SHOCK PRESSURE OF BREAKING WAVES

The pressure sensitive elements of the pressure gauges consist of plates of tourmaline crystal. This material is sensitive to hydrostatic pressure changes. The plates are separated from the water by only thin layers of wax, rubber, and shellac. The element, consisting of four one-inch disks or wafers, is set in and backed by a strong metal case. The possibility of spurious signals caused by resonance or of loss of sensitivity in connecting parts is greatly reduced by the simple and strong construction of the gauges.


INTRODUCTION
Most of you have observed waves breaking against rocks or structures, and have noted that water is frequently thrown high in the air.The pressure required to project water in a vertical direction is about one half pound per square inch for each foot of height.We may therefore expect to find substantial pressure involved in the mechanics of a wave breaking against a structure.
Pressures as great as 100 psi caused by waves breaking on a structure at Dieppe, France, have been observed by Besson and Petry (1938).Bagnold (1939) has observed pressures as high as 80 psi caused by 10-inch waves in a wave tank.
The Beach Erosion Board, being especially interested in the subject of wave pressures on shore structures, has continued the study of the pressures of breaking waves.This study was designed to investigate the high-intensity shock pressures on the structures as contrasted to the much smaller hydrostatic pressures developed by the rise on the wave against the face of the structure.

EQUIPMENT USED IN THE TESTS
The pressure sensitive elements of the pressure gauges consist of plates of tourmaline crystal.This material is sensitive to hydrostatic pressure changes.The plates are separated from the water by only thin layers of wax, rubber, and shellac.The element, consisting of four one-inch disks or wafers, is set in and backed by a strong metal case.The possibility of spurious signals caused by resonance or of loss of sensitivity in connecting parts is greatly reduced by the simple and strong construction of the gauges.
The application of pressure to the gauges produces a small charge of electricity: 3U micro-micro coulombs for one pound per square inch change in pressure.The surfaces of the tourmaline disks are covered by thin conducting coatings which collect the charge.A voltage is produced which is inversely proportional to the capacitance of the gauge and leads.It is necessary that the resistance or the insulation be in the order of 1000 megohms to prevent the charge from leaking away too quickly.The voltage is carried to the grid of a radio tube by coaxial cable.The tube is biased so that the grid draws no current.The output of the radio tube can then be connected to the oscilloscope which has an input resistance of only 2 megohms.

Figure S
This trace represents a pressure of 13*2 psi and is number 25 in Table 1.The sweep time is 1/60 second.The trace of the square wave which is used to oalibrate the amplifiers is also present* By comparison with the square wave the voltage represented by the wave traoe can be found.A comparison with the results of the calibration tests with release of pressure then indicates the pressure in psi* Figure 6 The larger traoe represents a pressure of 18*9 psi* This is number 39 in Table 1*   Figure 7 These traoes represent pressures of 8*5 and 4*9 psi* The pressure oells were at different elevations* The sweep time was 1/60 seoond.This wave is number 47 in Table 1.

Figure 8
These traoes represent pressures of 6*3 and 6*6 psi oaused by a breaking wave* The sweep time was 1/60 seoond.They are number 51 in Table 1.

Figure 9
These traoes represent pressures of 6*3 and 5*6 psi* The sweep time was 1/60 seoond.They are number 65 in Table 1.Tiro pressure oells were used with a dual ehatmel oseilloseope.One of the amplifiers of the oscilloscope was an AC type and the other a DC type.The sweep of the oseilloseope was triggered by the signal.
A 4 mioro-seoond delay line and speeial triggering device were used in many of the tests to insure that we were not losing the initial rise of the signal.
The traces on the oseilloseope screen were recorded by an oseilloseope oamera.
The oells and apparatus were calibrated by plaeing the oells in a snail chamber and releasing air pressure by the breaking of a diaphragm or the expulsion of a cork.The first method released the pressure in about 1/10,000 seeond and the other in about l/l,000 second.The eleetrio charge produced by tourmaline is linear with changing pressure so that the calibration with the release of pressure may be used with the increase of pressure produoed by the breaking wave.The oseilloseope traces from two calibration tests are shown in Figures 1 and 2

