Examination of empirical formulas for wave shoaling and breaking on steep slopes

Tsai, Ching‐Piao; Chen, Hongbin; Hwung, Hwung-Hweng; Huang, Ming-Jen

doi:10.1016/j.oceaneng.2004.05.010

Cited by 39 publications

(18 citation statements)

References 18 publications

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“…The wave energy dissipation on the righthand side of eq. (13) could be equal to zero if the energy was assumed without any loss, such as outside the surf zone [19]. According to the Airy wave theory, E = ρgH 2 / 8and the wave shoaling coefficient could be shown as Where, f s is the wave shoaling coefficient and n is the ratio of wave group velocity and the wave phase velocity due to the linear dispersion relation.…”

Section: Wave Energy Equation Wave Shoaling Effectmentioning

confidence: 99%

“…To overcome this shortcoming of the linear mild slope equation, Black and Rosenberg [17] raised a semi-empirical formula, but it is difficult to calculate the combined wave transformation on the coasts. Shuto's empirical nonlinear shoaling equations is applied by Tsai [19] to deduce the wave shoaling coefficient and improve the mild slope equation, which produced better wave heights prediction but emerge restrictions when Ursell number is less than 30.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Extended Elliptic Mild Slope Equation Incorporating the Nonlinear Shoaling Effect

Xiao

et al. 2016

Polish Maritime Research

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Section: Wave Energy Equation Wave Shoaling Effectmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Extended Elliptic Mild Slope Equation Incorporating the Nonlinear Shoaling Effect

Xiao

et al. 2016

Polish Maritime Research

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“…It appears thatx increases as ξ increases for a given slope, and that thex versus ξ dependence decreases as the slope increases. The wave shoaling distance over steep slopes is shorter than on milder slopes due to the wave base effect, implying that significant partial reflection from the steep slope during shoaling causes wave breaking earlier on steeper slopes (Grilli et al, 1995;Tsai et al, 2005). Moreover, the reflection coefficient of waves on sloping sea beds can be calculated using an empirical formula proposed by Battjes (1974):…”

Section: Onset Of Wave Breakingmentioning

confidence: 99%

“…Thus, most of the studies on breaking waves are limited to field and laboratory experiments. Many theories and formulas to predict the breaking wave characteristics have been proposed based on the physical experiments (Goda, 2010;Iwagaki and Sakai, 1972;Tsai et al, 2005). Due to the complexity in describing the wave breaking process, most of the existing formulas are empirical and semi-empirical, and thus subjected to the experimental conditions and scale effects.…”

Section: Introductionmentioning

confidence: 99%

Breaking characteristics and geometric properties of spilling breakers over slopes

Chella

Bihs

Myrhaug

et al. 2015

Coastal Engineering

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A two-phase flow CFD model based on the Reynolds-Averaged Navier-Stokes (RANS) equations coupled with the level set method (LSM) and k − ω turbulence model is used to simulate spilling breakers over a sloping bed. In order to validate the present numerical model, the simulated results are compared with the experimental data measured by Ting and Kirby (1996). The simulated horizontal velocities and free surface elevations are in good agreement with the experimental measurements. Moreover, the present model is able to model the prominent features associated with the breaking process such as the motion of air pockets in the water, formation of a forward moving jet, the splash-up phenomenon and the mixing of air and water in the breaking region. The numerical model has been utilized to study the influences of three important environmental parameters; water depth, offshore wave steepness and beach slope on the characteristics and geometric properties of spilling breakers over slopes. A total of 39 numerical experiment cases are performed to investigate the characteristics of breaking waves such as breaking location, incipient breaker height and water depth at breaking, incipient breaker indices and geometric properties with different offshore wave steepnesses at different water depths over a wide range of beach slopes. The geometric properties associated with breaking waves in shallow water are described using the wave steepness and asymmetry factors introduced by Kjeldsen and Myrhaug (1978). The computed results appear to give reasonable predictions and consistency with previous studies.

