48 OBSERVING SEA AND SWELL

181. THE FORMATION AND PROPERTIES OF WAVES

The mariner lives in intimate contact with the waves of the sea and is able to realise better than most people the extent to which their size and energy are related to the speed of the wind. Moving air exerts a drag upon the water surface and, even in a light breeze, tiny ripples form almost immediately on a previously-calm surface, as a result of the impact on the surface of downward-moving eddies in the air current. The pressure of the wind on the windward side of any wave will be greater than on its leeward side, with the net result that the wave is driven forward in the direction of the wind. Thus, when the wind has been blowing in the same direction for some time, the waves of the sea are observed travelling in the same direction, but with a speed somewhat less than the wind speed at the time.

A simple wave has four main properties: period, speed, length and height (see fig. 42-16(a)). A knowledge of some of these more basic properties of simple waves is very useful in understanding the behaviour of a vessel in a seaway:-

PERIOD                              = the interval in seconds between the passage of successive crests past a fixed point. 

SPEED                                = 3.1 x Period (in deep water), measured in knots. 

LENGTH                            = the distance in feet between successive crests.

                                            In deep water, Length   = 5.1 x (Period)2.

HEIGHT                             = the vertical distance between the top of a crest and the bottom of a trough, expressed in metres or feet.

The largest wave heights usually occur with the longest wavelengths. When the ratio of height to length exceeds 1 to 13, the wave crest begins to break and breaking waves are particularly dangerous for small craft. In a breaking wave, the leading slope may become so steep as to be wall-sided, the water in this “wall” often rising violently and exerting a strong capsizing lever on a small craft’s hull.

The sea water does not move appreciably forward with trains of waves, but its particles describe an approximate circle, moving forward in the crest of the wave, backwards in the trough, upward as a crest approaches and downward as it recedes, so that, after completing an orbit, each particle returns (almost) to its initial position (see fig. 42-17). The friction of the water due to this movement tends to decrease the height of the wave. ﷯It is found that if the wind speed exceeds about 10 knots, the energy imparted to the waves by means of a push behind the crests and a partial vacuum in front, is sufficient to make them increase in height, length and X speed until the speed of the waves is the same as that of the wind; this process may take several days with strong winds; after it, the wave dimensions remain nearly the same.

Although, as the previous paragraph has shown, the duration of blow is a factor determining the size of waves, an equally-important factor is a fetch – the distance upwind over which the wind is able to act upon the water from nearly the same direction. It is obvious that if the wind is blowing offshore, it cannot raise such big waves in a position, say, 1 mile from the shore as in another 10 miles off, no matter how long the wind may blow. Similarly, even in the open sea, when the isobars are much curved as, for instance, near the centre of a Low, the wind clearly cannot blow in nearly the same direction for any considerable distance. When estimating the dimensions of waves to be expected with a given wind speed, both these factors, duration and fetch, have to be borne in mind, and that which gives the smaller result will be the correct one to use, since the wave size may be limited by lack of sufficient time to grow fully.

The two Tables in fig. 48-3 give the average wave dimensions for given wind forces and a few Durations or Fetches respectively. Under any particular circumstances, the waves generated will be those from the Table which gives the smaller length and period. For example, a wind Force 8, blowing over a Fetch of 100 miles for 6 hrs, will generate waves 9 ft. in height, 340 ft. long and with an 8-second period: their size is limited by lack of time. After 12 hours, they will have grown to 11 feet high, 440 ft long, with a 9 sec period but, however much longer the wind blows at Force 8, they will grow no more, because they have attained the maximum size possible for the fetch available.

182. THE TRAVEL AND DECAY OF SWELL WAVES

The characteristics of waves are directly related to the force of the wind, but at some later time a stage occurs where the wind dies down over the area and, as a result, the train of waves it has generated will travel away from that area, and may travel for some time before their height becomes negligible. At the same time, their wavelengths will increase slowly. These kinds of wave trains, which are encountered beyond the region in which they were generated, are known as swell, and frequently travel thousands of miles before dying away. A swell wave on the open sea is distinguishable from a sea wave, because the former has an oily, unbroken surface, whereas a sea wave invariably ‘breaks’.

It is necessary to note carefully this distinction between “sea” and “swell”:-

Sea is the wave disturbance caused by the prevailing wind and, thus, runs in a direction within 10° or so of the wind blowing at the observer. 

