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Patent Searching and Data


Title:
WAVE POOL CURBING SYSTEM
Document Type and Number:
WIPO Patent Application WO/1998/003753
Kind Code:
A1
Abstract:
A foam-like panel (10) is provided which may be removably attached to a pool deck (30) by bolts (13) in a manner to provide a planar reflecting surface positioned parallel with the pool wall (20) at a height greater than the uppermost portion of the pool wall. The panel permits quick and easy conversion between wave action pools and non-wave action pools by avoiding the necessity of lowering the water level in a conventional pool when a wave-generating device is employed.

Inventors:
ELLIS HERBERT S
DELP THOMAS W
DUNN JAMES F
ELLIS KENNETH L
Application Number:
PCT/US1997/013004
Publication Date:
January 29, 1998
Filing Date:
July 24, 1997
Export Citation:
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Assignee:
AQUATIC AMUSEMENT ASSOCIATES L (US)
International Classes:
E04H4/00; E04H4/12; (IPC1-7): E04H4/14
Foreign References:
DE7400875U
US4080670A1978-03-28
US4007566A1977-02-15
US3737921A1973-06-12
US3546719A1970-12-15
US3813705A1974-06-04
US4170796A1979-10-16
US1404969A1922-01-31
USPP39797097P
Other References:
ARMY COASTAL ENGINEERING CENTER: "SHORE PROTECTION CENTER", vol. 1, pages: 2-115 TO - 2-117
See also references of EP 0914533A4
Attorney, Agent or Firm:
Heslin, Robert E. (P.C. 5 Columbia Circl, Albany NY, US)
Download PDF:
Claims:
We claim :
1. A swimming/wave pool comprised of : a pool defined, at least in part, by a vertical wall extending upwardly to a horizontal deck, said pool adapted to be filled with water up to a certain operating level proximate the deck for swimming; a selectively activatable wave generator associated with the pool and adapted to propagate waves in the pool toward the vertical wall; and at least one reflecting panel removably attachable to the deck for use during wave generation, said panel having a reflecting surface which extends upwardly from the wall in the same plane as the wall..
2. The swimming/wave pool of Claim 1 wherein the wall has a gutter formed therein proximate the deck and wherein the wave reflecting surface of the panel, when attached, extends upwardly from the gutter.
3. The swimming/wave pool of Claim 2 wherein the gutter has a lower lip proximate the said water operating level and wherein the reflecting surface meets said lip and extends upwardly therefrom.
4. The swimming/wave pool of Claim 3 wherein the panel has at least one opening through the reflecting surface proximate its meeting with the lip for admission of water from the pool into the gutter.
5. The swimming/wave pool of Claim 4 wherein the panel is made of a semirigid material.
6. The swimming/wave pool of Claim 5 wherein the semirigid material is closed cell polyethylene foam.
7. The swimming/wave pool of Claim 4 wherein the panel includes a handhold adjacent the pool.
8. The swimming/wave pool of Claim 4 wherein the panel is attached to the pool by means of a bolt assembly passing through the panel into a socket formed in the deck.
9. The swimming/wave pool of Claim 8 wherein the bolt assembly includes a resilient bushing positioned in the socket upon attachment of the panel to the deck, said bolt assembly being adapted to compress the bushing as the bolt is tightened so as to increase the diameter of the bushing and cause it to engage the socket .
10. A wave reflecting device for use with a swimming/wave pool during wave generation, said pool being of the type defined, at least in part, by a vertical wall toward which waves are to be propagated, said wall having an upper end proximate to a horizontal deck and said pool having a water operating level proximate the deck, said device comprising: a reflecting panel having a wave reflecting surface, said panel adapted to be removably attached to a pool deck proximate to a wall of the pool so that the reflecting surface lies above and coplanar with the vertical wall.
11. The wavereflecting device of Claim 10 wherein the vertical wall of the pool has a gutter formed therein proximate the deck and wherein the wave reflecting surface of the panel, when attached, extends upwardly from the gutter.
12. The wavereflecting device of Claim 11 wherein the gutter has a lower lip proximate the said water operating level and the reflecting surface meets said lip and extends upwardly therefrom.
13. The wavereflecting device of Claim 12 wherein the panel has at least one opening through the reflecting surface proximate its meeting with the lip for admission of water from the pool into the gutter.
14. The wavereflecting device of Claim 13 wherein the panel is made of a semirigid material .
15. The wavereflecting device of Claim 14 wherein the semirigid material is closed cell polyethylene foam.
16. The wavereflecting device of Claim 13 wherein the panel includes a handhold adjacent the pool .
17. The wavereflecting device of Claim 13 wherein the panel is attached to the pool by means of a bolt assembly passing through the panel into a socket formed in the deck.
18. The wavereflecting device of Claim 17 wherein the bolt assembly includes a resilient bushing positioned in the socket upon attachment of the panel to the deck, said bolt assembly being adapted to compress the bushing as the bolt is tightened so as to increase the diameter of the bushing and cause it to engage the socket.
19. A method for enhancing the wave reflecting ability of a swimming pool wall without having to lower the water level in the pool below its normal operating level comprising the step of: adding a wave reflecting surface to the pool above and coplanar with the pool wall .
20. The method of Claim 19 wherein the pool wall includes a gutter and the reflecting surface is added above the gutter.
21. The method of Claim 20 wherein the gutter includes a lip for permitting water from the pool at its normal operating level to spill into the gutter and wherein the added reflecting surface meets and extends above the lip and is provided with openings where it meets the lip so as to permit water frorr the pool to enter the gutter.
22. The method of Claim 21 comprising the further step of providing a handhold on the reflecting surface.
Description:
WAVE POOL CURBING SYSTEM