3,
Wares starting with the second and ending with roughly the tenth are called early waves* These early waves were caused to break in proper position by adjustment of the water depth.At this depth the backwash of the preceding wave is such as to cause each wave to break in proper position.
After 8 to 12 waves have broken on the bulkhead, the influence of the refleoted waves traveling from the bulkhead to the wave aaohine and then back to the bulkhead causes variation in height of the incident waves.The total distance is about 160 feet.These are called late waves.
The first two conditions are reproducible and reliable pressure producers.A slight variation of the period, depth, etc. would oause the waves to break too early or too late to produce much pressure.For the third wave condition, the production of pressure was infrequent.Sometimes very high pressures were produced, however.
The height of the waves varied from S to 7.5 inches as measured 30 feet from the bulkhead.The height of the third wave was measured because in subsequent waves the record was complicated by the refleoted wave.

PRESSURES PRODUCED BY BREAKING WAVES
Four wave pressures were recorded greater than 18 psi, twenty-one greater than 10 psi, and more than 300 greater than 5 psi* The maximum pressure whioh would be produced by hydrostatic pressure (olapotia) is only about 0*5 psi.
High pressures ocoured more frequently and over a larger area of the bulkhead with larger waves.However, sometimes a large wave would break with a big bang and produce a pressure of one or two psi and then a small parasitic wave between the larger waves would slap the bulkhead lightly and produce a pressure of seven or eight psi.

Twenty-two consecutive tests of the first wave type gave 44 values of the pressure with an average of 5 psi. Simultaneous pressures of from 3 to 5 psi oocured with the gauges separated vertically by 2 inches*
The gauges are separated 9 inches horizontally.This indicates that high pressures occurred over a relatively large area of the bulkhead at the same time.
Most of the shook pressures were observed when the pressure gauges were between one inch below and three inches above the still water line.
A sample of the wave data with experimental conditions is given in Table 1. 4 to 9.

Some osoilloscope traoes indicating the shook pressures are shown in Figures
The durations of the shook pressures are short.Bagnold has noted that the time integral of the pressures seems to approach an upper limit.Numerous measurements were made of the time integral of the pressures produoed by the waves in these tests.The maximum values found were slightly greater than 0.02 psi-seoonds.

