Significant of Edge Waves and Shear Waves - Essay Example

Order # 154744 Significant of Edge Waves and Shear Waves Introduction Waves are caused by wind, it changes the water's surface and made it into the ripples and then into waves. Waves travel effortlessly along the water's surface. This is made possible by small movements of the water molecules. As waves grow in height, the wind pushes them along faster and higher. Waves can become unexpectedly strong and destructive. As waves enter shallow water, they become taller and slow down, eventually breaking on the shore.There are several types of waves; among them are the edge wave and the shear wave. The paper will able to evaluate the significant of the edge wave and the shear wave. Edge Waves Edge waves or low frequency gravity motion waves are water waves that are trapped at the shoreline by refraction. It is produce by the variability of wave energy reaching shore. An edge-wave is a low frequency wave attached to the beach. The edge waves have periods of a minute, a long-shore wave-length of around a kilometer, and amplitude that decays exponentially offshore as shown in figure 1 (Cutchin and Smith, 1973).While they were originally considered to be a curiosity, these waves play a significant role in near shore hydrodynamics. (Eckart C., 1951). Figure 1 Computer-assisted sketch of an edge wave. Such waves exist in the breaker zone near the beach and on the continental shelf. From Cutchin and Smith (1973). The edge waves are modeled by creating incident waves that approach perpendicular to the direction of the constructed shoreline. The numerical modeling of edge waves was first described by Stokes equation in 1946. Eq.1 = standing edge wave height Ae = constant Ke = edge wave number X = distance from shore line = slope of beach A further numerical model is used to demonstrate the dispersion relation. It proposes for a given frequency that only mode of edge wave is able to be excited. Eq.2 Shear Wave Shear Wave is also known as the voticity wave. The stability of a steady alongshore current V(x) to small perturbations using a linear vorticity equation based on the shallow water equations and the rigid-lid approximation. They showed that in the region of strong seaward shear (d|V|/dx < 0), instabilities develop in the form of alongshore propagating velocity oscillations (shear waves). Ratios between variances of shear wave velocities and associated pressure fluctuations scale roughly as Whereas the velocity to pressure variance ratios of the individual u and components of gravity waves are sensitive to the edge-leaky wave mode mix the normalized ratio of total velocity to pressure variance R, is 1 (i.e., equi-partitioning of kinetic and potential energy) independent of the mode mix. For shear waves , R = O(gh/V2), that is, 1 for natural alongshore currents with typically small Froude numbers (e.g., Oltman-Shay et al. 1989). Hence, can be used to estimate the contributions of gravity waves and shear waves to the infragravity band. If the gravity and shear wave velocity fluctuations are assumed to be statistically independent, then the fraction of the infragravity velocity variance contributed by shear waves is approximately given by = 1 1/R.(17). The effects of Shear and Edge Wave in the Environment The shape of the land under sea determines the strength and direction of the wave toward the coastline, while above ground it determines the run-up. Since the generation of a wave is defined by transferance of energy, or force in simple mathematical terms, the decrease in sea floor depth has the proportional effect of focusing and speeding up the movement of the wave. Thus a wave generated from a large, deep body of water will produce larger waves than those produced from a shallower body of water. Beach coastlines. As shown by Adams & Lewis, (1979) offshore coastline has a modifying effect on the wave shape as it breaks on land. The most destructive waves are where the force of the wave is focused as it breaks on land. Beaches, with their concave sea floor relief are thus more susceptible are than promontories to damage from a tsunami of equal force, because the convex relief of the sea floor deflects the wave off centre and out to the side. Beach breaking waves have potentially more threat for two reasons. Land behind beaches tends to be lower than land behind promontories; therefore the penetration by a wave would be greater. Secondly, populations tend to congregate around beaches for reasons of leisure, and practicality of access for fishing vessels. Estuarine shorelines Low tides, where the water's edge recedes off shore due to lowering of the sea level have a mitigating effect of reducing the threat of tsunami. Combined with a high tide period where the sea level is higher and closer in shore, tsunamis pose more of threat. A tsunami hitting an estuarine environment will also have devastating effects for several important reasons. Since estuarine environments are not subject to normal wave action from the sea, only indirect tidal influences, the coastline topography can be quite different, particularly with large delta regions such as Zhujiang. Most of the land mass around the shorelines of a delta