Waves Shadow Hills

[Germain Aguilera]

Anobstacle in front of a coast such as a rock outcrop, an offshore breakwater, or even a shipwreck will reduce the wave activity in the zone of wave shadow between the object and the shore. Since the reduced wave activity in the shadow zone will result in a reduced sediment transport capacity, material being carried along the shore will be deposited in the shadow zone forming a tombolo. Initially only a shoal will form that we refer to as a salient. This can, however, develop into a point of land connecting the original shoreline to the obstacle (see Figs. 8.20 and 8.21). We now speak of tombolo. A tombolo completely blocks the longshore transport in the zone landward of the obstacle.

These shadow zone effects can be used to stimulate and preserve a recreational beach (Sect. 10.5.4). Have a look at Fig. 10.41, which shows salient and tombolo formation behind a series of emerged (i.e. having their crests above MSL) offshore breakwaters.

The development of a tombolo as explained above depends upon a transport of material parallel to the coast; the reasoning is that in the shadow zones behind obstacles, the breaking wave heights and thus longshore transport capacity is reduced and sediment is deposited. Note that due to diffraction of waves around the ends of the breakwater still some wave action will be present behind the breakwater (the wave heights at the end of the breakwater are in the order of magnitude of 50% of the original incoming wave height, see Sect. 5.2.4). Example 8.4.3.1 discusses the shoreline development resulting from an emerged breakwater (partly) blocking the longshore sediment transport by obliquely incident waves.

Besides the shoreline development, as a result of breaking wave height reduction in the shadow zone and subsequent gradients in longshore sediment transport (illustrated in Example 8.4.3.1), two subtler effects play a role, namely: 1) due to the changes in wave angles in the shadow zone; and 2) due to secondary current patterns as a result of set-up differences. These additional effects enhance the pattern of deposition behind the obstacle for obliquely incident waves and are the reason that even for normally incident waves a salient or tombolo can be formed (Fig. 8.23). This can be explained as follows. Due to diffraction into the shadow zone not only the wave heights, but also the wave angles are affected. Hence, even in the case of normally incident waves, the diffracted waves behind the breakwater approach the original coastline at some angle. This results in an initial sediment transport pattern with transports from both breakwater ends towards the shadow zone. Further, as shown in Fig. 5.46, nearshore currents run towards the shadow zone from both sides of an emerged obstacle. This secondary current pattern also enhances the transport towards the shadow zone.

Figure 8.23 shows the resulting symmetrical shoreline development, for normally incident waves, with erosion on either side of the breakwater and accretion behind the structure. The initial shoreline development takes the form of a salient (lower panel), which may or may not develop over time into a tombolo (upper panel). A tombolo is more likely to develop if the breakwater is located in or just outside the surf zone (since the responsible currents are generated in the surf-zone) and if its length is relatively large. If the length is larger than, say, twice the distance from the coast, the diffracted wave heights reduce to zero in the centreline of the structure (Fig. 8.24, left figure). In that case the sediment stirring and transporting capacity behind the breakwater is not enough to keep a passage open. For a relatively short breakwater, the equilibrium shoreline will take the form of a salient (Fig. 8.24, right figure).

Also in the case of submerged obstacles, tombolos or salients may develop. However in those cases, any accretional tendency may be counteracted by a (possibly stronger) erosional effect. This is related to the wave-induced current pattern as shown in Fig. 5.49. The onshore directed wave forces, as a result of waves breaking on a shoal or submerged breakwater, result in a large on-shore flow of water. This is compensated for by rip currents returning seaward at either side of the shoal or breakwater. These currents can carry large amount of sediments from the shadow zone seaward and hence create large erosion. Some consequences for submerged breakwater design are discussed in Sect. 10.5.4.

This page titled 8.4.3: Shadow effects due to obstacles away from the shoreline is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Judith Bosboom & Marcel J.F. Stive (TU Delft Open) via source content that was edited to the style and standards of the LibreTexts platform.