EFFECT OH STRUCTURES
If we consider the pressure of 18 psi developed by 7-inch laboratory waves, we nay well be interested in what full-scale ocean waves may do to a structure.In these tests, the larger pressures are of too short duration for a structure of muoh weight to be moved appreciably* At model scale, most types of pressure gauges have too muoh inertia and resiliency for them to even deteot these pressures.
Measurements have shown that the velooity of the peak of a breaking wave approaches the wave velooity.The velooity of the face of the wave decreases rapidly with lower elevation.If we assume a horisontal thickness of the breaking' wave as 3 inches and its velocity at the same elevation as 3 feet per second, we find a momentum of 0.32 lbs-ft/ sec-in.2,equivalent to an impulse or a pressure-time integral of 0.01 psi-seoond.If the velooity is reversed, this amount is doubled.This is the approximate magnitude for the higher values of the impulse measured.It may be remembered that a variable amount of the momentum will be overcome by hydrostatic pressure which may account for the lower values.Some of the momentum is not reversed but is converted to turbulenoe and into the vertical motion of the spray.
If air were not present, we might well expect the pressure to approaoh the pressure of water hammer.However, some air is always trapped by the breaking wave.The more air trapped, the lower the shook pressure and the longer its duration.
When we oonsider waves of larger size, we may expect the shape to be similar.The corresponding horisontal section of the breaking wave will be increased in length by the scale ratio.
The velooity of waves in shallow water is proportional to the square root of the depth of the water.Since the larger waves may be expected to break in proportionally greater depth, the velooity will then be greater by the square root of the scale ratio.
The soale ratio for the impulse should be the product of these or the soale ratio raised to the three-halves power.If 7-inch waves produoe an impulse of JO.02, a 14-foot wave should then produce an impulse of 0.02 x 24 s / 2 or 2.35 psi-seconds.
The range of wave sices in these tests was not large enough to oheok this soale ratio.We hope to make some tests on a much larger scale when our wave machine is completed for our 635-foot tank.
Pressure measurements have been made with full-scale waves at Dieppe, Franoe.The pressure records of 7 waves give values of from 0.38 to 0.75 psi-seconds for the impulse.When corrected for the soale of the wave, these values become 0*003 to 0.010 psi-seoonds as 7-inch waves.
Bagnold found the time-integral of the pressure for his 10-inch waves to approaoh 0.018 psi-seoonds.This beoomes 0.010 when reduced to the soale of these tests.The data in Table 1 is selected to show conditions which gave high wave pressures.Many tests were made in which low pressures or no pressures were produced.For many conditions (wave periods, wave size, beach slope, etc.) the waves could be caused to break and give pressures by adjusting the water depth in the wave tank.The depth for pressure depended on the type of wave.
The motion of the bulkhead producing the waves is about twice the length of the crank arm.
"F" indicates that the wave causing the pressure was the first full wave; "E" indicates a wave after the first but before the influence of any reflection of the first wave travels from the bulkhead to the wave machine and back againj and "L" indicates a wave after the heights of the waves becomes somewhat variable because of variation of depths caused by reflected waves at the wave machine. FigureFigure2

Figure 2
Figure 2 These traoes represent the release of 36 psi pressure by the expulsion of a cork* The sweep time is l/l4 second* The pressure release ooourred in slightly more than 1/1,000 second.The traoes indicate the error oaused by the loss of signal with time.The D.C* amplifier trace falls only about 6 per cent in 1/14 second.This drop is oaused by the loss of obarge through the insulation of the cell and leads.The A.C. amplifier will hold the signal for only about 1/60 second with a similar loss of signal.

Figure 3 Figure 3
Figure 3 Figure 3 is a diagram of the wave tank in which the tests were made.

Figure 4
Figure 4These traoes represent the pressures of two breaking waves.The larger one represents a pressure of 13*5 psi and is number 8 in Table1.The smaller one represents a pressure of 2*4 psi.The time-pressure integrals are the same, however.0.011 pound-seconds per square inch.The sweep time is 1/120 seoond.

.
The tests were made in an indoor tank with a length of 96 feet, a depth of 2 feet, and a width of 1 l/2 feet.A diagram of the wave tank is shown in Figure3.The waves were generated by a ware maehine of the moving bulkhead type.The bulkhead was oaused to move by a orank wheel and oonneoting rod.The speed of rotation of the wheel could be varied to give waves with periods from 1 to 5 seconds.The length of the orank arm was variable in l/2-inch steps from 2 to 11 inches to give waves of various heights.The pressure oells were mounted in two 1/2-lnch steel plates.Xaoh plate formed one half of the bulkhead representing the vertical structure against which the waves were to break.The sensitive faces of the oells were flush with the surface of the plates.The plates were mounted on a steel frame and oould be raised or lowered to ohange the vertical position of the gauges* The waves were oaused to break by a beach formed of concrete slabs.The height at the bulkhead was 10 inches.Various beach slopes were used from 0*078 to 0.176.A recording wave gauge was used to give a time profile of many of the waves.It was looated about 30 feet in front of the bulkhead.TYPES OF BHEAKIHO WAVESThree types of wave conditions were used in the tests.First, a small wave is formed by starting the wave maehine at a certain point in its cycle.If the site of the small wave is regulated oorrectly by the starting position of the maehine, the baokwash of this small wave will eause the next or first full-sized wave to break against the bulkhead.