A re-assessment of wave run up formulae

Roux, Abraham Pierre (2015-03)

Thesis (MEng)--Stellenbosch University, 2015.

Thesis

ENGLISH ABSTRACT: Over the last few decades, wave run up prediction has gained the interest of numerous researchers and every newly-published paper has aimed to predict wave run up with greater accuracy. Wave run up is defined as the vertical elevation reached by a wave's, front water edge as it runs up a beach, measured relative to the still water line. Wave run up is dependent on the incidental wave height, the wave period, the beach slope and the wave steepness. The majority of publications incorporate all of these factors, but some do not, which has led to numerous debates. The goal of this study is to do a re-assessment of previously published wave run up formulae, to obtain a more informed understanding about wave run up and the available predictive empirical formulae. The study also seeks to evaluate the Mather, Stretch & Garland (2011) formula. The method for undertaking this objective comprised a physical model test series with 10 regular wave conditions on a constant slope, being 1/24, performed with an impermeable floor. Also, a beach study in the field was done on Long Beach, Noordhoek, where run up measurements were taken for 30 minute intervals, resulting in five test conditions. A numerical model was employed in conjunction with the beach study to determine the local offshore wave parameters transformed from a deep water wave rider. This information was used to correlate the run up measurements with known wave parameters. Firstly, the physical model assessment was performed to provide a proper foundation for run up understanding. Plotting empirical normalised run up values (R2/H0 ) versus the Iribarren number for different formulae, a grouping was achieved with upper and lower boundaries. The physical model results plotted on the lower end of this grouping, resulted in prediction differences of more than 10%. These differences may have been caused by the unevenness of the physical model slope or the fact that only one slope had been tested. Despite this, the results fell within a band of wave run up formulae located on the lower end of this grouping. An assessment of the beach measurements in the field gave a better correlation than the physical model results when compared to normalised predicted wave run up formulae. These measurements also plotted on the lower end of the grouping, resulting in prediction differences of less than 10% for some empirical formulae. When comparing these empirical predictions to one another, the results demonstrate that the formulae comparing best with the beach measurements were Holman (1986) and Stockdon, Holman, Howd, & Sallenger Jr. (2006). Extreme over predictions were found by Mase & Iwagaki (1984), Hedges & Mase (2004) and Douglass (1992). Nielsen & Hanslow (1991) only compared best with the beach measurements and De la Pena, Sanchez Gonzalez, Diaz-Sanchez, & Martin Huescar (2012) only compared best to the physical model results. This study supports the formula proposed by Mather, Stretch, & Garland (2011). Applying their formula to the measured results presented a C constant of 3.3 for the physical model and 8.6 for the beach results. Both values are within the range prescribed by the authors. Further reasearch minimized the array of possible „C‟ values by correlating this coefficient to Iribarren numbers. „C‟ values between 3.0~5.0 is prescribed for low Iribarren conditions (0.25-0.4) and values between 7.0~10 for higher Iribarren conditions are 0.75-0.8. However, this formula is still open for operator erros whereby the „C‟ value has a big influence in the final result. The best formulae to use, from results within this thesis, is proposed by Holman (1986) and Stockdon et.al (2006). These formulae are not open to operator erros and uses the significant wave height, deep water wave length and the beach face slope to calculate the wave run up.

