1 The global surface current pattern to some extent reflects the surface wind field, but ocean currents are constrained by continental boundaries and current systems are often characterized by gyral circulations.
2 Maps of wind and current flows of necessity represent average conditions only: at any one time the actual flow at a given point might be markedly different from that shown.
3 The frictional force caused by the action of wind on the sea-surface is known as the wind stress. Its magnitude is proportional to the square of the wind speed; it is also affected by the roughness of the sea-surface and conditions in the overlying atmosphere.
4 Wind stress acting on the sea-surface generates motion in the form of waves and currents. The surface current is typically 3% of the wind speed. Motion is transmitted downwards through frictional coupling caused by turbulence. Because flow in the ocean is almost always turbulent, the coefficient of friction that is important for studies of current flow is the coefficient of eddy viscosity. Typical values are 10~5 to 10"' m2s_l for A-and 10 to lO^nvV forAh.
5 Moving water tends towards a state of equilibrium. Flows adjust to the forces acting on them so that eventually those forces balance one another. Major forces that need to be considered with respect to moving water are wind stress at the sea-surface, internal friction (i.e. eddy viscosity), the Coriolis force and horizontal pressure gradient forces; in some situations, friction with the sea-bed and/or with coastal boundaries also needs to be taken into account. Although deflection by the Coriolis force is greater for slower-moving parcels of water, the magnitude of the force increases with speed, being equal to mfit.
6 Ekman showed theoretically that under idealized conditions the surface current resulting from wind stress will be 45° cum sole of the wind, and that the direction of the wind-induced current will rotate cum sole with depth, forming the Ekman spiral current pattern. An important consequence of this is that the mean flow of the wind-driven (or Ekman) layer is 90° to the right of the wind in the Northern Hemisphere and 90° to the left of the wind in the Southern Hemisphere.
7 When the forces that have set water in motion cease to act. the water will continue to move until the energy supplied has been dissipated, mainly by internal friction. During this time, the motion of the water is still influenced by the Coriolis force, and the rotational flows that result are known as inertia currents. The period of rotation of an inertia current varies with the Coriolis parameter/= 2Q sin and hence with latitude. <)).
8 The currents that result when the horizontal pressure gradient force is balanced by the Coriolis force are known as geostrophic currents. The horizontal pressure gradient force may result only from the slope of the sea-surface. and in these conditions isobaric and isopycnic surfaces are parallel and conditions are described as barotropic. When the water is not homogeneous, but instead there are lateral variations in temperature and salinity, part of the variation in pressure at a given depth level results from the density distribution in the overlying water. In these situations, isopycnic surfaces slope in the opposite direction to isobaric surfaces; thus, isobars and isopycnals are inclined to one another and conditions are described as baroclinic.
9 In geostrophic flow, the angle of slope (6) of each isobaric surface may be related to u, the speed of the geostrophic current in the vicinity of that isobaric surface, by the gradient equation: tan 0 =fii/g. In barotropic flow, the slope of isobaric surfaces remains constant with depth, as does the velocity of the geostrophic current. In baroclinic conditions, the slope of isobaric surfaces follows the sea-surface less and less with increasing depth, and the velocity of the geostrophic current becomes zero at the depth where the isobaric surface is horizontal. The types of geostrophic current that occur in the two situations are sometimes known as 'slope currents' and 'relative currents', respectively. In the oceans, flow is often a combination of the two types of flow, with a relative current superimposed on a slope current.
10 In baroclinic conditions, the slopes of the isopycnals are very much greater than the slopes of the isobars. As a result, the gradient equation may be used to construct a relationship which gives the average velocity of the geostrophic current flowing between two hydrographic stations in terms of the density distributions at the two stations. This relationship is known as the geostrophic equation or (in its full form) as Helland-Hansen's equation. It is used to determine relative current velocities (i.e. velocities relative to a selected depth or isobaric surface, at which it may be assumed that current flow is negligible) at right angles to the section. This method provides information about average conditions only, and is subject to certain simplifying assumptions. Nevertheless, much of what is known about oceanic circulation has been discovered through geostrophic calculations.
11 Departures of isobaric surfaces from the horizontal (i.e. from an equipotential surface) may be measured in terms of units of work known as dynamic metres. Variations in the dynamic height of an isobaric surface (including the sea-surface) are known as dynamic topography On a map of dynamic topography, geostrophic flow is parallel to the contours of dynamic height in such a direction that the 'highs' are on the right in the Northern Hemisphere and on the left in the Southern Hemisphere. Dynamic topography represents departures of an isobaric surface from the (marine) geoid, which itself has a relief of the order of 100 times that of dynamic topography.
12 Surface wind stress gives rise to vertical motion of water, as well as horizontal flow. In particular, cyclonic wind systems lead to a lowered sea-surface, raised thermocline and divergence and upwelling, while anticyclonic wind systems give rise to a raised sea-surface, lowered thermocline and convergence and downwelling. Relatively small-scale linear divergences and convergences occur as a result of Langmuir circulation in the upper ocean.
