scholarly journals An Extended Analytic Solution of Combined Refraction and Diffraction of Long Waves Propagating over Circular Island

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Yu-Shu Kuo ◽  
Tai-Wen Hsu ◽  
Chia-Cheng Tsai ◽  
Yu-Hsuan Huang
Keyword(s):  
Wave Scattering ◽  
Analytic Solution ◽  
Complex Variables ◽  
Long Waves ◽  
Wave Refraction ◽  
Long Wave ◽  
Present Solution ◽  
Circular Island ◽  
Frobenius Series ◽  
Independent Parameters

An analytic solution of long waves scattering by a cylindrical island mounted on a permeable circular shoal was obtained by solving the linear long wave equation (LWE). The solution is in terms of the Bessel function expressed by complex variables. The present solution is suitable for arbitrary bottom configurations described by a power function with two independent parameters. For the case of the paraboloidal shoal, there exists a singular point (α=2) which can be removed using Frobenius series, whereαis a real constant. The present solution is reduced to Yu and Zhang’s (2003) solution for impermeable circular shoal. The numerical results show some special features of the combined effect of wave refraction and diffraction caused by a porous circular island. The effect of key parameters of the island dimension, the shoal slope, and permeability on wave scattering was discussed based on the analytic solution.

5. Long Waves and Conjunctures of Democratization

2018 ◽  
pp. 67-81
Author(s):  
Dirk Berg-Schlosser
Keyword(s):  
Eighteenth Century ◽  
Long Waves ◽  
Political Equality ◽  
Short Term ◽  
Late Eighteenth Century ◽  
Long Wave ◽  
Late Eighteenth ◽  
The Future ◽  
History Of

This chapter focuses on the history of democratization since the late eighteenth century. It introduces the concepts of ‘waves’ (trends) and ‘conjunctures’ (briefer turmoils) and delineates the major developments in this respect. In this way, the major long-term and short-term factors leading to the emergence and breakdowns of democracies are also highlighted. The first long wave occurred during the period 1776–1914, followed by the first positive conjuncture in 1918–19, the second long wave (with some intermittent turbulences) in 1945–88, and the latest conjuncture in 1989–90. The chapter identifies the main ingredients to democratization throughout history, namely: republicanism, representation, and political equality. It concludes by considering some of the current perspectives and dangers for the future of democracy.

Analytical study on long wave refraction over a dredge excavation pit

Wave Motion ◽  
2011 ◽  
Vol 48 (3) ◽  
pp. 259-267 ◽  
Author(s):  
Xiaojing Niu ◽  
Xiping Yu
Keyword(s):  
Analytical Study ◽  
Wave Refraction ◽  
Long Wave

scholarly journals Upstream Propagating Long-Wave Modes at a Microtidal River Mouth

2020 ◽  
Vol 2 (1) ◽  
pp. 15
Author(s):  
Matteo Postacchini ◽  
Lorenzo Melito ◽  
Alex Sheremet ◽  
Joseph Calantoni ◽  
Giovanna Darvini ◽  
...  
Keyword(s):  
Wave Propagation ◽  
Field Data ◽  
Tide Gauge ◽  
Low Frequency ◽  
River Mouth ◽  
Long Waves ◽  
Tidal Forcing ◽  
Long Wave ◽  
Low Frequency Waves ◽  
Wave Modes

We illustrate recent findings on the upriver propagation of long waves entering the mouth of the Misa River (Senigallia, Italy). Such a microtidal environment has been recently studied to understand river–sea interactions: it has been found that the river forcing dominates over the marine actions in winter, especially during storms. However, upriver wave propagation is not negligible with low-frequency waves propagating upriver for distances of the order of kilometers. With the aim to better understand the behavior of low-frequency waves propagating upriver, the analysis of the present work builds on field data collected by instruments installed close to the mouth and along the final reach of the Misa River: a tide gauge, two hydrometers and an acoustic Doppler sensor. It has been here observed that the tidal forcing (periods of the order of hours/days) is significantly strong at a distance of more than one kilometer from the river mouth, while shorter waves, like seiches (periods of some hours), are less important and are supposed to largely dissipate at the estuary, although their role could be of importance during relatively short events (e.g., floods).

