Date 2013
Auttior S.A. Schmied, J.R. Binns, M.R. Renilson, G.A. Thomas,
G J . Macfarlane and R.H.M. Huijsmans
Address Delft University of Technology
Ship Hydromechanics and Structures Laboratory
Mekelweg 2, 2628 CD Delft
TUDelft
Delft U n i v e r s i t y of T e c h n o l o g y
Limitations on tlie creation of continuously surfable
w a v e s generated by a pressure source moving in a
circular patti.
by
S.A. S c h m i e d , J . A . Binns, M.R, Renilson, G.A. T h o m a s ,
G.J. I^acfarlane and R.H.M. Huijsmans
Report No. 1 8 7 6 - P 2013
P r o c e e d i n g s o f t h e A S M E 2 0 1 3 3 2 " " I n t e r n a t i o n a l C o n f e r e n c e o n O c e a n , O f f s h o r e a n d A r c t i c E n g i n e e r i n g , O M A E 2 0 1 3 , J u n e 9 - 1 4 , 2 0 1 3 , N a n t e s , F r a n c e , P a p e r 1 0 1 7 4 .
Proceedings of tlie ASME 2013 32nd International Conference on Ocean, Offshore and Arctic Engineering
OMAE2013
June 9-14, 2013, Nantes, France
OMAE2013-10174
L I M I T A T I O N S ON T H E C R E A T I O N O F C O N T I N U O U S L Y S U R F A B L E WAVES
G E N E R A T E D B Y A P R E S S U R E S O U R C E M O V I N G I N A C I R C U L A R PATH
M r Steven A . S c h m i e d D r J o n a t h a n R . B i n n s A u s t r a l i a n M a r i t i m e C o l l e g e A u s t r a l i a n M a r i t i m e C o l l e g e L a u n c e s t o n Tasmania A u s t r a l i a L a u n c e s t o n Tasmania A u s t r a l i a P r o f . M a r t i n R . R e n i l s o n A u s t r a l i a n M a r i t i m e C o l l e g e L a u n c e s t o n Tasmania A u s t r a l i a and H i g h e r Colleges o f T e c h n o l o g y , U A E A s s o c . P r o f . G i l e s A . T h o m a s A u s t r a l i a n M a r i t i m e C o l l e g e L a u n c e s t o n Tasmania A u s t r a l i a D r G r e g o r J . M a c f a r l a n e A u s t r a l i a n M a r i t i m e C o l l e g e L a u n c e s t o n T a s m a n i a A u s t r a l i a P r o f . R e n e H u i j s m a n s D e l f t U n i v e r s i t y o f T e c h n o l o g y D e l f t , N e t h e d a n d s A B S T R A C TI n t h i s paper, a n o v e l idea to produce c o n t i n u o u s b r e a k i n g waves is discussed, w h e r e b y a pressure source is rotated w i t h i n an annular w a v e p o o l . T h e concept was that the pressure source generates n o n - b r e a k i n g waves that propagate i n w a r d t o the inner r i n g o f the annulus, w h e r e a s l o p i n g b a t h y m e t r y (beach) t r i g g e r s w a v e b r e a k i n g . I n order to r e f i n e the technique, research w a s c o n d u c t e d to better understand the m e c h a n i c s o f waves generated b y a pressure source m o v i n g i n a c i r c u l a r t r a c k i n a constrained w a t e r w a y , the t r a n s f o r m a t i o n o f these w a v e s as t h e y t r a v e l across the channel and the e f f e c t o f the s l o p i n g beach o n the w a v e q u a l i t y f o r s u r f i n g .
T h e q u a l i t y o f the w a v e s w a s d e f i n e d i n t e r m s o f w a v e height, speed and shape, w i t h the desired a i m t o create p l u n g i n g waves, k n o w n as "barrels", that are h i g h l y desired b y surfers. S u r f e r s also r e q u i r e a l o n g steep crestline or " w a l l " , t o a l l o w a f u l l range o f m a n o e u v r e s to be p e r f o r m e d . F i n a l l y , the p o o l needed t o be able t o create waves suitable f o r surfers f r o m beginner to e x p e r t l e v e l , d e f i n e d i n terms o f b o t h the w a v e h e i g h t and angle b e t w e e n the w a v e break p o i n t angle and the beach, k n o w n a peel angle.
T h e p r i m a r y n o v e l o u t c o m e o f the research c o n d u c t e d was t o be able t o design a pressure source that m o s t e f f i c i e n t l y i m p a r t e d w a v e m a k i n g energy i n t o the water, and thus
generated the largest possible w a v e s w h i l s t t r a v e l l i n g at the r e q u i r e d speed f o r s u r f i n g .
T h e m a j o r finding was that the design parameters are g e n e r a l l y i n c o m p e t i f i o n , and to determine a balance o f l i m i t i n g values, the design parameters cannot be considered i n i s o l a t i o n . T h e r e f o r e , a set o f e m p i r i c a l r e l a t i o n s h i p s b e t w e e n the d e s i g n parameters w e r e d e v e l o p e d t o a l l o w t h e p o o l to be designed f o r a c o m b i n a t i o n o f desired w a v e h e i g h t at the b r e a k p o i n t , w a v e shape and g i v e n p o o l radius.
T h e l i m i t i n g values f o r the parameters w e r e d e t e r m i n e d e x p e r i m e n t a l l y , w i t h the w a v e l i f e - c y c l e fi-om g e n e r a t i o n thi-ough t r a n s f o r m a t i o n to w a v e b r e a k i n g and d i s s i p a t i o n used t o f o c u s the i n v e s t i g a t i o n . Scale m o d e l e x p e r i m e n t s w e r e c o n d u c t e d i n b o t h linear and c i r c u l a r tracks. I n a d d i t i o n t o t a k i n g q u a n t i t a t i v e measurement o f w a v e h e i g h t a n d c u r r e n t f o r m a t i o n , a m e t h o d o f q u a l i t a t i v e l y s c o r i n g the w a v e s w a s d e v e l o p e d t o a l l o w v a r i o u s pressure source shapes, o p e r a t i n g c o n d i t i o n s a n d b a t h y m e t r i e s t o be c o m p a r e d i n t e r m s o f t h e i r s u i t a b i l i t y f o r s u r f i n g . T h e best q u a l i t y w a v e s were p r o d u c e d b y a wedge-shaped w a v e d o z e r pressure source, such as the d e v i c e detailed i n D r i s c o l l and R e n i l s o n [ 1 ] .