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“…Rattanapitikon et al (2003) reported the correlation between H0/L0 and Hb/Lb, proposing a new breaker height formula to estimate Hb, this being updated later in Rattanapitikon and Shibayama (2006). Tsai et al (2005) investigated breaking conditions on steep bottom slopes because most existing equations were based on gentle bottom slopes. Camenen and Larson (2007) compared some of the aforementioned equations and concluded that none achieved more than 50% accuracy, so they proposed a new one which combined trigonometric and offshore steepness relationships.…”

Section: Ii222 Water Depthmentioning

confidence: 99%

Mound Breakwater Design in Depth-Limited Breaking Wave Conditions

Gamboa¹,

Piedad²

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i Agradecimientos Esta tesis doctoral es el fruto de varios años de trabajo, pero su culminación no habría sido posible sin el apoyo y la ayuda de todas aquellas personas importantes que me rodean.A mi padre, por su dedicación y precocupación por mí. Porque sin él, probablemente no estaría escribiendo estas líneas.A mi madre, por su apoyo incondicional, su alegría y su capacidad de ponerse en el lugar del otro. Gracias por estar siempre a mi lado.A mis hermanos, Patricia y Pepe, a los que quiero con locura aunque siempre estemos de 'peleillas'.A mis amigos, porque a pesar de la distancia que nos separa, sois mi segunda familia.A mis compañeros del LPC y departamento, Ainoha, Gloria, Quique, Vicente, Guille, Tomás, César, Pepe, Ana, Esther, Jose Alberto, Joaquín, Miguel…por la ayuda prestada.A Jorge, por todo. Por sus ánimos, su confianza, su paciencia y su ayuda. Porque siempre has estado ahí sin esperar nada a cambio.A mi director de tesis, Josep, quien me ha transmitido su pasión por la ingeniería marítima. Gracias por haberme ofrecido la posibilidad de trabajar contigo, por la ayuda, la confianza y la disponibilidad mostrada todos estos años.Al Ministerio de Educación, Cultura y Deporte, por la financiación brindada a través del programa de Formación de Profesorado Universitario (FPU 13/01872) para la realización de esta tesis doctoral.Al Ministerio de Economía y Competitividad, por la financiación del proyecto ESCOLIF (BIA2012-33967).A Debra Westall, por revisar este documento.iii Resumen El manto principal de los diques en talud suele estar formado por escollera natural o elementos prefabricados de hormigón; su función es resistir la acción del oleaje. Una revisión del estado del arte pone de manifiesto que son numerosas las fórmulas existentes para el diseño de mantos derivadas de ensayos físicos a escala reducida con oleaje sin rotura por fondo. Sin embargo, la mayoría de diques en talud se construyen en la zona de rompientes con oleaje limitado por fondo, donde las ecuaciones de diseño habituales no son del todo válidas. En esta tesis doctoral se analiza la estabilidad hidráulica de mantos bicapa de escollera, a partir de ensayos a escala reducida con pendiente de fondo m=1/50. En base a los resultados obtenidos de los ensayos físicos, se propone una nueva relación potencial para el diseño de mantos de escollera en condiciones de oleaje limitado por fondo, válida para taludes con cotα=1.5, números de estabilidad 0.98≤Hm0/(ΔDn50)≤2.5, y profundidades relativas a pie de dique de 3.75≤hs/(ΔDn50)≤7.50.Cuando el manto principal está formado por elementos de hormigón, es habitual construir una berma de pie que proporciona apoyo a los elementos del manto y, en su caso, colabora en la protección de la zona inferior del dique contra la socavación. Dicha berma suele construirse con escollera natural y su peso está condicionado al de los elementos del manto en el caso de no haber rotura por fondo. El peso de los elementos de la berma de pie suele ser un orden de magnitud inferior al peso de las unidades del manto; ...

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Examination of empirical formulas for wave shoaling and breaking on steep slopes

Cited by 39 publications

References 18 publications

Extended Elliptic Mild Slope Equation Incorporating the Nonlinear Shoaling Effect

Extended Elliptic Mild Slope Equation Incorporating the Nonlinear Shoaling Effect

Breaking characteristics and geometric properties of spilling breakers over slopes

Mound Breakwater Design in Depth-Limited Breaking Wave Conditions

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