Field of the Invention

The following invention relates to wave pool systems. More particularly, the present invention relates to a wave pool curbing system for improving wave generation within pools.

Background of the Invention

In the past several years, the popularity of wave pools has grown considerably. Today there exists numerous pools specifically designed for the generation and maintenance of waves. However, it will be appreciated that the vast majority of existing pools are primarily designed for swimrr.ing and not the maintenance of waves. Nevertheless, pools capable of offering multiple functions, such as a swimming pool and a wave pool , are becoming increasingly popular. This versatility in the function of the pool allows the owner to maximize use of same.

In this regard, there are wave generating systems which have been designed to generate waves in pools that were originally designed for swimming. However, many wave generating systems or devices designed to generate waves in existing swimming pools require extensive structural and mechanical modifications to the pool. Effecting such modifications is expensive and often detraccs from the appearance of the pool. Further, even those wave generating devices that function without requiring extensive structural and mechanical modifies-ions to

the pool often require that the water level be lowered in the pool prior to generating waves. However, lowering the water level can cause significant health concerns. For example, when the water level is significantly lower than the gutter, the normal flow of water into the gutter is stopped, and, accordingly, the flow of water through the gutter to the filtering, disinfecting and recirculation systems of the pool cannot occur. In addition, repeatedly raising and lowering the water

.level is itself expensive, requiring additional water tanks or allowing substantial quantities of water to be wasted.

Thus, there exists a need for wave pool systems which allow wave generating devices to be used in connection with standard swimming pool designs without the need for significant mechanical, structural or other modifications to the pool that may prevent the pool from functioning in its intended capacity. There further exists a need for such a wave pool system which will allow the swimming pool to function as either a swimming pool or as a wave pool and that allows for quick and easy conversion between wave-action pools and non-wave action pools. Moreover, there exists a need for such a wave pool system that functions in accord with the working limitations of numerous and varied pool designs and that allows waves to be made without interfering with the filtration, recirculation and disinfectant systems of the pool either during periods of wave action or non-wave action when the system is installed.