B l o c k a g e , d e f i n e d as the pressure source cross s e c t i o n a l area t o c h a n n e l cross-sectional area, was f o u n d to have a s i g n i f i c a n t l i m i t a t i o n o n t h e generation o f h i g h q u a l i t y w a v e s suitable f o r
s u r f i n g i n a c o n s t r a i n e d w a t e r w a y . L a t e r a l w a v e decay, l e n g t h and depth F r o u d e N u m b e r s also s t r o n g l y i n f i u e n c e d the waves d u r i n g t h e i r l i f e - c y c l e . F u n d a m e n t a l l y , i t was d e t e r m i n e d that o n l y a v e r y s m a l l range o f design parameter values p r o d u c e the desired h i g h and shapely waves i n the e x t r e m e l y c o n s t r a i n e d w a t e r w a y undei' c o n s i d e r a t i o n . N O M E N C L A T U R E ji K B l o c k a g e V V o l u m e d i s p l a c e m e n t 1^ W a v e b r e a k i n g i n t e n s i t y S u r f a c e e l e v a t i o n
(,,,pi S u r f a c e e l e v a t i o n measured close t o the pressure source
CO A n g u l a r v e l o c i t y
head, W a v e l e n g t h i n deep water j u s t b e f o r e the beach Ac C h a n n e l cross-sectional area
As Pressure source cross sectional area B Pressure source b e a m
B* N o r m a l i s e d pressure source beam — no
Cp W a v e p h a s e s p e e d d D r a u g h t
d* N o r m a l i s e d pressure source draught — «O
Fri, D e p t h F r o u d e n u m b e r Fri,„ D e p t h F r o u d e n u m b e r at Rg ho Water d e p t h at Ro
Hbeadi W a v e h e i g h t at the start o f the beach hheach W a t e r d e p t h at the start o f the beach
H* N o n - d i m e n s i o n a l i s e d w a v e h e i g h t 3 ^ v v LWL Pressure source w a t e r l i n e l e n g t h R R a d i u s Ro P o o l radius Ro B e a c h r a d i u s s B e a c h slope T w a v e p e r i o d li T a n g e n t i a l c o m p o n e n t o f the v e l o c i t y ( p a r a l l e l w i t h the pressure source l i n e o f t r a v e l )
ito Pressure source v e l o c i t y y L a t e r a l distance f r o m Ro
) ' * N o r m a l i s e d lateral distance f r o m 7?o — "0 ybead, L a t e r a l distance to the start o f the beach
ytead* N o r m a l i s e d lateral distance to the start o f the beach ybeac h
Ro Ybead, W i d t h o f the beach
WP W a v e p r o b e Zbead, H e i g h t o f the beach
INTRODUCTION
S u r f i n g is f u n . H o w e v e r , i t is also e x t r e m e l y d i f f i c u l t to l e a r n and master T h i s d i f f i c u l t y is n o part helped b y ever c h a n g i n g nature and short d u r a t i o n o f the b r e a k i n g waves; w i t h the w a v e s c h a n g i n g b o t h day to day w i t h the weather, and as the w a v e breaks on the shore. W i t h the average w a v e b r e a k i n g f o r less than 7 seconds, the s u r f e r can o n l y r i d e the waves f o r less t h a n 8% o f the t i m e i n the w a t e r [ 2 ] . T h e r e f o r e , the d r e a m o f e v e r y s u r f e r is f o r consistent, l o n g l a s t i n g , h i g h q u a l i t y waves. T h i s search concentrates s u r f e r s o n to those areas o f coastline that are exposed t o r e g u l a r surf, a n d w i t h a b a t h y m e t r y suitable t o cause the w a v e to break i n a consistent manner and p r o v i d e a l o n g ride.
M a n y surfers do n o t h a v e the l u x u r y o f l i v i n g near s u r f breaks, and must t r a v e l l o n g distances i n o r d e r to s u r f Further, as coastal p o p u l a t i o n s increase, and s u r f i n g becomes m o r e popular, e x i s t i n g s u r f breaks b e c o m e o v e r c r o w d e d , s h o r t e n i n g their o v e r a l l r i d i n g t i m e even f u r t h e r . Surfers have responded b y t r a v e l i n g t o m o r e distant a n d r e m o t e l o c a t i o n s t o chase u n c r o w d e d and better waves [ 2 ] , even t h o u g h t h i s increases the cost o f s u r f i n g and does n o t reduce c r o w d i n g at t h e i r h o m e breaks. A n o t h e r s o l u t i o n has b e e n t o b u i l d a r t i f i c i a l reefs i n the ocean, h o w e v e r these s t i l l r e l y o n the natural w a v e c o n d i t i o n s . I n t h i s u n c o n t r o l l e d e n v i r o n m e n t , the w a v e s are a f f e c t e d b y the c o n s t a n d y c h a n g i n g and p o t e n t i a l adverse a f f e c t s o f the weather, i n c l u d i n g w a v e d i r e c t i o n and p e r i o d , w i n d ( d i r e c t i o n and strength), t i d e , a n d currents. A t h i r d s o l u t i o n is t o generate waves i n a c o n t r o l l e d e n v i r o n m e n t : the w a v e p o o l .
W a v e p o o l s are not a n e w concept. I n 1934, t h e W e m b l e y S w i m m i n g P o o l i n L o n d o n was the first t o t h r i l l its v i s i t o r s w i t h s m a l l a r t i f i c i a l w a v e s . I n 1966, the first i n d o o r surfers r o d e w a i s t - h i g h w a v e s i n the S u m m e r l a n d w a v e p o o l i n T o k y o , Japan [ 4 ] . Since then, m o r e s u r f p o o l s have been b u i l t a r o u n d the w o r l d , r e c e i v i n g m i x e d r e v i e w s f r o m surfers. T h e o r i g i n a l linear w a v e p o o l s , w h e r e the w a v e s are generated at one end and t r a v e l t o a beach at the other end, t r y t o m i m i c n a t u r a l l y o c c u r r i n g waves w i t h p i s t o n - d r i v e n paddles or s i m i l a r m e c h a n i c a l devices. Such m a n - m a d e waves are not v e r y appealing to surfers as the r i d e s are short, a n d the w a v e s generally w e a k and p o o r l y shaped.
Some m a n u f a c t u r e r s b e n d the p o o l a r o u n d a c u r v e to concentrate the s w e l l , or shape the p o o l floor t o i m p r o v e the w a v e height [ 5 ] . A n o t h e r m e t h o d used to s i m u l a t e s u r f i n g waves is t o shoot a t h i n sheet o f w a t e r o v e r a w a v e shaped surface. H o w e v e r , t h i s m e t h o d does n o t p r o v i d e an authentic s u r f i n g experience (a m o v i n g w a v e b r e a k i n g a l o n g a s h o r e l i n e ) and, l i k e the linear p o o l s , g e n e r a l l y o n l y a l l o w s o n e r i d e r at a t i m e [ 6 ] . A t h i r d concept aims t o d r a w an o b j e c t t h o u g h s h a l l o w w a t e r a l o n g a linear t r a c k c r e a t i n g w a v e s i n fi-ont o f the o b j e c t [ 7 ] .
A s the e x i s t i n g techniques generate the w a v e s b y m o v i n g large v o l u m e s o f water, they are p o w e r i n t e n s i v e . Instead, the n o v e l m e t h o d discussed i n this r e p o r t m o r e e f f i c i e n t l y generates the waves b y the pressure source i m p a r t i n g w a v e energy i n t o w a t e r w i t h m i n i m a l water m o v e m e n t .
K e y d e f i c i e n c i e s w i t h these approaches i n v o l v e b o t h the l a c k o f an authentic, scalable s u r f i n g w a v e m o t i o n o f a m o v i n g w a v e b r e a k i n g o n a shoreline, t h e large p o w e r r e q u i r e m e n t s t o generate the waves and a l i m i t a t i o n o f a s i n g l e r i d e r b e i n g able to s u r f at one t i m e , l i m i t i n g the financial v i a b i l i t y o f the p o o l .