Propagation of obliquely incident water waves over a trench

1983 ◽  
Vol 133 ◽  
pp. 47-63 ◽  
Author(s):  
James T. Kirby ◽  
Robert A. Dalrymple
Keyword(s):  
Numerical Solution ◽  
Water Waves ◽  
Analytic Solution ◽  
Small Scale ◽  
Obliquely Incident ◽  
Long Wave ◽  
Propagating Waves ◽  
Tank Experiment ◽  
Wave Region ◽  
Wave Limit

The diffraction of obliquely incident surface waves by an asymmetric trench is investigated using linearized potential theory. A numerical solution is constructed by matching particular solutions for each subregion of constant depth along vertical boundaries; the resulting matrix equation is solved numerically. Several cases where the trench-parallel wavenumber component in the incident-wave region exceeds the wavenumber for freely propagating waves in the trench are investigated and are found to result in large reductions in wave transmission; however, reflection is not total owing to the finiteness of the obstacle.Results for one case are compared with data obtained from a small-scale wave-tank experiment. An approximate solution based on plane-wave modes is derived and compared with the numerical solution and, in the long-wave limit, with a previous analytic solution.

Numerical and Experimental Investigations of Wave Field Around a Circular Island with the Presence of Weak Currents

2002 ◽  
Vol 18 (1) ◽  
pp. 35-42
Author(s):  
Ming-Chung Lin ◽  
Chao-Min Hsu ◽  
Shou-Cheng Wang ◽  
Chao-Lung Ting
Keyword(s):  
Experimental Data ◽  
Wave Field ◽  
Wave Height ◽  
Incident Wave ◽  
Numerical Calculations ◽  
Experimental Investigations ◽  
Wave Refraction ◽  
Circular Island ◽  
Incident Waves ◽  
A Current

ABSTRACTThis study elucidated the complicated phenomena of wave refraction and diffraction around a circular island due to random incident waves traveling with a current. Various combinations of random incident wave and current conditions were used to investigate the wave height distributions around a circular island numerically and experimentally. Numerical calculations were carried out based on the theory derived by Lin & Hsu [1]. According to the results, it shows that numerical calculations can predict experimental data quantitatively well.

Scattering of long waves around a circular island mounted on a conical shoal

Wave Motion ◽  
1996 ◽  
Vol 23 (4) ◽  
pp. 353-362 ◽  
Author(s):  
Songping Zhu ◽  
Yinglong Zhang
Keyword(s):  
Long Waves ◽  
Circular Island

A nonlinear mechanism for the generation of sea waves

1969 ◽  
Vol 311 (1506) ◽  
pp. 371-389 ◽  
Keyword(s):  
Wave Propagation ◽  
Surface Waves ◽  
Orbital Motion ◽  
Long Waves ◽  
Shear Instability ◽  
Sea Waves ◽  
Short Waves ◽  
Long Wave ◽  
Nonlinear Mechanism ◽  
Surrounding Fluid

Recent observations of the growth of sea waves under the action of wind have established that the rate of growth is several times greater than has yet been accounted for. In this paper a new mechanism of wave generation is proposed, based on the idea of a maser-like action of the short waves on the longer waves. It is shown that when surface waves decay they impart their momentum to the surrounding fluid. Short waves are readily regenerated by shear instability. But a longer wave passing through shorter waves causes the short waves to steepen on the long-wave crests. Hence the short waves impart more of their momentum to the crests of the long waves, where the orbital motion of the long waves is in the direction of wave propagation. If the short waves are decaying only weakly (under the action of viscosity), the effect on the long waves is slight. But when the short waves are forced to decay strongly by breaking on the forward slopes of the long waves the gain of energy by the latter is greatly increased. Calculations suggest that the mechanism is capable of imparting energy to sea waves at the rate observed.

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