Suiπinarv of the Invention

The aforesaid needs are fulfilled and the problems of the prior art overcome by the present invention, which in one aspect, includes a wave pool comprising a swimming pool having a body of water within a pool wall and a removably attachable reflecting panel and/or containment panels positioned along an upper portion of the pool wall wherein a reflecting surface faces the water and extends to a height greater than the uppermost portion of the pool wall. The reflecting panel may be adapted for any one of numerous pool curb designs including pools having an open gutter or no gutter at all . The reflecting panel may extend over a lower lip and above an upper lip of an open gutter such that the reflecting panel contacts the lower lip and is substantially parallel with and in the same plane as the pool wall . The reflecting panel over the lower lip may have a plurality of openings adjacent its interface with the lower lip whereby water from within the pool may enter the gutter. The reflecting panel may have a planar reflecting surface that extends to a height of a few inches to several feet above the normal water level of the pool . In addition, the reflecting panel may have a handhold proximate to the body of water; the handhold may be integrally formed within the reflecting surface or attached to the reflecting surface. The reflecting panel may comprise a semi-rigid or foam-like matter, such as closed cell polyethylene. Means for easily attaching and removing the reflecting panel to and from the pool may be provided.

Brief Description of the Drawincrs

FIG. 1 is a perspective view of a portion of a swimming/wave pool incorporating the subject invention.

FIG. 1A is a cross-sectional view of a portion of FIG. 1 taken on line 1A - 1A.

FIG. 2 is a cross-sectional view of a curbing device of the present invention shown installed on a pool having a common type of a gutter system.

FIG. 3 is a cross-sectional view of a curbing device of the present invention shown installed on a pool having another type of a gutter system.

FIG. 4 is a cross-sectional view of a curbing device of the present invention shown installed on a pool having another common type of a gutter system.

FIG. 5 is a front view of the curbing device of FIG. 4 viewed in the direction of arrow 4.

FIG. 6 is a cross-sectional side view of a curbing device of the present invention shown installed on a pool having another common type of a gutter system.

FIG. 7 is an enlarged view of a portion cf FIG. 1 (A) showing one means for attaching a curbing device of the present invention to a pool deck.

FIG. 8 is a cross-sectional view of a curbing device of the present invention incorporating a hand hold.

FIG. 9 is a top view of a pool employing a curbing device of the present invention.

Description of the Preferred Embodiment

FIG. 1 is a perspective view of a portion of a swimming/wave pool incorporating the subject invention. Vertical wall 20 is an interior wall of the pool which is normally filled with water to operating water level 26. Wall 20 is formed with a lower lip 23 which allows water to spill into gutter 28. Gutter 28 is bounded at the rear by upper lip or shoulder 22 which is formed into deck 30. A reflecting panel 10 is removably bolted into wall 20 by means of bolt assembly 13 shown in greater detail in FIG. 7. It may be seen in FIG. 1(a) that there is a gap 25 between lower lip 23 and the adjacent portion of reflecting block 10. Reflecting block 10 includes an inner support rib 27 and an outer support rib 29 which serve to hold block 10 at the proper height above wall 20. Inner support rib 27 is provided with a series of openings (not shov/n) which allow water to pass from lower lip 23 through inner support rib 27 and into gutter 28. From gutter 28, the water passes through a conventional filtering, disinfecting and recirculation system and is eventually returned to the pool .

It will be readily understood that if one were to generate waves for propagation across the surface

of the pool toward wall 20 of FIG. 1, those waves would be reflected by reflecting surface 12 of reflecting panel 10. If reflecting panel 10 were not in place, then the waves would pass over lower lip 23 and be dissipated on deck 30. It has been found that with reflecting panel 10 in place, as shown in FIG. 1, it is possible to generate more sizeable waves with a given wave generator, operating at a given energy level, than would be the case without reflecting panel 10. This appears to occur because reflecting panel 10, and reflecting surface 12 in particular, reflects waves back into the pool and, if the originally generated waves are of an appropriεite wave length and if the phasing between the generated waves and the reflected waves is appropriate, the reflected waves will add to the amplitude of the incoming waves. Accordingly, for a given amount of wave generating energy, and without having to lower the water level in the pool from its normal swimming operating level, one can generate waves of greater amplitude using reflecting panel 10 than one can generate without it. It is believed that the physics of this phenomenon are well understood to those skilled in the art. However, attached hereto as Appendix A and made a part hereof are the cover page and section 2.53 (pages 2-115 to 2-117 of the U.S. Army Coastal Engineering Center - Shore Protection Manual, Volume I which contains a more detailed technical explanation.