W E B B E R WAVE POOL CONCEPT
I n o r d e r t o find the s o l u t i o n t o these p r o b l e m s w i t h current w a v e p o o l t e c h n o l o g y , a n o v e l idea t o p r o d u c e c o n t i n u o u s s u r f a b l e b r e a k i n g w a v e s has been patented [ 8 ] b y L i q u i d T i m e Pty L t d , the Webber Wave P o o l , w h e r e b y one o r m o r e pressure sources are rotated w i t h i n an annular w a v e p o o l ; F i g u r e 1 and F i g u r e 2 . T h e pressure source is any o b j e c t that disrupts the w a t e r surface, such as a s h i p - l i k e h u l l o r submerged body.
T h e inner r i n g o f the annulus has a s l o p i n g b a t h y m e t r y (i.e. a beach) to induce b r e a k i n g o f the w a v e s ( o r i g i n a t i n g at the pressure sources), w i t h the b r e a k p o i n t f o l l o w i n g t h e c i r c u l a r path a r o u n d the c e n t r a l i s l a n d at a g i v e n w a t e r depth at the b r e a k p o i n t (lueach) p r o p o r t i o n a l t o the w a v e h e i g h t (//imc/;); n o t i n g that f o r this analysis, the b r e a k p o i n t was d e f i n e d t o be at the start o f the beach. T h e q u a l i t y o f the w a v e s generated b y the pressure sources is c r i t i c a l f o r s u r f i n g , w i t h the w a v e s o n l y b r e a k i n g w h e n t r i g g e r e d b y the s l o p i n g b a t h y m e t r y o f the beach.
T h e design consists o f m u l t i p l e pressure sources t r a v e l l i n g a r o u n d the outer c i r c u m f e r e n c e o f the p o o l w h i l s t c o n t i n u a l l y p u s h i n g w a k e waves t o w a r d s the centre i s l a n d w h e r e they are f o r c e d t o break o n the m a n - m a d e beach due t o the change i n w a t e r depth. S h o u l d the pressure sources be s y m m e t r i c a l about t h e i r centre, a l l o w s the p r o d u c t i o n w a v e s i n b o t h the c l o c k w i s e a n d a n t i - c l o c k w i s e d i r e c t i o n s . R o t a t i n g the pressure sources c l o c k w i s e w i l l f o r m l e f t - h a n d e d w a v e s a n d a n t i - c l o c k w i s e w i l l p r o d u c e r i g h t - h a n d e d waves. A n artist's i m p r e s s i o n o f the c o n c e p t and c o m m e r c i a l a p p l i c a t i o n s are s h o w n i n F i g u r e I and F i g u r e 2 respectively.
I t is i n t e n d e d that b y p r o v i d i n g a safe l e a r n i n g e n v i r o n m e n t w i t h repeatable w a v e c o n d i t i o n s a n d l o n g ( u n l i m i t e d ) r i d e lengths, the o v e r a l l s u r f i n g a b i l i t y o f the p a r t i c i p a n t s can q u i c k l y i m p r o v e . Hull f Beach F i g u r e 1. C o n c e p t d e s i g n f o r the e f f i c i e n t m e t h o d o f g e n e r a t i n g c o n t i n u o u s l y s u r f a b l e b r e a k i n g waves u s i n g m o v i n g pressure sources. ( R e p r o d u c e d w i t h p e r m i s s i o n o f L i q u i d T i m e P t y ) . F i g u r e 2. A r i s t ' s i m p r e s s i o n o f the w a v e p o o l f o r a w a t e r p a r k ( R e p r o d u c e d w i t h p e r m i s s i o n o f L i q u i d T i m e P t y L t d ) .
FULL S C A L E VALIDATION
T h e c o n c e p t w a s p r o v e n , at least f o r a linear t r a c k , u s i n g a f i s h i n g vessel g e n e r a t i n g waves i n a r i v e r esmary, w h e r e the vessel t r a v e l l e d i n a straight l i n e close t o the b a n k . F i g u r e 3 shows that one o f the s m a l l e r waves generated b y a m o v i n g pressure source w a v e s can consistently s u r f e d .F i g u r e 3. R i v e r t e s t i n g such as that s h o w n i n t h i s f i g u r e has p r o v e n that even t h e smallest o f pressure source generated waves can be consistently s u r f e d . ( R e p r o d u c e d w i t h p e r m i s s i o n o f L i q u i d T i m e P t y L t d ) .
APPROACHES
T h e m a i n a i m i n d e s i g n i n g a w a v e p o o l is t o p r o d u c e h i g h q u a l i t y s u r f a b l e w a v e s w i t h the longest d u r a t i o n possible. T h e m a i n constraint o n the d e s i g n is t o p r o d u c e the w a v e s i n the smallest space possible w i t h a m i n i m u m a m o u n t o f energy. T o determine the d e s i g n parameter values to generate the desired waves, three approaches w e r e used: E m p i r i c a l , n u m e r i c a l a n d e x p e r i m e n t a l .
A s the e m p i r i c a l analysis has s i m p l i f i c a t i o n s and assumptions, e x p e r i m e n t a l a p p r o a c h c o n d u c t e d b o t h l i n e a r and c i r c u l a r scale m o d e l t e s t i n g , w i t h the l i m i t i n g values f o r the d e s i g n parameters established f r o m the e x p e r i m e n t a l results.
EiVlPIRICAL APPROACH
T h e f i r s t m e t h o d w a s an e m p i r i c a l analysis to d e t e r m i n e a series o f e m p i r i c a l r e l a t i o n s h i p s b e t w e e n the design parameters. T h e e m p i r i c a l analysis c o m b i n e d e x i s t i n g r e l a t i o n s h i p d e f i n i n g the e f f e c t o f the pressure source shape and o p e r a t i n g c o n d i t i o n s , and b a t h y m e t r y o n the w a v e l i f e c y c l e ; f r o m w a v e g e n e r a t i o n , t h r o u g h t r a n s f o r m a t i o n to b r e a k i n g a n d d i s s i p a t i o n ; F i g u r e 4.
T o a l l o w the p o o l to be designed f o r a c o m b i n a t i o n o f Hi,^ach< w a v e shape and p o o l radius {RQ,) the e m p i r i c a l analysis d e t e r m i n e d the r e l a t i o n s h i p s b e t w e e n the design parameters w a s d e v e l o p e d . T h e p o o l b a t h y m e t r y parameters, r e f e r r e d t o i n t h i s paper, as s h o w n i n F i g u r e 5. I n c o n d u c t i n g the e m p i r i c a l analysis, the w a v e s w i l l be assumed to break a\yteach w i t h w a v e h e i g h t of Hteach.
Geuer.ition Trai\.4onii.nlioii Brc.ikiHg Dissi|i.ition
F i g u r e 4. W a v e l i f e - c y c l e i l l u s t r a t e d i n the c i r c u l a r scale m o d e l at Fri,o = 0.975 w i t h B* = 2 7 5 m m , c/* = 0.2 and ho = 2 5 0 m m .
The m o d e l is t r a v e l l i n g t o w a r d s the camera.
Water depth
Beach width ( V j ^ r t )
V^tóter depth at the start of the beach
Start of the Beach
^ ^ ^ . ^ ^ Slope (s) 1 _ Beach height (Zj,^,) Beach radius (R^^J Pool radius (RJ F i g u r e 5. B a t h y m e t r y parameters
SURFING WAVES
To c o m m e n c e t h e e m p i r i c a l analysis; the f i r s t e l e m e n t o f the w o r k w a s t o d e f i n e the r e q u i r e m e n t s o f the w a v e p o o l f r o m the end-user perspective, b e i n g the s u r f e r K e y parameters w e r e w a v e speed, b r e a k i n g w a v e shape and w a v e h e i g h t at the b r e a k p o i n t
(HteacI,)-WAVE S P E E D FOR SURFING
T h e i n i t i a l d e s i g n parameter t o be d e t e r m i n e d w a s the w a v e speed (Cp), f o r s u r f i n g , b y c o n s i d e r i n g t w o q u e s t i o n s :
a. W h a t is the design range o f Cp f o r a s u r f i n g w a v e ?
b. W h a t is the m i n i m u m Cp f o r a w a v e t o be s u r f a b l e ?
