Spectral Wave Attenuation by Bottom Friction: Experiments

Madsen, Ole Secher; Rosengaus, Moises Michel

doi:10.1061/9780872626874.064

Cited by 4 publications

(4 citation statements)

References 4 publications

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“…The practical limitation of the present results is that they require a priori knowledge of the bottom roughness, kb. Experimental results directed towards overcoming this limitation are presented in a companion paper by Madsen and Rosengaus (1988).…”

Section: Discussionmentioning

confidence: 99%

Spectral Wave Attenuation by Bottom Friction: Theory

Madsen

Poon

Graber

1988

Int. Conf. Coastal. Eng.

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160

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Based on the linearized form of the boundary layer equations and a simple eddy viscosity formulation of shear stress, the turbulent bottom boundary layer flow is obtained for a wave motion specified by its directional spectrum. Closure is obtained by requiring the solution to reduce, in the limit, to that of a simple harmonic wave. The resulting dissipation is obtained in spectral form with a single friction factor determined from knowledge of the bottom roughness and an equivalent monochromatic wave having the same root-mean-square near-bottom orbital velocity and excursion amplitude as the specified wave spectrum. The total spectral dissipation rate is obtained by integration and compared with the average dissipation obtained from a model considering the statistics of individual waves defined by their maximum orbital velocity and zero-crossing period. The agreement between the two different evaluations of total spectral dissipation supports the validity of the spectral dissipation model.

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Section: Discussionmentioning

confidence: 99%

Spectral Wave Attenuation by Bottom Friction: Theory

Madsen

Poon

Graber

1988

Int. Conf. Coastal. Eng.

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160

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“…They were placed along the bottom of the flume at 10 cm intervals, crest to crest, measured perpendicular to their axes. The height and spacing of the ripples were chosen to represent the bed form characteristics observed by Madsen and Rosengaus [1989] in wave experiments over a movable bed. In the present experiments, four configurations were used depending on the angle of incidence 0 (0 ø, 30 ø, 45 ø and 60 ø) between the ripple axis and the y direction as shown in Figure 2a.…”

Section: Methodsmentioning

confidence: 99%

Near‐bottom flow and flow resistance for currents obliquely incident to two‐dimensional roughness elements

Barrantes¹,

Madsen²

2000

J. Geophys. Res.

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Abstract. Measurements of the three components of the velocity when a steady current is flowing over a rippled bottom are presented. The bottom consisted of equally spaced triangular bars placed at angles of 0 ø, 30 ø, 45 ø, and 60 ø to the incident flow. The experiments show that close to the bottom, there is a transverse component of the velocity, which, for the larger angles of incidence, can be of the same order of magnitude as the main flow. The spatial average velocity profiles obtained from the measurements performed between two ripple crests show that close to the bottom, there is a well-defined logarithmic region. The bottom roughness obtained by fitting a logarithmic law in the near-bottom region to the longitudinal component of the flow depends strongly on the angle of incidence. In contrast, the analysis of the near-bottom velocity component in the direction perpendicular to the ripple axis shows that the bottom roughness is independent of the angle of incidence. These experimental observations support the concept of a direction-dependent equivalent bottom roughness when currents are obliquely incident to two-dimensional bottom roughness elements, such as wave-generated ripples. IntroductionThe characterization of the bottom roughness experienced by combined wave-current flows over a rippled bed is important for the description of many physical processes on continental shelves. When ripples are present on the seabed, the main contribution to the bottom roughness is the pressure form drag produced by flow separation at the ripple crests. In the coastal environment, waves and currents are generally not in the same direction. In shallow water, waves tend to be perpendicular to the shore because of refraction, whereas currents tend to be more or less parallel to the shore. Field and laboratory observations have shown that in a wave-dominated environment a two-dimensional ripple bed form aligned with the wave crests is formed. The ripple axis is perpendicular to the direction of wave propagation and at an angle to the incident current. In this situation it is not clear that the bottom roughness length scale describing the bed resistance experienced by the current is the same as the one experienced by the In this case the bottom roughness is expected to be smaller than the one experienced by the same current when it is incident perpendicular to the ripples. This simple argument based on the concept of a drag force suggests that the bottom roughness experienced by the current will depend on the angle between the current direction and the ripple axis, i.e., on the angle between waves and currents. This hypothesis is supported by field experiments performed on the inner shelf of northern California by Drake and Cacchione [1992]. The horizontal components of the velocity were measured up to 1 m above the bottom. The bottom topography was also characterized by symmetrical wave generated ripples. The analysis of the experiments revealed a correlation between the bottom roughness and the angle between the current...

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“…According to Nelson [66], the breaking parameter for wave breaking caused by changes in depth can be determined by considering the bottom slope and depth, and a value of 0.46 improves the wave setup estimations instead of the default value of 0.54. The bottom friction applied was the Madsen et al [67] formulation with an equivalent roughness length scale of 0.05 providing a more reasonable wave height than the default bottom friction JONSWAP [68]. The bottom drag formulation was computed using Manning's value of n = 0.22 for reefs [25], and wind drag was computed using the Garratt formulation [69].…”

Section: Adcirc and Swan Modelsmentioning

confidence: 99%

Quantifying Mechanisms Responsible for Extreme Coastal Water Levels and Flooding during Severe Tropical Cyclone Harold in Tonga, Southwest Pacific

Tu’uholoaki

Espejo

Wandres

et al. 2023

JMSE

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The South Pacific region is characterised by steep shelves and fringing coral reef islands. The lack of wide continental shelves that can dissipate waves makes Pacific Island countries vulnerable to large waves that can enhance extreme total water levels triggered by tropical cyclones (TCs). In this study, hindcasts of the waves and storm surge induced by severe TC Harold in 2020 on Tongatapu, Tonga’s capital island, were examined using the state-of-the-art hydrodynamic and wave models ADCIRC and SWAN. The contributions of winds, atmospheric pressure, waves, and wave-radiation-stress-induced setup to extreme total water levels were analysed by running the models separately and two-way coupled. The atmospheric pressure deficit contributed uniformly to the total water levels (~25%), while the wind surge was prominent over the shallow shelf (more than 75%). Wave setup became significant at locations with narrow fringing reefs on the western side (more than 75%). Tides were dominant on the leeward coasts of the island (50–75%). Storm surge obtained from the coupled run without tide was comparable with the observation. The wave contribution to extreme total water levels and inundation was analysed using XBEACH in non-hydrostatic mode. The model (XBEACH) was able to reproduce coastal inundation when compared to the observed satellite imagery after the event on a particular coastal segment severely impacted by coastal flooding induced by TC Harold. The coupled ADCIRC+SWAN underestimated total water levels nearshore on the reef flat and consequently inundation extent as infragravity waves and swash motion are not resolved by these models. The suite of models (ADCIRC+SWAN+XBEACH) used in this study can be used to support the Tonga Meteorological Service Tropical Cyclone Early Warning System.

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Spectral Wave Attenuation by Bottom Friction: Experiments

Cited by 4 publications

References 4 publications

Spectral Wave Attenuation by Bottom Friction: Theory

Spectral Wave Attenuation by Bottom Friction: Theory

Near‐bottom flow and flow resistance for currents obliquely incident to two‐dimensional roughness elements

Quantifying Mechanisms Responsible for Extreme Coastal Water Levels and Flooding during Severe Tropical Cyclone Harold in Tonga, Southwest Pacific

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