In essence, the subject invention provides a suitable surface for reflecting incoming waves back into the pool where they may increase the overall amplitude of waves being maintained in the pool. Thus, the wave action in the pool is enhanced whiLe

adequate amounts of pool water are allowed to enter gutter 28 for transport to the filtering, disinfecting and recirculation systems. As a result, the invention provides the same wave enhancing benefits as might be obtained by lowering water level

26 in the pool so as to expose a greater reflecting surface on wall 20. However, use of the invention provides the desired wave enhancement without the disadvantages associated with lowering the water level, as mentioned above.

Those skilled in the art realize that there are a variety of gutter systems used in swimming pools. In some cases as, for example, in FIG. 2, lower lip 23 is directly below upper lip 22 and gutter 24 is recessed in wall 20. A number of these various gutter configurations will now be described with reference to the subject invention. However, it should be understood that the operating principal is essentially the same in each case.

As shown in reference to FIGs . 2 and 3, when the pool encompasses a design with a vertical gutter opening 25, the reflecting panel 10 may comprise a reflecting surface 12 placed proximate the uppermost portion 22 of the pool wall 20. In the embodiment shown in FIGs. 2 and 3, the reflecting panel 10 comprises a rectangular shaped block that may be removably attached to the pool deck 30 such that a reflecting surface 12 of the block is positioned substantially flush with the upper most portion 22 of the pool wall 20. One can, of course, also provide a reflecting surface to be inserted in opening 25 of the gutter systems shown in FIGs. 2 and 3. Providing such a reflecting surface could be accomplished by

attaching a sheet material to the reflecting surface 12 so that the sheet depends downwardly therefrom so as to meet wall 20 at lower lip 23. Alternatively, one could instead merely insert a properly shaped block of material into opening 25 so as to provide a continuous reflecting surface flush with wall 20. As yet another alternative, one could suspend sheet material from upper lip 22 downwardly to lower lip 23 and achieve the same result. Regardless of the approach taken, however, the material covering opening 25 can be provided with perforations or openings in order to allow a reasonable flow of water to enter gutter 24. This concept is discussed with reference to FIGs. 4 and 6 below. As shown in FIGs. 4 and 6, the present invention may be readily adapted for use with pool designs incorporating various other filtering structures and gutter designs, such as fully-recessed gutters, semi- recessed gutters, rollout gutters and deck-level type gutters. As used herein, the term open gutter section refers to a semi-recessed or deck-level type gutter, such as gutter 28 in which the opening to the gutter 28 is defined by an upper lip 22 and lower lip 23 in which the upper lip 22 is not directly above the lower lip 23, the upper lip 22 being further removed from the pool water than the lower lip 23 Examples of open gutters 28 are shown in FIGs. 1, 4 and 6. In a preferred embodiment with an open gutter, as shown in these figures, the reflecting panel 10 is positioned over both the upper lip 22 and lower lip 23 of the open gutter 28 with a rear portion of the reflecting panel 10 being attached to the pool deck 30. The reflecting panel 10 may extend over the upper lip 22 towards the body of water and may further extend across the gutter opening. The

reflecting panel 10 may be positioned over the pool deck 30 and pool wall 20 such that the lower portion of the panel 10 rests on the lower lip 23 thereby placing a reflecting surface 12 adjacent the water

• 5 and substantially flush with the lower lip 23. When positioned in such a manner; the panel forms a planar reflecting surface substantially parallel to the pool wall, extending a height above that of the upper gutter lip 22, thereby increasing the ability to

10 reflect and maintain waves within the pool without

.the need to modify the water level 26.