T o determine Cp range f o r s u r f i n g , an i n i t i a l a n a l y s i s was c o n d u c t e d b y a meta-analysis o f e x i s t i n g s u r f i n g w a v e studies f o r m e a n Cp f o r d i f f e r e n t s u r f breaks a r o u n d the w o r l d b y D a l l y [ 5 5 ] and H u t t et. a l . [ 3 8 ] . T h e average Cp o f all o b s e r v a t i o n s w a s 6 m/s, w i t h t h i s v a l u e used as the i n i t i a l d e s i g n w a v e speed f o r the w a v e p o o l .
F i e l d observations o f s u r f i n g w a v e s w e r e c o n d u c t e d at L o r n e P o i n t , V i c t o r i a [ 3 ] . L o r n e p o i n t w a s chosen as the w a v e s break p a r a l l e l w i t h the s h o r e l i n e , a n d w i t h a desirable shape at s m a l l (less t h a n I m ) w a v e h e i g h t s . T h u s , L o r n e P o i n t is c o n s i d e r e d a close representation o f w a v e s desired f o r the final w a v e p o o l .
T o d e t e r m i n e the m i n i m u m Cp that s t i l l p r o d u c e s s u r f a b l e w a v e s , the field o b s e i v a t i o n s w e r e u n d e r t a k e n a n d a n a l y s e d at
L o m e P o i n t . T l i e smallest s u r f a b l e waves observed h a v i n g
hheach = 0 . 5 m w i t h a w a v e p e r i o d ( 7 ) = 3s, the m i n i m u m Cp w a s
estimated as b e i n g 3m/s u s i n g s h a l l o w w a t e r estimate f r o m A n t h o n i [ 4 ] . T h i s o b s e r v a t i o n w a s s u p p o r t e d b y D a l l y [ 5 ] and H u t t et al. [ 6 ] , w h o observed a m i n i m u m Cp = 2m/s.
T o translate the linear a p p r o x i m a t i o n t o the case o f a pressure source t r a v e l l i n g i n a c i r c u l a r t r a c k , i t was observed that the w a v e s t r a v e l l e d w i t h the pressure source; that is the w a v e field w a s obsei-ved to have the same angular v e l o c i t y ( t y ) as the pressure source. F o r the w a v e field t o have the same m as the pressure source at a l l r a d i i , the t a n g e n t i a l c o m p o n e n t o f the v e l o c i t y ( p a r a l l e l w i t h the pressure source l i n e o f t r a v e l ) {u) m u s t be p r o p o r t i o n a l to the radius (i?).
WAVE HEIGHT
W h e n t a l k i n g about surf, the first question that surfers ask is " h o w b i g are the w a v e s ? " H o w e v e r the answer to t h i s q u e s t i o n is n o t straight f o r w a r d , as surfers s t i l l cannot agree o n h o w t o measure w a v e height, w h e r e i t is the w a v e face ( o n w h i c h the s u r f e r r i d e s ) [ 7 ] , the w a v e h e i g h t i n deep w a t e r b e f o r e the w a v e breaks (that is measured u s i n g s w e l l b o u y s a n d r e p o r t e d o n w e a t h e r reports), or some other measure.
I n c o n d u c t i n g the e m p i r i c a l analysis, the waves w i l l be assumed t o break at yteach w i t h w a v e h e i g h t o f Ht^ach F o r a t h r i l l i n g desirable r i d e , the w a v e m u s t be large e n o u g h f o r the average s u r f e r A s an i n i t i a l d e s i g n r e q u i r e m e n t , Hteach = > 2 m is desirable as i t is overhead f o r the average h e i g h t s u r f e r (assumed as 1.75m), p r o v i d i n g an e x c i t i n g r i d i n g e x p e r i e n c e ; F i g u r e 6. O f course, smaller waves are also v e r y e n j o y a b l e t o r i d e , especially f o r less s k i l l e d surfers. T h e r e f o r e , s m a l l e r diameter, cheaper w a v e p o o l s that generate w a v e s o f Hheach < 2 m m a y also be v i a b l e .
WAVE SHAPE
T h e shape o f the w a v e at the b r e a k p o i n t is a c r i t i c a l element o f the s u i t a b i l i t y o f the w a v e f o r s u r f i n g . G a l v i n [ 8 ] and B a t t j e s [9] f o u n d the w a v e w i l l break i n d i f f e r e n t breaker shapes dependent o n the beach slope {s), Hheach and the w a v e l e n g t h i n deep w a t e r j u s t b e f o r e the beach (Xhead), w h e r e the w a v e crests p a r a l l e l w i t h the beach slope. B a t t j e s [ 9 ] used the I r i b a r r e n n u m b e r ( f ) ( o r s u r f s i m i l a r i t y parameter) t o describe the b r e a k e r t y p e o n the basis o f p r e v i o u s results o f G a l v i n [ 8 ] :
^ ^ t a n ( 5 ) ( 1 )
'J^lbeac h /^beac h
B a t t j e s [ 9 ] f o u n d the range o f values f o r f f o r the d i f f e r e n t w a v e breaker types, as detailed i n T a b l e 1.
B r e a k e r type
S p i l l i n g f < 0 . 4 P l u n g i n g 0 . 4 < = ^ < = 2 . 0 S u r g i n g / c o l l a p s i n g ^ > 2 . 0
T a b l e 1 . B r e a k e r type and ^ ( f r o m [ 9 ] )
T h e types o f breaker shapes w e r e d e f i n e d b y G a l v i n [ 8 ] as:
a. S p i l l i n g breakers. These waves are surfable, h o w e v e r they are n o t the highest quality.
b. P l u n g i n g breakers. These waves are the h i g h e s t q u a l i t y waves.
c. C o l l a p s i n g breakers. These waves are not s u r f a b l e .
d. S u r g i n g breakers. These waves are not s u r f a b l e .
For surfers, the u l t i m a t e experience is to r i d e i n s i d e a p l u n g i n g " b a r r e l i n g " w a v e ; F i g u r e 6. Surfers r o u t i n e l y t r a v e l a l l o v e r the w o r l d to r i d e " b a r r e l s " p l u n g i n g waves as not a l l s u r f i n g breaks generate p l u n g i n g w a v e s , and due to the d i s t r i b u t i o n of Hteach i n a w a v e g r o u p ( k n o w n i n s u r f i n g as a "set" o f w a v e s ) not e v e r y w a v e plunges. T h e r e f o r e , to constantly generate p l u n g i n g waves is the u l t i m a t e a i m o f the w a v e p o o l .
F i g u r e 6. S u r f e r r i d i n g p l u n g i n g w a v e o f Hheach ~ 2 m .
