a downwelling of the surface waters and a decrease in their angular momen- tum and vorticity by way of their change in height. Vorticity is a measure of the rotation rate of a small fluid element, and is equal to twice the angu- lar velocity of the element. It is termed cyclonic if it has the same sense of rotation as the earth, and anticyclonic if opposite. Since rotating fluids must move so as to maintain constant their total angular momentum per unit mass and per unit area, the loss of vorticity caused by sinking must be made up by an increase in vorticity caused by the earth's rotation. As will be shown in Chapter 6 , this may be accomplished by the movement of an extensive mass of the interior, deeper fluid toward the equator. Thus in the Northern Hemisphere gyres, water at depth moves southward, a motion called Sverdrup interior flow.
The small surface elevation is termed setup, and has associated with it a
40 Principles of Ocean Physics
hydraulic head and a horizontal pressure gradient, - vhp, that is opposed by the horizontal component of Coriolis force, p(2n x u)h. The currents resulting from this balance of forces are called geostrophic (earth-turning) flows, and in the absence of time variations and friction, move approximately along surfaces of constant elevation. Thus the geostrophic equation is
(2.12) where p is the density of seawater and h denotes the horizontal component.
Geostrophic balance is not confined to surface currents, but may exist at all depths. This equation for balanced flow forms an important tool in the analytical tool kit of the oceanographer.
As the geostrophically balanced deeper waters vacate the northern regions of the gyre as Sverdrup flow, they must be replaced by a return flow to the north in such a manner as to ensure continuity of the flow and local conser- vation of vorticity, i.e., angular momentum. Additionally, the northward- flowing water will become concentrated along the western boundary of the basin (the eastern edge of the continent) because of reasons of the overall vorticity balance of the gyre; since, in the longer term, the gyre is neither increasing nor decreasing its rotation rate, approximate equilibrium must exist between sources and sinks of vorticity on each side of the ocean basin. This circumstance, which is somewhat difficult to grasp conceptually without a more extensive discourse on its causes and effects, results in the formation of intense, narrow current systems off the east coasts of continents every- where in the world, which are called, appropriately enough, western bound- ary currents. The Gulf Stream is the best-known example of such a vorticity-balancing flow. Along with the concentration of the flow, there is a concomitant large increase in fluid friction along the western, inshore side of the Stream as a result of flow instability and eddy production. This “eddy viscosity” is an important source of positive, cyclonic vorticity in the over- all balance. In a sense, a western boundary current in the Northern Hemi- sphere will produce vorticity by “rubbing its left shoulder” against the continental shelf; in the Southern Hemisphere it is the right shoulder that is rubbed. At some point along the continental margin, the boundary cur- rents leave the land mass and turn seaward to complete the flow circuit by rejoining the eastward-flowing wind-driven current. Thus the overall gyre has the appearance of the surface flow shown in Fig. 2.21
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which gives sur- face streamlines of an idealized subtropical gyre. It is estimated that the time required for a typical water parcel to circulate around the entire gyre is of order five years. It should be noted that the subsurface flow is generally quite different from this (see below), and that the overall circulation is a compli- cated function of all three spatial coordinates. Additionally, there are majorFig. 2.21 Surface streamlines of an idealized subtropical gyre. Intensification of flow along the western boundary is due to the overall vorticity balance of the gyre.
time variations in the currents caused by wind stress variations and large- scale flow instabilities.