The reflecting panel 10 may be designed for either closure of the recessed gutter or non-closure of the recessed gutter. For example, in reference to

15 FIG. 5, portions of the reflecting panel 10 directly over the lower lip 23 may have openings 14 therein in order to allow water to enter the gutter 28. This allows the gutter 28 to draw water from the pool and continue to function in its intended capacity.

20 Preferably, the openings 14 are symmetrically placed in a saw-toothed like manner. However, the configuration and spacing of the openings 14 within the panels 10 may vary. Preferably, the openings 14 are uniformly spaced along the interface between

25 reflecting panel 10 and lower lip 23 and are sized to be just large enough to permit a sufficient flow of water into gutter 28 to maintain adequate filtering and disinfecting of the water. There is no advantage in making openings 14 so large that a substantial

30 portion of reflecting surface 12 is lost.

Accordingly, the optimum design from the point of view of wave enhancement is to make openings 14 just large enough to accommodate the desired amount of water to flow into gutter 28. Of course, it is not

necessary that every reflecting panel incorporate openings. The system could be designed, for example, with a series of reflecting panels laid end to end with alternate ones of these panels having openings and the others none .

The height that the reflecting surface 12 extends above the normal water level 26 and pool wall 20 may be dictated by the specific pool design and the size of the desired waves. Preferably, the upper edge of the reflecting surface is positioned at a height of about 12 to 14 inches above water level 26.

It will be appreciated upon comparison of FIGs. 2, 4 and 6, that the particular configuration of the reflecting panel may be varied in accord with the particular pool design. For example, the reflecting panel 10 may have a more block-like shape when there is less disparity in height between the upper lip 22 and lower lip 23 of the gutter. Further, upon comparison of FIGs. 3 and 6, it will be seen that the height of the reflecting surface 12 may likewise vary in accord with the particular pool design as each of the reflecting panels in FIGs. 3 and 6 provides an extension of the pool wall to a height of about 14 inches above water level 26.

The material comprising the reflecting surface 12 should be a solid material capable of reflecting and containing water. However, preferably the reflecting panel 10 is made of a light semi-rigid material which does not readily absorb water. As used herein, the term "semi-rigid" material refers to a material sufficiently rigid to reflect water yet which is resilient enough such that a person would

not be seriously injured upon bumping or striking the reflecting panel. Such semi-rigid materials include foam-like materials, an example being closed cell polyethylene foam. However, there exists numerous other suitable materials such as various plastics, non-corrosive metals and other materials, which may or may not be coated with an outer protective layer, sufficiently rigid and non-corrosive so as to be suitable for use in the present invention. In addition, for safety reasons the corners of the

•reflecting panel may be rounded.

The reflecting panels 10 may be attached to the pool deck 30 by any one of numerous means. For example, the reflecting panel may be attached to the pool deck 30 by a fastener connected to both the panel 10 and the pool deck 30. In FIG. 7, for example, an attachment assembly is shown which is comprised of a bolt 40 contained within a sleeve 18. Sleeve 18 passes through reflecting panel 10 and protrudes about two inches below panel 10. Bolt 40 is provided with a nut 41 at its lower end and rubber bushing 34 is captured between a washer 43 on nut 41 and a flange 45 formed on the lower end of sleeve 18. As bolt 40 is tightened, thus causing nut 41 to be drawn upwardly, rubber bushing 34 is compressed between washer 43 and flange 45, thereby increasing its diameter and causing it to make intimate contact with and press against the interior of socket 32 which is formed in deck 30. As a result, panel 10 becomes locked in place. It will be appreciated that such a fastening mechanism can be quickly deployed and removed. Of course, the reflecting panel 10 may be removably attached to the pool deck via other means of attachment, including, but not limited to,

latches, hooks, hook and eye type fasteners such as those sold under the Velcro ® trademark.

In reference to FIG. 8, the reflecting panel may have a hand hold or handle 16, proximate the pool water, capable of supporting persons within the water and/or aiding a person exiting the pool. The handle may be integrally formed within the material comprising the reflecting panel, as shown in FIG. 3, or a separate handle may be attached to reflecting panel 10.