WAVE WIDTH
T h e l e n g t h o f s m o o t h , u n b r o k e n w a v e crest is d e f i n e d as the usable " w a l l " w i d t h . A s d e f i n e d b y H a r t l e y [ 1 0 ] , a w i d e steep w a l l is r e q u i r e d t o p r o v i d e surfers s u f f i c i e n t v e r t i c a l a n d lateral space to p e r f o r m t y p i c a l manoeuvres. A n e x a m p l e o f such a h i g h q u a l i t y w a v e is s h o w n i n F i g u r e 7.
M e a d et. al. [ 1 1 ] f u r t h e r associates the d i f f e r e n t parts o f the b r e a k i n g w a v e w i t h the d i f f e r e n t manoeuvres . T h e ' p o c k e t ' is j u s t i n f r o n t o f the b a r r e l and is w h e r e the m a j o r i t y o f the waves p o w e r is located. I t f o r m s the steepest part o f the w a v e a n d thus is the section w h e r e s u r f e r s are able to generate the m o s t speed. T h e ' s h o u l d e r ' is w h e r e t h e w a v e is the least steep a n d generally surfers w i l l s t r u g g l e to generate speed w h i l s t s u r f i n g on this section. A d v a n c e d surfers w i l l o f t e n use a c u t b a c k m a n o e u v r e t o p o s i t i o n themselves b a c k i n the p o c k e t . T h e ' l i p ' is the u p p e r m o s t p o i n t o f the w a v e and can b e used f o r p o w e r f u l t o p - t u r n s o r aerials. T h e ' w h i t e w a t e r ' i s the b r o k e n part o f the w a v e i n w h i c h is g e n e r a l l y a v o i d e d b y s u r f e r s o f a
reasonable s k i l l l e v e l . W h i t e w a t e r m a y be s u r f e d by beginners w h i l e they are l e a r n i n g t o stand u p .
T h e w a l l w i d t h is n o m i n a l l y the distance b e t w e e n the outer w a l l and the break p o i n t , m i n u s the pressure source beam. F u r t h e r , a b o w w a s h ( b r e a k i n g b o w w a v e ) is created as the pressure source t r a v e l , causing a n area o f t u r b u l e n t water; t e r m e d the n e a r - f i e l d r e g i o n ; F i g u r e 8. T h i s near field r e g i o n is u n s u i t a b l e f o r s u r f i n g a n d reduces the usable w a l l w i d t h .
F i g u r e 7. A h i g h q u a l i t y w a v e shape. T h e elements o f the w a v e
as described b y M e a d et. al. [11] are s h o w n .
F i g u r e 8. E x a m p l e o f near field e f f e c t s f o r m o d e l 6.
NUMERICAL APPROACH
O n c e the set o f e m p i r i c a l relationships b e t w e e n the design parameters w e r e d e v e l o p e d t o a l l o w the p o o l to be designed f o r a c o m b i n a t i o n o f desired Hteaci,, ^ and RQ, a n u m e r i c a l a p p r o a c h w a s u n d e r t a k e n u s i n g the Michlet linear p o t e n t i a l flow m o d e l [ 1 2 ] . Michlet had the advantage o f b e i n g able t o e f f i c i e n t l y m o d e l a large n u m b e r o f test c o n d i t i o n s . A n e f f i c i e n t m o d e l i n g m e t h o d w a s r e q u i r e d t o c o n d u c t an i n i t i a l analysis o f the waves generated b y the pressure sources g i v e n the f r e e d o m t o c o n t r o l m a n y o f the design parameters, i n c l u d i n g pressure source c o n f i g u r a t i o n (shape, l e n g t h , beam, draught, a n d v o l u m e d i s p l a c e m e n t ) , w a t e r depth, and pressure source speed.
A s d e t a i l e d i n M i c h e l l [ 1 3 ] , the waves are created b y a pressure source w h e r e there is a change i n the b e a m i n the s t r e a m w i s e d i r e c t i o n ; the c o m p o n e n t o f a pressure source w h e r e the w a t e r l i n e is p a r a l l e l ( f l a t sided) does not c o n t r i b u t e t o w a v e m a k i n g [ 1 4 ] . T h e r e f o r e , the i n i t i a l f o c u s w a s o n d e t e r m i n i n g a pressure source design that has c o n t i n u a l l y c h a n g i n g beam w o u l d e f f i c i e n t l y generate waves. E x a m p l e s o f t h i s d e s i g n w e r e the h y p e r b o l i c tangent w a t e r l i n e pressure sources, w i t h
w a t e r l i n e l e n g t h {LWL) t o b e a m {B) r a t i o o f 1.3 and 1.75, used i n i n h i a l i n v e s t i g a t i o n b y S c h i p p e r [ 1 5 ] and V r i e s [ 1 6 ] .
To p r o v i d e e x p e r i m e n t a l data t o v a l i d a t e the a b i l i t y t o accurately p r e d i c t the w a v e h e i g h t s u s i n g Michlet, linear t o w tank t e s t i n g w a s c o n d u c t e d u s i n g three d i f f e r e n t pressure source m o d e l s and c o m b i n a t i o n s o f speed, water d e p t h and d r a u g h t . H o w e v e r the Michlet m o d e l was n o t able to accurately p r e d i c t the w a v e shape generated b y the w i d e ( n o n - t h i n ) pressure sources. These e a r l y results w e r e p u b l i s h e d b y the authors [ 1 7 ] [ 1 8 ] , w i t h the w o r k presented at a conferences [ 1 9 ] [ 2 0 ] a n d other venues.
A f l i r t h e r n u m e r i c a l a p p r o a c h consider the e f f e c t o f the w a v e d o z e r b e a m and e n t r y angle o n the generated w a v e h e i g h t was c o n d u c t e d b y Essen [ 2 1 ] u s i n g the RAPID n o n - l i n e a r p o t e n t i a l flow m o d e l . F i n a l l y , a thi-ee d i m e n s i o n a l F i n i t e V o l u m e M e t h o d ( F V M ) n u m e r i c a l approach t o m o d e l the entire w a v e p o o l system w i t h a beach i n place to a l l o w the b r e a k i n g w a v e shape to be p r e d i c t e d is c u r r e n t l y b e i n g u n d e r t a k e n b y Javanmardi [ 2 2 ] using ANSYS-CFX/ FLUENT, t h a t solves the R A N S equations w i t h finite-volume a p p r o a c h a n d uses the v o l u m e o f fiuid t e c h n i q u e t o s i m u l a t e the fi-ee-surface m o t i o n .
T h e authors changed the f o c u s t o the e x p e r i m e n t a l a p p r o a c h , g i v e n the l i m i t a t i o n s o f the p o t e n t i a l fiow n u m e r i c a l approaches and w i t h the m o r e c o m p l e x F V M approach b e i n g u n d e r t a k e n b y J a v a n m a r d i [ 2 2 ] .
EXPERIMENTAL APPROACH
T h e t h i r d approach w a s d e v o t e d t o a series o f f o u r e x p e r i m e n t a l scale m o d e l e x p e r i m e n t s . T h e f o c u s o f the e x p e r i m e n t a l approach was first to deal w i t h the pressure source shape and the o p e r a t i n g c o n d i t i o n s t o m a x i m i s e the size and q u a l i t y o f the generated w a v e s . Subsequently, the e f f e c t s o f t h e b a t h y m e t r y o n the w a v e t r a n s f o r m a t i o n b r e a k i n g and d i s s i p a t i o n w e r e e x a m i n e d .
