Ocean currents

The maximum speed in the centre of the Gulf Stream is about 2 m s-1, corresponding to an energy density % pw Vw2 = 2 kJ m-3 and a power of % pw Vw3 = 4 kW m-2. This power level, for example, approaches that of wave power at reasonably good sites, taken as power per metre of wave crest rather than per square metre perpendicular to the flow, as used in the above case. However, high average speed of currents combined with stable direction is found only in a few places. Figure 3.50 shows the isotachs in a cross section of the Gulf Stream, derived from a single set of measurements (in June 1938; Neumann, 1956). The maximum current speed is found at a depth of 100-200 m, some 300 km from the coast. The isotachs expand and become less regular further north, when the Gulf Stream moves further away from the coast (Niiler, 1977).

Horizontal distance ( I05 m)

Figure 3.50. Contours of equal speed (in 10-2 m s-1) along a cross section through the Gulf Stream from Bermuda to the US coast. The measurements were performed over a limited period of time (in June 1938, by Neumann, 1956), but they are consistent with other measurements in the same region (e.g. Florida Strait measurements by Brooks and Niiler, 1977).

Horizontal distance ( I05 m)

Figure 3.50. Contours of equal speed (in 10-2 m s-1) along a cross section through the Gulf Stream from Bermuda to the US coast. The measurements were performed over a limited period of time (in June 1938, by Neumann, 1956), but they are consistent with other measurements in the same region (e.g. Florida Strait measurements by Brooks and Niiler, 1977).

Even for a strong current like the Gulf Stream, the compass direction at the surface has its most frequent value only slightly over 50% of the time (Royal Dutch Meteorological Institute, as quoted by Neumann and Pierson, 1966), and the power will, on average, deviate from that evaluated on the basis of average current speeds (as is the case for wind or waves) owing to the inequality of <V3> and <V>3.

The geographical distribution of the strongest surface currents is indicated in Fig. 3.51. The surface currents in the Atlantic Ocean, along with the horizontal currents at three different depths, are sketched in Fig. 3.52. The current speeds indicated are generally decreasing downwards, and the preferred directions are not the same at different depths. The apparent "collision" of oppositely directed currents, e.g. along the continental shelf of Central America at a depth of around 4 km, conceals the vertical motion which takes place in most of these cases. Figure 3.53 gives a vertical cross section with outlined current directions. This figure shows how the oppositely directed waters "slide" above and below each other. The coldest water is flowing along the bottom, while the warmer water from the North Atlantic is sliding above the cold water from the Antarctic.

180 90 0 90 18

Figure 3.51. Indication of the location of strong surface currents (approximately defined as having average speeds above 0.5 m s-1). Currents drawn with dashed lines are characterised by seasonal changes in direction (based on Defant, 1961).

180 90 0 90 18

Figure 3.51. Indication of the location of strong surface currents (approximately defined as having average speeds above 0.5 m s-1). Currents drawn with dashed lines are characterised by seasonal changes in direction (based on Defant, 1961).

Variability in current power

Although the general features of circulation in the open ocean were described in section 2.3.2, the particular topography of coastal regions may have an important influence on currents. As an example, water forced through a narrow strait may acquire substantial speeds. The strait Storeb^lt ("Great Belt") between two Danish isles, which provides an outlet from the Baltic Sea, may serve as an illustration. It is not extremely narrow (roughly 20 km at the measurement site), but narrow enough to exhibit only two current directions, separated by 180°. The currents may seem fairly steady, except for periods when the direction is changing between north-going and south-going velocities, but when the energy flux is calculated from the third powers of the current speeds, the fluctuations turn out to be substantial. Figure 3.54, which gives the power at 3-h intervals, during two weeks of January 1972, clearly illustrates this.

Figure 3.52. Indication of average horizontal current speeds (in 10-2 m s-1) in the Atlantic Ocean for different depths (based on Defant, 1961).
Figure 3.53. Indication of average current directions within a vertical cross section of the Atlantic Ocean (based on Neumann and Pierson, 1966).