AFRIKAANSE OPSOMMING: Gedurende die afgelope paar dekades, het golf-oploop voorspellings die aandag van talle navorsers gelok en elke nuwe geskrewe voorlegging het gepoog om meer akkurate golf-oploop voorspellings te verwesenlik. golf-oploop kan definieer word as die vertikale elevasie bereik deur 'n golf se voorwaterkant soos dit op die strand uitrol, gemeet relatief vanaf die stilwaterlyn. golf-oploop is afhanklik van die invals-golfhoogte, die golfperiode, die strandhelling en die golfsteilheid. Die oorgrote mederheid publikasies uit die literaturr inkorporeer al hierdie faktore, maar sommige nie, wat groot debatvoering tot gevolg het. Die doel met hierdie studie is om vorige gepubliseerde golf- oploop formules te re-evalueer, om 'n meer ingeligte begrip van golf- oploop en beskikbare voorspellende formules te verkry. Die studie poog terselfdertyd ook om golf-opvolg tendense, uniek aan Suid Afrikaanse strande te evalueer deur die huidige formule wat tans hier gebruik word, te assesseer. Om hierdie doelwit te bereik, is gebruik gemaak van 'n fisiese model toets reeks bestaande uit 10 reëlmatige golfstoestande op 'n konstante ondeurlaatbaare strandhelling van 1/24. 'n Veldstudie was ook uitgevoer op Langstrand, Noordhoek, waar golf-oploopmetings met 30 minute tussenposes uitgevoer is, vir vyf toets-toestande. Tesame met die veldstudie, is 'n numeriese model aangewend om die gemete diepsee data nader ann die strand wat bestudeer is te transformeer. Hierdie inligting is benodig om 'n verband tussen tussen oploop-metings en bekende golf parameters te bepaal. Eerstens is die fisiese model assessering uitgevoer om 'n behoorlike basis vir die begrip van golfoploop in die veld te verkry. Deur die emperiese, genormaliseerde oploop waardes (R₂/H₀) vir verkeie formules teenoor die Iribarren getal te plot, is 'n groepering met hoër en laer grense gevind. Daar is gevind dat die fisiese modelwaardes op die laer grens plot, en het verskille met die emperiese waardes van meer as 10% getoon. Hierdie verskille is moontlik veroorsaak as gevolg van 'n oneweredige fisiese model strandhelling of deur die feit dat slegs een helling getoets is. Ten spyte hiervan, het die model oploop waardes binne die bestek van golf- oploop formules geval. Assessering van die veldmetings het 'n beter korrelasie as die fisiese modelresultate getoon, tydens vergelykings met genormaliseerde golf-oploop formules van die emperiese formules. Die oploop waardes van hierdie metings het ook geplot aan die laer grens van die groepering, met verskille van minder as 10% vir die meeste gevalle van die emperiese formules. Wanneer hierdie emperiese voorspellings vergelyk word, is gevind dat die formules wat die beste ooreenstem met die fisiese model, die van Holman (1986) en Stockdon, Howd, & Sallenger Jr. (2006) is. Die emperiese formules van Mase & Iwagake (1984), Hedges & Mase (2004) en Douglas (1992) het die golf-oploop oorvoorspel. Nielsen & Hanslow (1991) het slegs die beste met die strandmetings vergelyk, terwyl De la Pena, Sanchez Gonzalez, Diaz-Sanchez & Martin Huescar (2012) slegs die beste vergelyk het met die fisiese-model resultaat. Hierdie studie ondersteun die formule voorgestel deur Mather, Stretch, & Garland (2011). Deur hul formules op die gemete bevindings toe te pas, is 'n C konstante van 3.3 vir die fisiese model resultate, en 8.0 vir die stranduitlslae bepaal. Beide waardes lê binne die grense wat deur die outeurs voorgestel is. Verdere navorsing het getoon dat moontlike waardes vir die „C‟ konstante tussen 3.0 en 5.0 moet wees vir Iribarren waardes van tussen 0.25 en 0.4. Vir hoër Iribarren waardes, 0.75-0.8, moet die „C‟ kosntante tussen 7.0 en 10 wees; dog is die formule steeds oop vir operateur foute. Die hoofbevindinge van die tesis is gevind dat die beste golf-oploop formules, om tans te gebruik, die van Holman (1986) en Stockdon et.al (2006) is. Hierdie formules kan glad nie beinvloed word deur operateurs foute nie en maak gebruik van die invals golfhoogte, die golfperiode en die strandhelling om die golf-oploop te bepaal.

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