T h e results w e r e also used to d e t e r m i n e o f the d e s i g n parameter l i m i t i n g values f o r i n p u t to the e m p i r i c a l analysis, and t o v a l i d a t e the a u t h o r ' s M i c h l e t p r e d i c t i o n s , Essen's RAPID predicrions, and J a v a n m a r d i ' s F V M m o d e l [ 2 2 ] .
L i n e a r and c i r c u l a r scale m o d e l s w e r e b u i l t a n d tested at the A u s t r a l i a n M a r i t i m e C o l l e g e ( A M C ) . T h e l i n e a r t e s t i n g w a s conducted i n the 1 0 0 m t o w t a n k , w i t h the c i r c u l a r scale m o d e l b u i l t i n the M o d e l Test B a s i n ( M T B ) ; F i g u r e 9. Cameras and w a v e probes w e r e used t o r e c o r d and e x a m the shape a n d d e v e l o p m e n t o f the w a v e s .
F i g u r e 9. Circular scale model
PRESSURE SOURCES
Most studies into ship wave generation have focused on miminising the wave generation [23] [24] [25], thus reducing the ship wave resistance [26] [27], nuisance to other users o f the waterway [28] and destructive wave-shore interaction [29]. Previous work by Macfarlane [26] and others has found that wave making increased with the beam to length ratio; that is a short, wide pressure source; Figure 10. A more efficient pressure source shape, being a wavedozer, was investigated by Standing [30], and further developed by D r i s c o l l [1] and Renilson [31]. T h e wavedozer is also a very simple structure to form, essentially simply being an inclined flat plate. T h e initial wavedozer design is shown in Figure 11. T h e wavedozers used differed from those previously tested by Standing [30], D r i s c o l l and R e n i l s o n [1] [31], that spanned the channel, where the wavedozer tested by the author had limited beam.
T h e pressure sources tested for different shapes and values o f beam, draught, UVL and entry angle ( « ) (for the wavedozers) as detailed in Table 2. T h e pressure sources were configured so they were fixed in heave and trim.
F i g u r e 10. M o d e l 2 parabolic pressure source o f 7 0 0 m m length, 6 0 0 m m beam, 500mm height.
F i g u r e 11. T h e first wavedozer shape M o d e l 3 tested. T h e direction o f travel was from left to right.
S e r i a l M o d e l T y p e . B e a m [mm] A [deg] L i n e a r 1 Parabolic 300 N / A 2 Parabolic 600 N / A 3 Wavedozer 300 14 C i r c u l a r S e r i e s 1 4 Wavedozer 176 14 5 Wavedozer 251 14 6 Wavedozer 176 14 7 Wavedozer 251 14 C i r c u l a r S e r i e s 2 8 Wavedozer 75 4 - 18 9 Wavedozer 175 14 10 Wavedozer 275 14 11 Wavedozer 150 14 C i r c u l a r S e r i e s 3 12 Wavedozer 275 7 13 Wavedozer 550 7
T a b l e 2. Pressure sources tested in each series
QUALITATIVE ASSESSIMENT
T h e next question surfers ask each other when c h e c k i n g the surfer is "how good is it". That is, for surfing, wave quality is as important, i f not more important, than the w a v e height
(Hbeac!,)- T h i s qucstion is again subjective, however, the w a v e
quality can be broken down into a number o f elements.
In addition to the wave shape ( Ö , the w a v e quality is also determined by wall width, w a v e steepness and smoothness o f the wave face. T h e s e qualities determine the type o f manoeuvres that a surfer may do on the wave.
T o support the q u a l i t a t i v e assessment o f the w a v e q u a l i t y , the w a v e s c o r i n g system d e v e l o p e d b y the A s s o c i a t i o n o f S u r f i n g Professions [ 3 2 ] w a s used. T a b l e 3, w i t h t w o examples o f excellent w a v e s s h o w n i n F i g u r e 12. T h e j u d g i n g c r i t e r i a w e r e c l a r i f i e d t o a l l o w f o r the steady state nature o f the w a v e s generated i n the p o o l . S c o r e D e s c r i p t i o n R e q u i r e m e n t s 0 N o w a v e tJnrideable 0 . 0 - 1.9 B a r e l y s u r f a b l e N o turns. S p i l l i n g w a v e . 2 . 0 - 3 . 9 F a i r S i m p l e turns. S p i l l i n g w a v e . 4.0 - 5.9 A v e r a g e T u r n s , s m o o t h w a v e . S p i l l i n g w a v e . 6.0 - 7.9 G o o d P l u n g i n g w a v e w i t h s m o o t h , steep w a l l 8 . 0 - 1 0 . 0 E x c e l l e n t P l u n g i n g w a v e w i t h l o n g , s m o o t h , steep w a l l T a b l e 3. W a v e scores F i g u r e 12. E x a m p l e s o f e x c e l l e n t w a v e s generated i n the c i r c u l a r scale m o d e l b y m o d e l 10 w i t h d* = 0.2 i n ho = 2 5 0 m m at Fri,o = 0.975.
EXPERIMENTAL RESULTS
et. al. t h e o r e t i c a l c r i t i c a l i t y b o u n d a r y ; F i g u r e 14. C o n d i t i o n sw e r e d e t e r m i n e d to be i n the Critical Zone w h e n the n o n -d i m e n s i o n w a v e height (H*) as a f u n c t i o n o f n o n - -d i m e n s i o n a l lateral distance (y*) w a s less t h a n c o n d i t i o n 6 2 K = 0; an e x a m p l e is s h o w n i n F i g u r e 15 f o r c o n d i t i o n 56 K= 0.07.
T h e r e f o r e , t o m a x i m i s e the w a v e h e i g h t at the b r e a k p o i n t {Hbeaci), the p r e f e r e n c e w o u l d be f o r b l o c k a g e to b e m i n i m i s e d ; i.e. «: = 0. H o w e v e r , a beach is r e q u i r e d t o t r i g g e r the w a v e to b r e a k w i t h the desired p l u n g i n g shape. F r o m F i g u r e 14, the presence o f t h e beach m a y a l l o w c o n d i t i o n s s l i g h t l y w i t h i n the
Critical Zone to be used, l i m i t e d t o K <= 0.07 and Frm < 1.
I t m u s t be n o t e d that b y R o b b i n s el. al. [ 3 3 ] a n d the present w o r k d i f f e r :
a. P r e s s u r e sources. R o b b i n s et. al. used a catamaran w h i l s t the present w o r k used w a v e d o z e r s .
b. B a t h y m e t r y . R o b b i n s et. al. used a rectangular channel w i t h a constant water d e p t h . T h e present w o r k used s l o p i n g beaches.
F o r a l l c o n d i t i o n s , a bow wave was generated i n f r o n t o f the pressure source, i n c l u d i n g f o r K ~ 0 % ; F i g u r e 16. T h e bow wave is b e l i e v e d t o be due t o a c o m b i n a t i o n o f the t w o p h e n o m e n a ; a p r i m a r y w a v e and / or a s o l i t o n . T h e f o r m a t i o n o f the bow M'ave resuhed i n less energy b e i n g a v a i l a b l e f o r the d i v e r g e n t w a v e s , and t h e r e f o r e the reduced m a x i m u m Cwpi o f the t r a i l i n g d i v e r g e n t w a v e s , as i n d i c a t e d b y the r e d u c t i o n i n d i v e r g e n t w a v e e l e v a t i o n f o r c o n d i t i o n 56 w i t h i n c r e a s i n g s o l i t o n f o r m a t i o n ; F i g u r e 16.