FIG. 9 is a plan view of a pool showing a plurality of reflecting panels 10 installed end to end along its perimeter. Although the pool in FIG. 9 is rectangular, it will be appreciated that other pool shapes can be used with the subject invention. Pool 52 shown in FIG. 9 is proλ'ided with wave generators 50 at one end. Thus, waves are propagated from wave generators 50 to the opposite end of the pool where they are reflected and returned toward wave generators 50. Panels 10 may incorporate notices to swimmers indicating the depth of the pool or placing restrictions on diving or other activities, especially where such notices on the pool itself would be covered when panels 10 are installed.

Pools designed to provide a body of water for swimming exist in a vast number of configurations. Such pools range in sizes for private use, such as those in an individual's backyard, to much larger pools designed for serving the public at large.

Swimming pools often incorporate both shallow sections for wading and a deeper section which allows a person to freely swim without touching the pool

bottom. However, the specific configuration of the pool is not believed to be critical as the present invention may be adapted and used in connection with pools of almost any size or design.

There are numerous wave generating systems and wave generating devices which may be used to generate waves within standard swimming pool designs. Examples of such systems and devices are the "Waveball" manufactured by S.A. WOW Co. of Belgium and the Wave Generating System taught in U.S. Patent

Application Serial No. 08/397,970; the contents of the aforesaid ' 970 application are incorporated herein by reference. As with pool design, the particular wave generating system or wave generating device is not believed to be critical as one skilled in the art will appreciate that the present invention may be used in connection with numerous types cf wave generating systems and/or devices.

Thus, the present invention provides a means of extending the height of the pool wall, relative to the water level, in order to allow the generation of waves in the swimming pool without the need to lower the water level . This has significant advantages m that it will not detract from the water quality maintenance systems since the water level may be maintained at the level originally designed for that particular pool. Moreover, the time and expense in raising and lowering the water level of the pool is completely avoided.

While the invention has been particularly shown and described with reference to the preferred embodiments thereof, it will be understood bv those

skilled in the art that other changes in form and details may be made therein without departing from the spirit and scope of the invention.

For example, in the claims that follow, it is stated that the reflecting surface of reflecting panel 10 is "in the same plane as the wall" or "coplanar" with the wall of the pool. It will be readily understood that it is not essential that the reflecting surface be exactly coplanar with the we.ll of the pool. Indeed, it could be offset somewhat in a parallel plane or even tilted somewhat one way or the other and still retain its essential wave reflecting function. Thus, these terms should be interpreted as meaning that the reflecting surface is sufficiently coplanar with the wall of the pool to provide enough wave reflecting action to achieve the objectives of the subject invention.

- 16 -

remains aτ tne S L or all values of r and o ?- ;;-.c: s^[ar. inodes.)- ' t.-hcir t - t he water partic excursion at the surface, is 1 ^ or twice the incident wave height. The equations describing the water particle motion show that the velocity is always horizontal under the nodes and always vertical under the antinodes. At intermediate points, the water particles move along diagonal lines as shown in Figure 2-61. Since water motion at the anti- nodes is purely vertical, the presence of a vertical wall at any antinode will not change the flow pattern described since there is no flow across the vertical barrier and equivalently, there is no flow across a vertical line passing through an antinode. (For the linear theory discussion, here, the water contained between any two antinodes will remain between those two antinodes.) Consequently, the flow described here is valid for z. barrier at 2;rx/L = 0 (x - 0) since there is an antinode at that location.

