Figure 3.3 In a surface wave, water particles make orbits in the vertical plane. The particles advance slightly further in the crest (the top of the orbit) than they retreat in the trough (bottom of the orbit), so a small net forward motion (known as 'wave drift') results. In deep water, this motion may be of the order of several millimetres to several centimetres per second.
When wind blows over the ocean, energy is transferred from the wind to the surface layers. Some of this energy is expended in the generation of surface gravity waves (which lead to a small net movement of water in the direction of wave propagation; see Figure 3.3) and some is expended in driving currents. The processes whereby energy is transferred between waves and currents are complex; it is not a simple task to discover, for example, how much of the energy of a breaking wave is dissipated and how much is transferred to the surface current.
Nevertheless, it is still possible to make some general statements and predictions about the action of wind on the sea. The greater the speed of the wind, the greater the frictional force acting on the sea-surface, and the stronger the surface current generated. The frictional force acting on the sea-surface as a result of the wind blowing over it is known as the wind stress. Wind stress, which is usually given the symbol x (Greek 'tau'), has been found by experiment to be proportional to the square of the wind speed, W. Thus:
where the value of c depends on the prevailing atmospheric conditions. The more turbulent the atmosphere overlying the sea-surface (Section 2.2.2), the higher the value of c.
How would \ou expect the value of c to he affected h\ llic wind speed'?
The value of c will increase with increasing wind speed, which not only increases the amount of turbulent convection in the atmosphere over the sea (Section 2.2.2) but also increases the roughness of the sea-surface.
Because of friction with the sea-surface, wind speed decreases with increasing proximity to the sea, and so the value of c to be used also depends critically on the height at which the wind speed is measured; this is commonly about 10 m, the height of the deck or bridge of a ship. As a rough guide, we can say that a wind which has a speed of 10 m s-1 (nearly 20 knots) 5-10 m above the sea-surface, will give rise to wind stress on the sea-surface of the order of 0.2 N m~2 (1 newton = 1 kg m s-2).
QUESTION 3.2 What value does thai imply lore, given the relation\hip in Equation 3.1? What are its units?
It is important to remember that, for the reasons given above, c is not constant. Nevertheless, a value of c of about 2 x 10"3 gives values of x that are accurate to within a factor of 2, and often considerably better than that.
Another useful empirical observation is that the surface current speed is typically about 39c of the wind speed, so that a 10 m s~' wind might be expected to give rise to a surface current of about 0.3 m s-1. Again, this is only a rough 'rule of thumb', for reasons that should become clear shortly.
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