13 Flow in the ocean occurs over a wide range of time-scales and space-scales. The general circulation, as represented by the average position and velocity of well-established currents such as the Gulf Stream, is known as the 'mean flow' or 'mean motion".
14 Most of the energy of the ocean, both kinetic and potential, derives ultimately from solar energy. The potential energy stored in the ocean is about 100 times its kinetic energy, and results from isobars and isopycnals being displaced from their position of least energy (parallel to the geoid) as a result of wind stress or changes in the density distribution of the ocean. If the ocean were at rest and homogeneous, all isobaric and isopycnic surfaces would be parallel to the geoid. The ocean's kinetic energy is that associated with motion in ocean currents including tidal currents (plus surface waves). The kinetic energy associated with a current is proportional to the square of the current speed, and for any given area of ocean, the total kinetic energy associated with a range of periods/frequencies may be represented by a kinetic energy density spectrum.
15 The ocean is full of eddies. They originate from perturbations in the mean flow, and their formation has the overall effect of transferring energy from the mean flow. There is effectively a 'cascade' of energy through (generally) smaller and smaller eddies, until it is eventually dissipated as heat (through molecular viscosity). Mesoscale eddies, which have length scales of 50-200km and periods of one to a few months, represent the ocean's 'weather' and contain a significant proportion of the ocean's energy. Current flow around most mesoscale eddies is in approximate geostrophic equilibrium. They are known to form from meanders in intense frontal regions like the Gulf Stream and the Antarctic Circumpolar Current, but may form in other ways too. Eddies of various sizes are generated by interaction of currents with the bottom topography, islands, coasts or other currents or eddies, or as a result of horizontal wind shear.
Now try the following questions to consolidate your understanding of this Chapter.
QUESTION 3 It i ai The forces acting on w aler or other fluids niav he div idcd into three categories: fit external forces, that arise Ironi outside the fluid: HU internal lor body) forces, thai act within the Mind:
inn secondary forces, that come into phi) only because (he fluid is in motion relative to die Earth's surface.
Some ol the main farces thai act on ocean water are:
1 w ind stress;
^ the tide-producing forces;
4 horizontal pressure gradient forces; and
Mow would you classify each of forces 1- 5 in terms of categories lit < iii i' ibi Motion in ihe oceans is in equilibrium when (he flow ha*, had lime to adjust so (hat the forces aciing on the water balance. In Ihe folkm mg types of How, which ol the lorces I 5 (above) are balancing one another ,' lit geostrophic flow.
tin the mean flow of ihe w hole Fkmaii layer at rigln angles to the w ind.
QUESTION 3.12 Use in form a lion troin the end ol Section 3.1.2 to show thai, theoretically, for a given wind Stress, the tola) volume transport in the wind-driven layer is independent of the value ol I , the coefficient of eddy viscosity
QUESTION 3.13 Inertia eiirrenis are manifestations of the Coriotis force in action. True or false '
QUESTION 3 14 In the Sn ails of Dover, water is w ell mixed by tidal currents and w ind. The mean geostrophic current is tow aids the east.
lal \re conditions in ihe Straits of Dover borotropic or haroclintc'.1
tbi Is ihe mean sea-level higher on the French or the English side ' Sketch a north south cross-section ol water in the Siraits ol Dover, looking down-current' Show the sloping sea-surface (of necessity, wilh the slope exaggerated) and isobars Select the correct symbol lor flow direction from Figure 3.1 7. and add labelled arrow s to represent Ihe balance of forces that cvtsis under conditions ol geoitrophic equilibrium.
Figure 3.33 Kinetic energy density spectrum for flow in the Drake Passage, between South America and Antarctica.
Figure 3.34 Variability in sea-surface height, as computed from satellite altimetry data. Colours represent different deviations from mean sea-level (for key, see bar along the bottom).
ICi Again assuming geostrophic equilibrium, it the mean geostrophic current through the straits is 0.2 m s_l. what is the slope of the sea-surface, i.e. what is tan H' What is the difference in sea-level between the French and the English side? < You will need to use 12 = 7.29 * 10~? s the Straits of Dover are at 51 N and are about 35 km wide.)
QUESTION 3.15 Until the 1970s, a large proportion of studies of ocean current1» had been made using the indirect geostrophic method (Section 3,3.3> combined with a lew direct current measurements. Hearing tins in mind, explain briefly why it is not surprising thai, before then, mesoscale eddies had only rarely been observed.
QUESTION 3.16 In Chapter 2. we mentioned that the surface I racks of tropical cyclones are marked mil by cooler water upwelled from a depth of 100 m or so. I sing information in Sections .1.1 and 3.4. can you now explain why this happens '
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