F r o m the e x p e r i m e n t a l results, a k e y parameter that related the w a v e l i f e - c y c l e t o the pressure shape, o p e r a t i n g c o n d i t i o n s and b a t h y m e t r y w a s t h e b l o c k a g e ( K ) is d e f i n e d as the pressure source cross s e c t i o n a l area (A,) to channel cross-sectional area (Ac):
R o b b i n s et al. [ 3 3 ] i n v e s t i g a t e d the e f f e c t o f K. o n the f o r m a t i o n o f a s o l i t o n i n a c o n s t r a i n e d c h a n n e l . R o b b i n s d e v e l o p e d a p l o t o f K as a f u n c t i o n o f Frj,; F i g u r e 13. T h i s was d i v i d e d i n t o : a. Sub-Critical Zone, w i t h no / l i m i t e d s o l i t o n f o r m a t i o n and a d i v e r g e n t w a v e field. b . Critical Zone w i t h s i g n i f i c a n t s o l i t o n f o r m a t i o n . c. Super-Critical Zone \ v i t h no / l i m i t e d s o l i t o n f o r m a t i o n and s u p e r - c r i t i c a l w a v e field. T h e b o w w a v e / s o l i t o n w a s g e n e r a l l y n o t steep e n o u g h to break, and t h e r e f o r e w o u l d n o t be used f o r s u r f i n g i n t h i s w a v e p o o l design. T h e r e f o r e , the f o r m a t i o n o f the bow wave is a m a j o r l i m i t a t i o n o n the g e n e r a t i o n o f s u r f a b l e d i v e r g e n t w a v e s , and was sought to be m i n i m i s e d .
T h e m a i n o u t c o m e o f the e m p i r i c a l a p p r o a c h w a s that the d e s i g n parameters are i n c o m p e t i t i o n . T h e r e f o r e , t h e values o f the d e s i g n parameters are c a r e f u l l y b a l a n c e d t o achieve the desired b r e a k i n g w a v e shape and h e i g h t , K a n d associated s o l i t o n f o r m a t i o n are f o u n d t o have the greatest l i m i t a t i o n o n the g e n e r a t i o n o f h i g h q u a l i t y w a v e s suitable f o r s u r f i n g i n a c o n s t r a i n e d w a t e r w a y . H o w e v e r , a w i d e , s h a l l o w e n t r y a n g l e w a v e d o z e r was f o u n d t o generate s m o o t h h i g h w a v e s , w h i c h w e r e able t o be t r i g g e r e d t o break w i t h a p l u n g i n g shape.
R o b b i n s et. ai. [ 3 3 ] obsei-ved that s o l i t o n f o r m i n g Critical Z o n e extended w i t h increased K. R o b b i n s et. al. [ 3 3 ] o n l y tested at
K < 0.02. T h e authors o f t h i s paper extended R o b b i n s ' results t o K <= 0.07 b y p l o t t i n g the c i r c u l a r scale m o d e l series 3 results
jub-CtrlltllIarM F i g u r e 13. K as a f u n c t i o n o f Fr/, f r o m R o b b i n s et. al. [ 3 3 ] . 1.00 0.95 0.90 A 0.85 0.80 A 0.75 0.70 A 0.65
\ Critical zone
« * « • « 4» • • • A ^ •Sub-critical zone
Robbins criticality
boundary
0.02 0.04 0.06 0.08 KF i g u r e 14. Sub-Critical ( o p e n t r i a n g l e s ) and Critical ( s o l i d
d i a m o n d s ) c o n f i g u r a t i o n s p l o t t e d against R o b b i n s et. al. t h e o r e t i c a l c r i t i c a l i t y b o u n d a r y ( a d o p t e d f r o m R o b b i n s et. al. [ 3 3 ] ) . I I
\ \ ^ ^
• Cond 62 k = 0 ACond 55 k = 0.07 V bcath A D F i g u r e 15. / / * as a f u n c t i o n o f f o r d i f f e r e n t values o f K f o r m o d e l 12-02 w i t h d* = 0.2 i n iio = 2 5 0 m m at Fri,o = 0.95; c o n d i t i o n 62 K = 0 and c o n d i t i o n 56 ;c = 0.07. T h e beach is i n place atytcach* = 0.15 f o r c o n d i t i o n 56. CO 201
0 - 4 0 •GO Reduced Bow w a v e / S o i i t o n-Cond 62 Model 12-02 k=0 No beach •Cond 56 Model 12-02 k = 0.07
20 22 24 26
Time [s]
28 30
F i g u r e 16. T i m e traces o f Qpi f o r m o d e l 12 f o r K = 0 and
5= 1 6 ° w i t h K = 0.07 at Fr^ = 0.95 w i t h d* = 0.2 i n
lio = 2 5 0 m m . M o d e l 11-12 was t i m e s h i f t e d t o a l i g n w i t h m o d e l
12-02. T h e pressure source b o w passed the w a v e p r o b e at t i m e = 24.5 seconds.
POOL RADIUS
(Ro)
CONCLUDING REMARKS
F i n a l l y , i n order to generate the m a x i m u m n u m b e r o f s u r f a b l ewaves, the c o m m e r c i a l w a v e p o o l requires m u l t i p l e pressure sources, w i t h o u t adverse w a v e i n t e r a c t i o n ; that is, the w a t e r surface needed t o c a l m s u f f i c i e n t l y a f t e r the passing o f one pressure source, p r i o r to the second pressure source t r a v e l l i n g t h r o u g h the same w a t e r so as n o t t o a f f e c t the w a v e q u a l i t y o f the waves generated b y second and subsequent pressure sources.
To determine the t i m e r e q u i r e d t o a l l o w the w a t e r s u r f to c a l m , by o b s e r v a t i o n , non-adverse residual waves i n t e r a c t i o n w a s d e f i n e d b e i n g w h e n surface e l e v a t i o n , measured close t o the pressure source (Cuyj/), e x c i t e d b y the pressure source w a s less than 1 0 % o f the m a x i m u m ^ „ ^ / o f the first w a v e generated. A s an e x a m p l e , C,,,^, o f the first w a v e was 5 6 m m at t i m e = 30s; F i g u r e 17. T h e r e f o r e , the w a t e r is d e f i n e d as b e i n g c a l m e n o u g h f o r the second pressure source to pass w h e n ^„.^,/ < 5 . 6 m m ; w h i c h occurs b y t i m e = 38s. W i t h the second pressure source passing at t i m e = 50s, the pressure sources s h o u l d be able to be placed closer together.
T h e design o f a c i r c u l a r w a v e p o o l concept has been p r o d u c e d by W e b b e r W a v e Pools and patented w i t h i n A u s t r a l i a and I n t e r n a t i o n a l l y . T h i s d e s i g n shows great p r o m i s e s to not o n l y p r o d u c e a unique f a c i l i t y f o r e x p a n d i n g the s u r f i n g i n d u s t r y b u t also to conduct s i g n i f i c a n t research i n t o repeatable b r e a k i n g w a v e s .
A k e y finding was that the pressure source shape, o p e r a t i n g c o n d i t i o n s and b a t h y m e t r i c design parameters w e r e i n c o m p e t i t i o n . T h e r e f o r e i n order to generate h i g h , p l u n g i n g w a v e s i n the constrained channel, these d e s i g n parameters c o u l d not be considered i n i s o l a t i o n . I t w a s f o u n d that the w a v e q u a l i t y was e x t r e m e l y sensitive to changes i n the design parameters.