Swell  is the wave system not caused by the prevailing wind but generated by past wind at a distance. Thus, swell waves in a certain area may have been caused by a storm, which raged four or more days previously in an area 2,000 miles away. It is possible, but improbable, that waves coming from within 20° of the direction of the prevailing wind are swell unless the wind has just dropped.

Although each individual wave travels at a speed approaching that of the wind which caused it, the speed of a group of swell waves is only one-half of that of an individual wave. If a brick is dropped into a pond, the outermost wave dies and is replaced as leader by the next wave behind it; this, in turn, decays and gives place to its successor; for every two steps forward, so to speak, they step back one. Hence, the important rule is that swells travel at nearly half the speed of the wind in the generating area. 

Provided you can tell from a weather map that long waves are being generated in an area and directed towards a locality with which you are concerned, it is simple to estimate very roughly when the swell will arrive.

The longer swell waves are, the faster they travel, and the more difficult they are to destroy. Waves lose about half their height every time they travel a distance in miles equivalent to their wavelength in feet. For example, waves produced by a wind of Force 5 (20 knots) and a 24-hour duration, will average no more than one foot in height after travelling 600 miles in 2% days (see Table 1 in fig. 42-18). Similarly, waves produced by a wind of Force 8 and 24-hour duration will average 4 feet in height after travelling 1,300 miles in nearly 3 days. In both these examples, it is assumed that the “group velocity” of the swell is about half that of the wind which caused it.

It should be appreciated that wave forecast Tables (such as those in fig. 42-18) are highly generalised. As every seaman knows, the heights of individual seas vary considerably. These wave irregularities are largely due to waves coming from different directions and crossing each other at angles as, for example, when a new sea runs over an old swell, or irregularities can be caused by the mixing of wave trains (groups or systems of related waves moving at approximately half the speed of the individual waves). When a train having waves of a certain length mixes with another train having waves of a different length or period, some waves are reinforced, while others are interfered with, so that an irregular pattern is produced, similar to that shown in fig. 42-19. This explains why there is some basis for the ancient belief that every wave train seventh or eleventh wave will be extra high, although there is really no invariable sequence number for outstandingly high or low waves; they may come regularly or irregularly, according to circumstances.

183. WAVE CHARACTERISTICS IN SHALLOW MATER

When the depth of water decreases to one half of the wavelength, it begins to affect the waves. As the depth decreases beyond this point, so do the length and speed of the wave become smaller, with the result that they become telescoped. Since the height remains nearly the same, the waves become steeper and, more especially on a very gently sloping beach, they foam at the crest if the angle between the front and rear slope of the wave becomes less than 120°, or when its height becomes greater than one-seventh of its length, for the wave is then unstable (see fig. 42-20). A wave breaks when depth of water is about 1½ times the height of the wave, so that a 4ft wave will break in about 6 feet of water. Only in the instance of long, low waves do they become higher before they break than they were in deep water.

There are two general types of breakers, plungers and spillers (see fig. 42-21). Spillers have a more concave back and the crest breaks gradually and continuously. A Plunger has a more convex back and its crest falls suddenly and more violently; this type is nearly always the more dangerous. While both kinds of breakers are found near the shore and at sea, deep-water breakers are usually of the spilling type.

When waves approach a beach obliquely, they wheel round so that they align themselves nearly parallel to the beach before they break. When looking for a sheltered landing place, it is well to remember that waves bend round a headland or island where the beach slopes gently and will only be reduced to about half their size on the far side where they approach the beach from a direction 120° or more from their original direction. If, however, the headland or island is steep-to, there will be very little surf on the sheltered side.

Strong tidal streams or currents have the effect of decreasing the speed and lengths of waves and increasing their height if they are flowing against the wind, but this effect is, as a rule, only marked in the vicinity of land, because the stream or current is seldom strong enough in deep water. Where it does occur, the wave begins to foam at the crest, i.e. partially to break. If the speed of the stream is as much as ¼ that of the wave, the latter will break, no matter what its speed or length, and a stream of 5 knots will break all but the longest waves, even if they are low. Hence, the well-known tidal races which are formed where strong tidal streams run against the direction of the waves. A spring out- going stream meeting a SW gale off Cowes, for example, can produce seas far in excess of what one might expect in sheltered waters. Yachtsmen should take careful note of this effect, especially when rounding headlands where shallow water effects are likely to occur. A lee tide (i.e. stream running with the wind) tends to flatten the seas.