Coastal Engineering 1964

The integration of the equations of the nonlinear shallow-water theory by a finite difference scheme based on the method of characteristics is programmed for digital computers. In the program, the equations of the bore propagation are coupled to the equations of the nonlinear theory, and thus a procedure for predicting the motion of the entire wave, including the bore, is established. Waves of irregular shape and experimental data are treated by an iterative method. Laboratory experiments on the inception and propagation of bores also are presented.

The distribution of permanent, vertical crustal dislocations, the times and directions of early water motion in and around the generation area, and the unusual lowfrequency character of the tsunami record obtained from Wake Island, all suggest that the tsunami associated with the great Alaskan earthquake of March 28, 1964 was produced by a dipolar movement of the earth's crust, centered along a line running from Hinchinbrook Island (Prince William Sound) southwesterly to the Trinity Islands. The positive pole of this disturbance encompassed most of the shallow shelf bordering the Gulf of Alaska, while the negative pole lay mostly under land. Thus, the early effect was the drainage of water from the shelf into the Gulf, thus generating a long solitary wave, which radiated out over the Pacific with very little dispersion.

This article introduces the longshore current computations based on theories published under the title "Longshore Currents and Longshore Troughs" (Bruun, 1963). Two approaches are used to formulate the longshore current velocities for a beach profile with one bar under the following assumptions: (1) that longshore current is evenly distributed (or a mean can be taken) along the depth; (2) that the solitary wave theory is applicable for waves in the surf zone; (3) that the statistical wave-height distribution for a deep water wave spectrum with a single narrow band of frequencies can be used near the shore, and (4) that the depth over the bar crest, D_cr, equal 0.8H_b(1/3). Breaking wave height H_b(1/3) is designated to be the actual height equal to H_1/3 (significant wave height).

Diagrams have been constructed for both approaches for beach profiles with one bar, from which longshore current velocities caused by various wave-breaking conditions can be read directly. As for longshore currents along the beach with a multibar system, fifteen diagrams covering a great variety of wave-breaking conditions are provided for obtaining longshore current velocities in different troughs.

Seasonal changes of eight Atlantic Ocean beaches along the East Coast of the United States from southern New Jersey to Rhode Island have been under study since September 1962. These beaches are surveyed at frequent intervals repeating profile lines perpendicular to the shoreline, spaced to indicate any major changes occurring to the beach shape or dimensions with as much assurance as is reasonably possible. Correlation of changes in beach profile with tide and wave data is being made. Changes in the beach profiles to date indicate variations on a seasonal basis.

As a result of a survey of damage caused by the severe storm of March 1962 which affected the entire east coast of the United States, a new and specially-shaped interlocking concrete block was developed for use in shon protection. This block is designed to be used in a revetment-type seawall that will be both durable and economical as well as reduce wave run-up and overtopping, and scour at its base or toe. A description of model investigations conducted on the interlocking precast concrete block seawall and results therefrom are presented. It is shown that effective shore protection can be designed utilizing these units.

For several years, some coastal engineers have been aware that the seaward face of rubble mound breakwaters of the common trapezoidal cross-section is conducive to relatively severe wave action and possible damage to the breakwaters. Further, it has been suggested that a preferable seaward profile would be that composed of three straight lines, with the middle line at a relatively small angle with the horizontal, to form what might be thought of as a broad berm.

In order to arrive at a more realistic knowledge of seaward profiles for which wave intensity and likelihood of breakwater damage are minimal, a laboratory study of shallow-water wave action on rubble breakwaters was initiated at Auburn University, It is hoped that such knowledge will lead to design procedures which will result in (a) less violent wave action, (b) less structural damage, and (c) the possible use of smaller stones.

Thus far, the study has been devoted to shallow-water waves of two types, steep, smooth waves and spilling breakers, acting, with normal incidence, upon breakwaters constructed of various materials and having an initial seaward slope of 1 on 1½.

For each set of conditions, the stable seaward profile was determined. Through dimensional analysis and curve fitting, an effort was made to describe the stable seaward profiles in terms of physical quantities which influence the profiles. It is the authors1 belief that the results of this study will be useful in leading to more rational design procedures.

