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Fundamental Physics
Published in Vanesa Magar, Sediment Transport and Morphodynamics Modelling for Coasts and Shallow Environments, 2020
As waves refract, they also become steeper, a process known as wave shoaling. Waves shoal due to conservation of wave energy flux, which causes the wave height to increase as the waves propagate into shallower water. If Hi is the wave height at depth hi, with hi decreasing as i increases, then Hi+1Hi=(cos αicos i+1)1/2(cgicg(i+1))1/2,
The offshore environment
Published in White David, Cassidy Mark, Offshore Geotechnical Engineering, 2017
A final class of wave deserving mention comprises tsunamis. Tsunamis are impact waves that can be caused by earthquakes, volcanic eruptions or submarine slides with sufficient impact to vertically displace the overlying water. In the open ocean, tsunami waves have a small wave height and a very long wavelength and can go unnoticed. A tsunami wave often has a wave height of less than a metre and a wavelength of tens or hundreds of kilometres compared to an everyday wind wave with a height of 2 m or so and a wavelength of 100–200 m. As tsunami waves approach shore, they are slowed down, reduce in length and grow in height in a process known as ‘wave shoaling’. The top of the wave moves faster than the bottom, causing the sea to rise dramatically and produce a distinctly visible wave. Tsunami waves do not generally break when they approach shore, unlike wind generated waves, but act more like a fast flowing tide that travels far onshore (hence the term ‘tidal wave’, although the waves have nothing to do with tides). A tsunami may comprise several waves, which may reach shore over a period of hours due to the long wavelength, and the first wave is not always the most severe. About 80 per cent of tsunamis occur in the Pacific Ocean but have been recorded at most major subduction zones (see Figure 2.2). Detailed information on tsunamis is provided by the National Oceanographic and Atmospheric Administration (NOAA) Centre for Tsunami Research (http://nctr.pmel.noaa.gov), the US Geological Survey Centre for Tsunami and Earthquake Research (http://walrus.wr.usgs.gov/tsunami) and the International Centre for Geohazards (www.geohazards.no).
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Published in Splinter Robert, Illustrated Encyclopedia of Applied and Engineering Physics, 2017
[fluid dynamics] In shallow water there is deviation from linear behavior in flow conditions. Liquid packages will be considered to circulate in closed loops during wave motion, however the particles moving with the wave motion and with the flow in the exterior of the wave have a higher velocity than liquid packages in the submerged part of the fluid, which is moving in the opposite direction as the surface package flow and against the fluid-flow direction breaking the presumed circular package pattern. A net fluid-package motion can be defined that accounts for this nonlinearity in a second order phenomena. This phenomena also contributes to the description of the occurrence of undertow. The second-order liquid flow average velocity (νStokes) is described by the Stokes-drift as νStokes=CStokes(awk)2e−2kba where the average depth of the liquid level is ha, the wavenumber is k = 2π/λ, CStokes is a constant and aw is amplitude of the wave. When the wave amplitude is in the range of the depth of the water a phenomenon called wave-shoaling occurs. During wave shoaling the water waves are subject to refraction, generating so called longshore currents. This nearshore circulation can cause hazardous swimming conditions with longshore current velocities reaching 2.5 m/s, and rip current velocities on the order of 1.5 m/s. This dispersion is associated with the phase and group velocities and is linked to the high waves followed by low waves, generating a periodic fluctuation in water level, referred to as “surf beat,” a pulsation effect. These rip currents can have a history tracing outward into sea for over 1.5 km (see Figure S.110).
Numerical investigation of wave propagation and transformation over a submerged reef
Published in Coastal Engineering Journal, 2019
Jinxuan Li, Jun Zang, Shuxue Liu, Wei Jia, Qiang Chen
Figure 6 shows the comparisons of the average wave heights between numerical results and experimental data for these three cases. At the locations in front of the reef, because of the reflection of the reef, wave heights are fluctuant. Thus, the wave heights listed in Table 1 are the results measured at location 1#, rather than the values inputted at the wavemaker in the experiment. For instance, in case A, the input wave height value is 0.093m. When a wave propagates on the reef flat, wave heights become larger due to wave shoaling, before wave breaking occurs. After wave breaking, wave heights decrease significantly due to energy dissipation. From Figure 6, it can also be seen that the present numerical model predicts the wave height accurately.
A study of long wave run-ups on a bi-linear beach slope induced by solitary and transient-focused wave group
Published in Coastal Engineering Journal, 2019
Haeng Sik Ko, Patrick J. Lynett
The wave amplitude spectra with low-frequency increase over nearshore regions because the wave amplitudes with low-frequency become increased in shallow water due to wave shoaling and the energy is transferred from the waves with higher frequency.