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A mathematical description of the edge diffraction of a narrow beam of millimeter waves in the deep geometric shadow of an obstacle is proposed. The description uses the Babinet principle, according to which the complex amplitude of the diffracted field is determined as the difference of the complex amplitude of the radiation generated by an antenna in free space and the complex amplitude corresponding to the virtual radiation of the shadowing silhouette (obstacle) considered an aperture. The results of field experiments on diffraction of a beam of millimeter waves performed on a Luch telecommunications system are presented. The obtained experimental data completely confirm the effect of diffraction-induced amplification of a beam of millimeter waves in the shadow zone of an obstacle relative to the field of an omnidirectional (spherical) wave.

After passing a month in this magnificent island, and finding that myhealth was not improving, I made up my mind to push on to South Americawhile my stock of strength, such as it was, lasted. But fortunately I couldnot find passage for any South American port. I had long wished to visitthe Orinoco basin and in particular the basin of the Amazon. My plan wasto get ashore anywhere on the north end of the continent, push on southwardthrough the wilderness around the headwaters of the Orinoco, until I reacheda tributary of the Amazon, and float down on a raft or skiff the wholelength of the great river to its mouth. It seems strange that such a tripshould ever have entered the dreams of any person, however enthusiasticand full of youthful daring, particularly under the disadvantages of poorhealth, of funds less than ahundred dollars, and of the insalubrityof the Amazon Valley.

Fortunately, as I said, after visiting all the shipping agencies, Icould not find a vessel of any sort bound for South America, and so madeup a plan to go North, to the longed-for cold weather of New York, andthence to the forests and mountains of California. There, I thought, Ishall find health and new plants and mountains, and after a year spentin that interesting country I can carry out my Amazon plans.

It seemed hard to leave Cuba thus unseen and unwalked, but illness forbademy stay and I had to comfort myself with the hope of returning to its waitingtreasures in full health. In the mean time I prepared for immediate departure.When I was resting in one of the Havana gardens, I noticed in a New Yorkpaper an advertisement of cheap fares to California. I consulted CaptainParsons concerning a passage to New York, where I could find a ship forCalifornia. At this time none of the California ships touched at Cuba.

"Well," said he, pointing toward the middle of the harbor,"there is a trim little schooner loaded with oranges for New York,and these little fruiters are fast sailers. You had better see her captainabout a passage, for she must be about ready to sail." So I jumpedinto the dinghy and a sailor rowed me over to the fruiter. Going aboard,I inquired for the captain, who it soon appeared on deck and readily agreedto carry me to New York for twenty-five dollars. Inquiring when he wouldsail, "To-morrow morning at daylight," he replied, "if thisnorther slacks a little; but my papers are made out, and you will haveto see the American consul to get permission to leave on my ship."

I immediately went to the city, but was unable to find the consul, whereuponI determined to sail for New York without any formal leave. Early nextmorning, after leaving the Island Belle and bidding Captain Parsons good-bye,I was rowed to the fruiter and got aboard. Notwithstanding the north windwas still as boisterous as ever, our Dutch captainwas resolved toface it, confident in the strength of his all-oak little schooner.

Vessels leaving the harbor are stopped at the Morro Castle to have theirclearance papers examined; in particular, to see that no runaway slaveswere being carried away. The officials came alongside our little ship,but did not come aboard. They were satisfied by a glance at the consul'sclearance paper, and with the declaration of the captain, when asked whetherhe had any negroes, that he had "not a d-- --d one." "Allright, then," shouted the officials, "farewell! A pleasant voyageto you!" As my name was not on the ship's papers, I stayed below,out of sight, until I felt the heaving of the waves and knew that we werefairly out on the open sea. The Castle towers, the hills, the palms, andthe wave-white strand, all faded in the distance, and our mimic sea-birdwas at home in the open stormy gulf, curtsying to every wave and facingbravely to the wind.

Two thousand years ago our Saviour told Nicodemus that he did not knowwhere thewinds came from, nor where they were going. And now inthis Golden Age, though we Gentiles know the birthplace of many a windand also "whither it is going," yet we know about as little ofwinds in general as those Palestinian Jews, and our ignorance, despitethe powers of science, can never be much less profound than it is at present.

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