Hidcasts were made for winds, waves and tides for several east coast locations for the storm of 5-8 March 1962. A limited amount of recorded data and a considerable amount of other observations were available from near-by and remote stations. The data were analyzed for correlation or "calibration" purposes in order to improve the "state of the art" of wave and storm surge hindcasting for locations where recorded data were not available. Wind records were analyzed to obtain sustained wind speeds, average gust factors, and probability distribution of gust factors. Isobaric patterns were used to determine sustained wind speeds over the water fetch for deep and shallow water waves and storm surge hindcasts. Wave run-up calculations were made to determine the wave activity on the beach and the dunes and were used to estimate the probable rate of beach erosion and dune evolution. The off-water wind speeds were modified to determine wind speeds over the beach and over the top of the dunes. Finally, by summarizing the time-history of the various meteorological, oceanographic, and coastal engineering events, a very interesting scientific and engineering evaluation of the causes and effects can be made.

Hurricane flooding has emerged as one of the major coastal engineering problems of the Atlantic and Gulf Coast areas of the United States. Engineering and scientific investigations have been made to determine the fundamental mechanics of the hurricane surges that cause inundation of coastal areas and to develop practical and economical protection. Mathematical models and large hydraulic models were used for the Narragansett Bay studies of two major projects.

The discussions presented herein are limited to the hydraulic studies of barriers at the mouth of the bay, known as the Lower Bay Barri Plan, and a brief description of this plan and the Fox Point Hurricane Barrier which is now under construction.

The paper discusses firstly mathematical problems on the numerical calculation of storm surges. The partial differential equations of motion adopted here take into account the Coriolis force and the nonlinear terms such as the inertial terms and a quadratic form of bottom friction. As a result, special care must be taken in order to obtain stable forms of finite-difference equations. It is shown that inadequate forms accumulate errors to cause divergence of the step by step calculations. A set of stable forms of the finite-difference equations of motion and continuity has been derived. Sometimes, it is convenient to divide the numerical integration region into two or more sub-regions, the mesh-dimensions of which are not equal. A method is described to calculate both regions by one procedure. Japan coasts were frequently damaged by severe storm surges (Typhoon Tides). To protect the metropolitan area from storm surges, a proposal has been made to construct a dike across Tokyo Bay. A numerical calculation has been made by means of IBM 7090 to estimate for several opening width of the proposed dike its effects on the reduction of surges. Interactions between daily tides (astronomical tide) and surges are also discussed.

Collection and study of field data relative to coastal engineering is underway for the following problems: wind over the lakes and its relationship with wind recorded on land; wave characteristics and effect of wind and environment; water level disturbances and mathematical relationship with acting forces; currents in harbors and factors affecting them; littoral transport.

Sea tests of motion and mooring force were conducted on an LST (Landing Ship Tank) of about 4400 long tons displacement. The LST was spread-moored by six 2-1/16 inch and one 1-1/4 inch (port breast) stud-link chains in simple catenary configuration in about 45 feet of water in the open Gulf of Mexico about 65 air miles south of New Orleans, Louisiana. Water-level variations at a single location, ship rotations and accelerations, mooring force, and wind were measured in sea states of 2 and 4. Three recordings of 38, 62, 67 minutes duration were analyzed, using timeseries techniques to provide apparent amplitude-response operators for all of the ship's motions and seven mooring chains. Theoretical prediction of the operators using long crested regular waves was made also. In longitudinal plane, theory predicts motions 1/3 to 4 times and chain tensions 1/4 to 9 times those measured. The most probable maximum-motion amplitude responses in sea state 4 are found to be 1.7, 1.1, and 1.7 feet, respectively, in surge, sway and heave, and 3.4 and 0.5 degrees, respectively in pitch and yaw. Roll was measured only in sea-state 2 with a corresponding maximum of 2.1 degrees. Maximum wave-induced chain tensions in kips were: 85.1 and 48.0 in port and starboard bow chains respectively; 10.6 (sea state 2) and 19.7 in port and starboard breast chains; 13.9 and 4.3 in port and starboard quarter chains (sea state 2) and 9.7 in stem chain. Total tension in port bow chain was 116.1 kips (85.1 plus initial tension of 31.0 kips). Chain response operators vary directly with initial tension, whicl complicates design.

It is concluded that: (i) moor was unbalanced, i.e., port bow chain took most of load; (ii) chains loaded lightly, e.g., maximum wave induced tension was 116 kips compared to new proof load of 300 kips for the particular chain, the port bow; (iii) water level should be measured at more than one point; (iv) discouragement over differences is balanced by encouragement over agreements between measurements and theoretical prediction of motion and chain tension; (v) toward improvement: Theory needs extension to include short crested waves and barge types; (vi) initial tension unique to problem of mooring design; (vii) propulsion devices may be needed toward maintaining design initial tension, especially in storm; (viii) if directional spectra had been measured and if theory involving short crested waves had been available and used, then discrepancies between observation and theory likely would have been less.