region is flat, and barely above the water line, and is somewhat static. In this type of environment, populations can and do congregate very close to shorelines, due to the lesser apparent wave threat (bearing in mind that people are thinking of ocean waves, not tsunamis), and also because of the easy access to plentiful food supplies. Most of these coastal communities have a lifestyle that revolves around water, fishing, boating, washing and irrigation are all activities associated with estuarine lifestyle. This familiarity with close proximity to water would lead people to have less fear of water, and hence possibly, less caution. Rivers Secondary to tsunami effects on coastlines, is the effect of the wave as it travels up rivers. Henry & Murty (1995) described the process of "resonance amplification", where the wave grows as it travels higher upstrem. Another effect is wave shear, where the river banks and their features are "scraped" by trapped "edge waves" as it travels upstream. This effect is almost identical in mechanics to tide surges and storm surges, and has been mentioned by Carrier in a paper on transverse waves travelling parallel to coastlines (Carrier, 1995) Sloped Shorelines Slopes cause a very destructive tsunami phenomenon known as run-up, where the wave will wash in over land, and the inertia will carry the water inland and push it up the slopes of a hill or mountain range, where it will then wash down, back into the sea. Historically, some absolutely incredible elevations have been reached by run-up. Classifying Waves Ways to classify waves: Disturbing force Free waves vs. forced waves Restoring force Wavelength Disturbing Force Wind waves: from wind energy - Seiche (really a function of shape of basin) - Tsunami: from seismic energy - Tides: gravitation attraction of moon and sun Free waves vs. forced waves Free waves moves without any further influence from the force that created them Forced waves movement is dependant upon the force that creates them Restoring Force The dominant force trying to return the water surface to flatness after a wave has formed If successful, energy would be transferred as heat not a wave Small waves (wavelengths < 1.73 cm) Surface tension Form capillary waves First waves to form when the wind blows Larger waves (wavelengths > 1.73 cm) Gravity Pulls crest down Wave moving forward, so crest becomes a trough Causes circular orbits of individual water molecules Can travel thousands of miles Wavelength Deep and Shallow water waves - Water depth a major control of wave characteristics - Water depth controls the shape of water orbits - Wave interact with bottom when water depth < wavelength - Below this depth orbits contain little energy - Called deep water waves Conclusion Estimates of velocity to pressure variance ratios indicate that shear waves contribute significantly (as much as 75%) to the total infragravity velocity variance in the region of strong seaward shear of the alongshore current profile. Both shoreward and seaward of this region the observed ratios are approximately equal to the gravity wave value g/h, indicating an infragravity spectrum composed primarily of gravity (edge and/or leaky) waves. Strong shear wave activity is consistently observed in the region of strong shear in the alongshore current, independent of large changes in the beach profile. This result is qualitatively consistent with numerical results of Dodd and Thornton (1990). The wave causes the tsunami which may cause a large destruction of the environment. It may be preempted by proper studying the location of the beaches as well as the present waves in this location. Thus a wave generated from a large, deep body of water will produce larger waves than those produced from a shallower body of water. Construction of buildings in this site maybe done according to the strength of the wave. People may be advised to stay away from these beaches to avoid incidents such as death and destruction due to tsunami. References: 1. Adams, W. M., Lewis, C. H., (1979) "Type Areas For Predicting Tsunami Inundation" Proceedings, Tsunami Symposium Canberra, December 1979, Griffith University and Intergovernmental Oceanographic Commission, p. 59-78 2. Carrier, G. F., (1995) "On-Shelf Tsunami Generation And Coastal Propagation" Tsunami: Progress in Prediction, Disaster Prevention and Warning. 1995 Kluwer Academic Publishers, Netherlands, p. 1 - 20 3. Cutchin D.L., and R.L. Smith. 1973. Continental shelf waves: Low-frequency variations in sea level and currents over the Oregon continental shelf. Journal of Physical Oceanography 3 (1): 73-82. 4. Dodd, N., and E. B. Thornton, 1990: Growth and energetics of shear waves in the nearshore. J. Geophys. Res., 95, 16075-16083 5. Henry, R.F. & Murty ,T.S. (1995) "Tsunami Amplification Due to Resonance in Alberni Inlet: Normal Modes" Tsunamis In The World: The Fifteenth International Tsunami Symposium, 1991. Kluwer Academic Publishers, Netherlands. p 117 6. Stewart, R. (2005), Chapter 17 Coastal Processes and Tides: http://oceanworld.tamu.edu/resources/ocng_textbook/chapter17/chapter17_01.htm 7. http://www.student.uwa.edu.au/cousem01/fm_edgewaves.htm 8. http://www.asian.gu.edu.au/tsunami/land.htm Read More