Subsequently, a set o f e m p i r i c a l r e l a t i o n s h i p s b e t w e e n the d e s i g n parameters w e r e d e t e r m i n e d t o a l l o w a p o o l to be designed f o r a c o m b i n a t i o n o f the desired height o f the largest w a v e s at the break p o i n t , a p l u n g i n g w a v e shape i n a g i v e n p o o l radius.
T h e r e f o r e , a l o n g w i t h pressure source speed (iio), Ro w i l l determine the l e n g t h o f t i m e f o r each pressure source t o t r a v e l around the p o o l , and t h e r e f o r e the n u m b e r o f pressure sources that m a y be used i n a s i n g l e p o o l . 60 40 20
E ,
1
1 +/-10% j\m
INI W M V \ n ; y ^ ' w « ^ ' ' ' ^-r
20 3 0 4 0 5 0 6 0 T i m e [s] F i g u r e 17. T i m e trace o f C,pj f o r C o n d i t i o n 6 m o d e l 5 w i t h (7* = 0.2 i n ho = 2 5 0 m m at Fri,o = 0 . 9 5 .T h i s w o r k c o n t i n u e d the research c o n d u c t e d b y R o b b i n s et. al. [ 3 3 ] . A s detailed i n R o b b i n s et. al. [ 3 3 ] , s o l i t o n f o i m a t i o n is t i m e dependent and s p e c i f i c to b l o c k a g e . R o b b i n s et. al. [ 3 3 ] a d v i s i n g that the w i d e r ( i . e . fiiU scale) i m p l i c a t i o n s o f these m o d e l test findings are p o t e n t i a l l y s i g n i f i c a n t , w i t h a l l p r e v i o u s w a v e measurements f o r critical values o f Fr/,, w i l l be t i m e dependant ( i . e . unsteady), e s p e c i a l l y i n h i g h b l o c k a g e e n v i r o n m e n t s such as r i v e r s o r canals. H o w e v e r , f a c i l i t i e s l i m i t a t i o n s ( i . e . l i m i t e d l e n g t h t o w t a n k s and test basins), m a y not a l l o w s u f f i c i e n t t i m e f o r the s o l i t o n t o f u l l y f o r m or reach a steady state w i t h a beach i n p o s i t i o n . T h e r e f o r e , t h e c i r c u l a r t r a c k scale m o d e l m a y p r o v i d e the f a c i l i t y to address t h i s l i m i t a t i o n .
H o w e v e r , s u f f i c i e n t results w e r e o b t a i n e d b y the end the p r o g r a m to a l l o w pressure source a n d b a t h y m e t r y to be c o n f i g u r e d to produce t w o h i g h q u a l i t y p l u n g i n g waves per pressure source. T h e present w o r k dealt w i t h d e t e r m i n i n g a c o n f i g u r a t i o n that was s u f f i c i e n t t o c o m m e r i c a l i s e the patented d e s i g n , and t h r o u g h the c o m b i n a t i o n o f the e m p i r i c a l analysis, t h i s was a c h i e v e d . T h e p r o m i s e o f m a k i n g the p e r f e c t repeatable-surfable w a v e seems t o be c o m i n g true.
Further work
Based o n the w o r k presented i n t h i s paper, a n u m b e r o f r e c o m m e n d a t i o n s and suggestions f o r f l i t u r e w o r k can be made.
Pool design steps
T o design a f u l l size p o o l , i t is r e c o m m e n d e d t o use the e m p i r i c a l r e l a t i o n s h i p s a n d d e s i g n parameter v a l u e s chosen f r o m the e x p e r i m e n t a l results.
T h e p r e d i c t e d design and the shape o f the w a v e s h o u l d then be c o n f i r m e d u s i n g the ANSYS-CFX/ FLUENT rmmnYK&i m o d e l d e v e l o p e d b y Javanmardi [ 2 2 ] . T h e m o d e l a l l o w s the i n v e s t i g a t i o n o f the w a v e shape, currents and forces o n t h e pressure source thi'oughout the w a t e r v o l u m e , and i n f a r greater d e t a i l , than c o u l d be achieved e x p e r i m e n t a l l y . T h e m o d e l a l l o w s the v i s u a l i s a t i o n o f the three d i m e n s i o n a l b r e a k i n g w a v e shape, f a c i l i t a t i n g a q u a l i t a t i v e assessment o f the w a v e q u a l i t y f o r s u r f i n g . T h i s v a l u a b l e data is n o t necessarily accessible b y the e x p e r i m e n t a l m e t h o d due t o the d i f f i c u l t y o f m e a s u r i n g the b r e a k i n g w a v e shape, especially once f u l l scale p o o l s are considered. T h e m o d e l has been v a l i d a t e d against the c u r r e n t c i r c u l a r t r a c k scale m o d e l test results.
Experimental approach
T h e n e x t c i r c u l a r t r a c k scale m o d e l s h o u l d be used to validate the i n i t i a l design p r e d i c t e d u s i n g the e m p i r i c a l relationships.
T h i s w o r k c o n t i n u e d the research c o n d u c t e d b y R o b b i n s et. al. [ 3 3 ] . A s detailed i n R o b b i n s et. al. [ 3 3 ] , s o l i t o n f o r m a t i o n is time dependent and s p e c i f i c t o b l o c k a g e . R o b b i n s et. al. [ 3 3 ] a d v i s i n g that the w i d e r (i.e. f u l l scale) i m p l i c a t i o n s o f these m o d e l test findings are p o t e n t i a l l y s i g n i f i c a n t , w i t h a l l p r e v i o u s w a v e measurements f o r critical values o f Fri„ w i l l be t i m e dependant ( i . e . unsteady), e s p e c i a l l y i n h i g h b l o c k a g e e n v i r o n m e n t s such as r i v e r s o r canals. H o w e v e r , f a c i l i t y l i m i t a t i o n s (i.e. l i m i t e d l e n g t h t o w tanks and test basins), m a y not a l l o w s u f f i c i e n t t i m e f o r the s o l i t o n t o fijlly f o r m or reach a steady state w i t h a beach i n p o s i t i o n . T h e r e f o r e , the c i r c u l a r t r a c k scale m o d e l m a y p r o v i d e the f a c i l i t y t o address t h i s l i m i t a t i o n .
T h e results o f this research m a y be also a p p l i e d t o other a p p l i c a t i o n s such as ship waves generated d u r i n g m a n o e u v r i n g ( c u r v e d tracks) and operations i n restricted w a t e r w a y s . S c i e n t i f i c a l l y , the research p r o v i d e s a m e t h o d to s i g n i f i c a n t l y e x t e n d the fxindamental k n o w l e d g e o f w a v e mechanics.
ACKNOWLEDGIVIENTS
T h e authors w o u l d l i k e to a c k n o w l e d g e the support o f our i n d u s t r y partner Webber Wave P o o l s . W e w o u l d also l i k e t o a c k n o w l e d g e the s u p p o r t o f the A u s t r a l i a n M a r i t i m e C o l l e g e t e c h n i c a l t e a m .
T h e authors w o u l d l i k e to a c k n o w l e d g e the support o f the A u s t r a l i a n Research C o u n c i l t h r o u g h t h e i r a w a r d o f our L i n k a g e P r o j e c t grant L P 0 9 9 0 3 0 7 .
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