pdz or dp
This is the hydrostatic equation (3.8), which relates the pressure at a given depth to the weight of the overlying seawater.
Question 4.9 The western boundary currents are fast and deep, while eastern boundary currents are slow and shallow. This allows the rate at which water is transported polewards in the western boundary currents to be equal to the rate at which water is carried equatorwards in the eastern boundary currents, despite the fact that western boundary currents are narrow, and flow in the eastern boundary currents occupies much of the rest of the ocean. (Here we are ignoring currents flowing into and out of the gyres - in the case of the North Atlantic gyre, the Labrador Current and the northern branches of the North Atlantic Current.)
Question 4.10 (a) The sections indicate that flow through the Florida Straits is baroclinic. Figure 4.21(a) and (b) show that there are strong lateral variations in T, S and hence density, and the slopes of the isotherms indicate that the isopycnals slope up to the left so as to intersect the sea-surface (the topmost isobaric surface). Furthermore, the velocity sections (c) and (d) show that the current changes with depth, decreasing to zero above the sea-bed, consistent with baroclinic conditions (cf. Figure 3.15(b)).
(b) As this is in the Northern Hemisphere, the sea-surface must slope up to the right and the current must flow 'into the page' so that Florida is on the left-hand (west) side of the section and Bimini on the right-hand (east) side.
(c) The isotherms and isohalines (Figure 4.21(a) and (b)) indicate that, in the upper 100 m, the least dense water (warmest and lowest salinity) is in the middle of the section. As a result, although the sea-surface will generally slope up to the right, there will be a slight 'hump' in the middle (see Figure A6).
Question 4.11 In geostrophic flow (to which flow in mesoscale eddies approximates), motion is along contours of dynamic height, in such a direction that (in the Northern Hemisphere) the 'highs' are on the right and the 'lows' are on the left. Thus, the positive numbers correspond to anticyclonic (here clockwise) flow, and the negative numbers to cyclonic
(anticlockwise) flow. As sh&Wti in Figure A7. flow in meso scale eddies resembles thai in the atmosphere - cyclonic around 'lows' and anticyclone around "highs'.
Question 4.12 Comparison of Figure 4.29(a) and (b) suggests that results obtained by Lagrangian methods may be more difficult to interpret than those obtained by Fulerian methods. On the other hand, they do provide an idea of current flow patterns, and give information about a large area Eulertan measurements provide information about how a current changes with time at a given place, which I agrangian methods do not. but a very large number of fixed current meters would be needed to give equivalent spatial coverage. In practice, experiments using drifters do involve a large number of them - in the MODF experiment. 2(3 Sofar floats were required to monitor adequately a region about 300 km w ide - but they are very much cheaper than moored current meters.
Question 4.13 (i) The blue area on Figure 4.31(a) must be the cold water of the Labrador Current; and (ii) the yellow area must be warm Sargasso Sea and Gull Stream water, with the reddest region corresponding to the warm core of the Stream. In image <bi these warm waters are shown blue, as they have tow primary' (phytopfankton) productivity.
Question 4.14 False. Both Franklin and Rennet! believed that the Gull Stream is driven by the 'head' of water in ihe Gulf of Mexico. j_e. by the horizontal pressure gradient in the direction of flow. They were not aware of the idea of geostrophic balance between the Coriolis force and a horizontal pressure gradient at right angles to the flow.
Queslion 4.15 As it is a frontal region, the edge of the Gulf Stream is also a convergence, where surface debris will tend to accumulate (cf. Section 3.4).
Question 4.16 The changes in depth associated with the seamoums mean that D m (/ + C)/D, the potential vorticity of water in tiie current, is changing. If (f+ i)/D is to remain constant, a reduction in D must be accompanied by a decrease in the value of/and/or - i.e by equalorward meanders (cf. Question 4.5) and/or a tendency to clockwise rotation, (Note that as the Gulf Stream is a region of strong velocity shear, we cannot assume that/» c,.)
Question 4.17 Flow is in geostrophic equilibrium when the only significant forces acting in a horizontal direction are the horizontal pressure gradient force and the Coriolis force, acting in opposite directions and at right angles lo the flow. In such circumstances, the How is steady and Hon-accelerating. Water circulating in a relatively small-scale meander or eddy experiences a centripetal fprce toward the centre of the eddy (as given in Equation 3.5). and its rate of change ol speed and direction (i.e. its acceleration) bccomes.significant,
Question 4.18 (a I This is true. The average velocity will he calculated from the estimates of the distance travelled and time taken. As the actual path taken by the drifter is likely lo be complicated, the distance it has travelled may well be underestimated, especially if its position has been Fixed infrequently or not at all (as in the case of cheap plastic drifters). Also, if a drifter is washed ashore and nol found for a long time, the iravel time will be overestimated.
lb) This is not strictly true. Some Lagrangian techniques rely on people voluntarily returning drifters, stating when and where they were found. However, any oceanographer will tell you that moored current meters are al the mercy of other users of the sea lanes, and may be easily damaged accidentally.
(c) False. The Doppler methods (ADCPs and OSCR) are Eulerian methods as they measure the velocity of patches of water at given positions. They provide no information about the paths taken by specific parcels of water.
Id) false. The calculation of surface currents using ship's drift is a Lagrangian technique because it relics on the deduction of the path taken by the ship under the influence of the current. It is the average current velocity over some distance that is calculated, rather than the current speed at any particular location. A significant proportion of all current measurements obtained by Lagrangian methods have been calculated from ship's drift.
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