2.S3 REFLECTIONS IN AN ENCLOSED BASIN

Some insight can be obtained about the phenomenon of the reson≤nt behavior of harbors and other enclosed bodies of water by examining the standing wave system previously described. The possible resonant oscilla - tions between two vertical walls can be described by locating the twc barriers so that they are both at antinodes; for example, barriers at x = 0 and π or x = 0 and 2π, etc. represent possible modes of oscillation. If the barriers are taken at x = 0 and x = r. t there is one-half of a wave in the basin or, if l β is the basin length, l β = L/2. Since the wave¬ length is given by Equation 2-4

the period of this fundamental mode of oscillation is,

The next possible resonant mode occurs when there is one complete wave in the basin (barriers at x = 0 and x =.2τr) and the next mode when there are 3/2 waves in the basin (barriers at x = 0 and x = 3τr/2, etc. In general, i.g = jL/2, where j = 1, 2, In reality, the length of a natural or manmade basin £g, is fixed and the wavelength of the resonant wave con¬ tained in the basin will be the variable; hence,

IS. L = — j = 1,2, . (2-81)

may be thought of as defining the wavelengths capable of causing resonance in a basin of length lg. The general form of Equation 2-80 is found by

substituting cαu- tion :o the expres sion for th; ϊngi fore ,

For an enclosed harbor, of approximately rectangular planforα with length, l t waves entering through a breakwater gap having a predominant period close to one of those given by Equation 2-82 for small values of j, may cause significant agitation unless some effective energy dissipation mechanism is present. The addition of energy to the basin at the resonant (or excitation) frequency (f j = 1/T^) is said to excite the basin.

Equation 2-82 was developed by assuming the end boundaries to be vertical; however, it is still approximately valid so long as the end boundaries remain highly reflective to wave motion. Sloping boundaries, such as beaches, while usually effective energy dissipaters, may be signifi¬ cantly reflective if the incident waves are extremely long. The effect of sloping boundaries and their reflectivity to waves of differing character¬ istics is given in Section 2.54, Wave Reflection from Beaches.

Long-period resonant oscillations in large lakes and other large enclosed .bodies of water are termed seich.es . The periods of seiches cay range from a few minutes up to several hours, depending upon the geometry of the particular basin. In general, these basins are shallow with respect to their length; hence, tanh (τrjd/£g) in Equation 2-32 becomes approximately equal to πjd/l β and

T; = — j = 1, 2, (small values) (2-83)

J (gd)*

Equation 2-83 is ' termed Merian's equation. In natural basins, complex geometry and variable depth will make the direct application of Equation 2-83 difficult; however, it may serve as a useful first approximation for enclosed basins. For basins open at one end, different modes of oscilla¬ tion exist since resonance will occur when a node is at the open end of the basin and the fundamental oscillation occurs when there is one quarter of a wave in . the basin; hence, l > = L/4 for the fundamental mode and T = Hl^/Zgά". In general ' = (2- - l)L/4, and

T = _^1 _L j = 1, 2, - (small values) . (2-84) (2. - l) (gd) *

Note that higher modes occur when there are 3, 5 , , etc . , quarters of a wave within the basin. 2 J 1

GIVEN: Lake Erie a mean depth of d = 61 feet ' a its length i_ > is 220 " miles or 116,160 feet.

FIND: The fundamental period of oscillation T-, if j = l.

SOLUTION: From Equation 2-83 for an enclosed basin,

Tl j <gd)*

2(116,160) 1

Tι. = W [32).-2(6Λ11)M]U*

T t = 52,420sec.or 14.56 hrs.

Considering the variability of the actual lake cross-section, this result is surprisingly close to the actual observed period of 14. 8 hours (Platzman and Rao, 1963). Such close agreement may not always result.

Note: Additional discussion of seiching is presented in Section 3.B4.

2.54 WAVE REFLECTION FROM BEACHES

The amount of wave energy reflected from a beach depends upon the roughness,, permeability and slope of the beach in addition to the steep¬ ness and angle of approach of incident waves. Miche (1951) assumed that the reflection coefficient for a beach χ, could be described as the product of two factors by the expression,

x = *ι*a . (2-85) where χ 1 depends on the roughness and permeability of the beach and is independent of the slope, while χ 2 depends on the beach slope and the wave steepness .

Based on measurements made by Schoemaker and Thij sse (1949) , Miche found that χ α_ a. 0.8 for smooth impervious beaches . A value o -- ' Y λ j « 0.3