Figure 3.55 shows, again for the Halskov Rev position in Storeb^lt, the variation in current speed with the hour of the day, based on one-month averages. A 12-h periodicity may be discerned, at least during January. This period is smaller than the one likely to be found in the open sea due to the motion of water particles in stationary circles under the influence of the Coriolis force

Figure 3.54. Power of surface current, based on observations made at 3-h intervals, for Halskov Rev, Denmark, during a 15-day period in 1972 (the strait is narrow enough to exhibit only two opposite current directions) (based on Danish Meteorological Institute, 1973).

Figure 3.55 shows, again for the Halskov Rev position in Storeb^lt, the variation in current speed with the hour of the day, based on one-month averages. A 12-h periodicity may be discerned, at least during January. This period is smaller than the one likely to be found in the open sea due to the motion of water particles in stationary circles under the influence of the Coriolis force

[see (2.61)] and having a period equal to 12 h divided by sin 0 (0 is the latitude).

Halskov Rev , 1972

Halskov Rev , 1972

Figure 3.55. Dependence of average current speed on the hour of the day, for a summer and a winter month, for Halskov Rev, Denmark (based on Danish Meteorological Institute, 1973).

4 7 10 13 16 19 22 Hour of day

4 7 10 13 16 19 22 Hour of day

Figure 3.55. Dependence of average current speed on the hour of the day, for a summer and a winter month, for Halskov Rev, Denmark (based on Danish Meteorological Institute, 1973).

In Fig. 3.56, the frequency distributions of current speed and power are shown for a summer and a winter month. These curves are useful in estimating the performance of an energy extraction device, and they can be used, for example, to construct the power duration curve of the current motion, as shown in Fig. 3.57. This is the power duration curve of the currents themselves. That of an energy extracting device will have to be folded with the efficiency function of the device.

The peak in the frequency distribution of power is at a lower current speed for July than for January, and the average power is 93 W m-2 in July, as compared with 207 W m-2 in January (the corresponding kinetic energy densities are 138 and 247 J m-3). This indicates that the fluctuations around the average values have a substantial effect on the energy and, in particular, on the power, because from the average current speeds, 0.46 m s-1 (July) and 0.65 m s-1 (January), the calculated kinetic energy densities would have been 108 and 211 J m-3, and the power would have taken the values 50 and 134 W m-2.

Few locations, whether in coastal regions or in open oceans, have higher average current speeds than the Danish location considered in Figs. 3.54-3.57, so that average power levels in the range 100-200 W m-2 are likely to be more representative than the 4000 W m-2 found (at least at the time of the measurement reported in Fig. 3.50) in the core of the Gulf Stream. This means that at many locations the power in currents is no greater than that found in the wind at quite low heights (cf. Fig. 3.34). Also, the seasonal variations and fluctuations are similar, which is not unexpected for wind-driven currents. For the currents at greater depths this may not hold true, partly because of the smoothing due to a long turnover time and partly because not all the deep sea motion is wind driven, but may also be associated with temperature and salinity gradients, as discussed in section 2.3.2.

Halskov Rev, Denmark, 1972

Halskov Rev, Denmark, 1972

Figure 3.56. Frequency distributions of current speeds and power, based on a summer and a winter month (full and dashed curves, respectively), for Halskov Rev, Denmark. The data (taken from Danish Meteorological Institute, 1973) have been smoothed in calculating the distributions. The monthly average speed and power are indicated on the figure (in parentheses).

Figure 3.56. Frequency distributions of current speeds and power, based on a summer and a winter month (full and dashed curves, respectively), for Halskov Rev, Denmark. The data (taken from Danish Meteorological Institute, 1973) have been smoothed in calculating the distributions. The monthly average speed and power are indicated on the figure (in parentheses).

The power duration curves in Fig. 3.57 may be compared to those of wind power shown in Figs. 3.39 and 3.40. The fraction of time in which the monthly average power is available in the Halskov Rev surface current is 0.3 in both January and July. The overall average power of about 150 W m-2 is available for about 45% of the time in January, but only 17% of the time in July.

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