scholarly journals Introduction: some recent developments of nonlinear water wave theory

2007 ◽  
Vol 365 (1858) ◽  
pp. 2195-2201 ◽  
Author(s):  
Adrian Constantin
Keyword(s):  
Water Waves ◽  
Water Wave ◽  
Mathematical Theory ◽  
Wave Theory ◽  
Research Literature ◽  
Recent Developments

The opening article of this issue is intended to provide a review of some relevant topics of the mathematical theory of water waves that have recently received considerable attention in the research literature. We also provide a brief discussion about the content and contribution of the articles that make up this issue.

scholarly journals WATER WAVE SCATTERING BY A THIN VERTICAL SUBMERGED PERMEABLE PLATE

2021 ◽  
Vol 26 (2) ◽  
pp. 223-235
Author(s):  
Rupanwita Gayen ◽  
Sourav Gupta ◽  
Aloknath Chakrabarti
Keyword(s):  
Integral Equation ◽  
Water Waves ◽  
Water Wave ◽  
Wave Theory ◽  
Hypersingular Integral Equation ◽  
Cauchy Type ◽  
Hypersingular Integral ◽  
Permeable Plate ◽  
Linear Water Wave Theory ◽  
Surface Water Waves

An alternative approach is proposed here to investigate the problem of scattering of surface water waves by a vertical permeable plate submerged in deep water within the framework of linear water wave theory. Using Havelock’s expansion of water wave potential, the associated boundary value problem is reduced to a second kind hypersingular integral equation of order 2. The unknown function of the hypersingular integral equation is expressed as a product of a suitable weight function and an unknown polynomial. The associated hypersingular integral of order 2 is evaluated by representing it as the derivative of a singular integral of the Cauchy type which is computed by employing an idea explained in Gakhov’s book [7]. The values of the reflection coefficient computed with the help of present method match exactly with the previous results available in the literature. The energy identity is derived using the Havelock’s theorems.

scholarly journals Approximation Models For Water Wave Equations

2019 ◽  
Vol 7 (08) ◽  
Author(s):  
Leonard Bezati ◽  
Shkelqim Hajrulla ◽  
Kristofor Lapa
Keyword(s):  
Phase Velocity ◽  
Water Waves ◽  
Water Wave ◽  
Wave Equations ◽  
Kdv Equation ◽  
Wave Theory ◽  
Finite Volume Methods ◽  
Linear Water Wave Theory ◽  
The Best Approximation ◽  
Non Linear

Abstract: In this work we are interested in developing approximate models for water waves equation. We present the derivation of the new equations uses approximation of the phase velocity that arises in the linear water wave theory. We treat the (KdV) equation and similarly the C-H equation. Both of them describe unidirectional shallow water waves equation. At the same time, together with the (BBM) equation we propose, we provide the best approximation of the phase velocity for small wave numbers that can be obtained with second and third-order equations. We can extend the results of [3, 4].  A comparison between the methods is mentioned in this article. Key words:  C-H equation, KdV equation, approximation, water wave equation, numerical methods. --------------------------------------------------------------------------------------------------------------------- [3]. D. J. Benney, “Long non-linear waves in fluid flows,” Journal of Mathematical           Physics, vol. 45, pp. 52–63, 1966. View at Google Scholar · View at Zentralblatt MATH  [4]. Bezati, L., Hajrulla, S., & Hoxha, F. (2018). Finite Volume Methods for Non-Linear          Eqs. International Journal of Scientific Research and Management, 6(02), M-  2018. 

scholarly journals A SHALLOW WATER DIRECTIONAL WAVE RECORDER

1984 ◽  
Vol 1 (19) ◽  
pp. 20
Author(s):  
S.J. Buchan ◽  
R.K. Steedman ◽  
S.A. Stroud ◽  
D.G. Provis
Keyword(s):  
Shallow Water ◽  
Water Wave ◽  
Wave Theory ◽  
Wave Climate ◽  
Shallow Water Wave ◽  
Routine Basis ◽  
Recent Developments ◽  
Small Craft ◽  
Directional Wave ◽  
Wave Recorder

Shallow water wave theory shows that estimates of directional wave climate may be obtained from the measurement of near-bottom pressure and horizontal velocity components. Recent developments in low powered sensors and high density data loggers, incorporated into a bottom-mounted directional wave recorder, make the collection of directional shallow water wave data possible on a routine basis. The instrument is compact, robust, reliable and easily manageable from small craft, providing deployment capacities of up to four months. Analysis methods have been developed which provide for conversion of the recorded data to useful, convenient information.

scholarly journals SCOUR OF SAND BEACHES IN FRONT OF SEAWALLS

1968 ◽  
Vol 1 (11) ◽  
pp. 40 ◽  
Author(s):  
John B. Herbich ◽  
Stephen C. Ko
Keyword(s):  
Mathematical Model ◽  
Shallow Water ◽  
Water Waves ◽  
Water Wave ◽  
Wave Theory ◽  
Beach Erosion ◽  
Theoretical Development ◽  
Scour Depth ◽  
Shallow Water Waves ◽  
Boundary Layer Equations

Many previous studies were confined to problem of beach erosion due to waves breaking on the structure. The investigation reported here involved regular non-breaking, shallow water waves progressing toward a seawall. An analytical solution was developed and compared with laboratory- scale experiments. The shallow-water wave theory and boundary layer equations were used in theoretical development, which resulted in a mathematical model for the ultimate scour depth in front of a seawall.

Assessment and Orff Schulwerk Pedagogy

2019 ◽  
pp. 538-560
Author(s):  
Daniel Johnson
Keyword(s):  
Teacher Educators ◽  
Authentic Assessment ◽  
Research Literature ◽  
National Standards ◽  
International Adoptions ◽  
Practical Applications ◽  
Orff Schulwerk ◽  
Recent Developments ◽  
Based Instruction ◽  
Assessment Strategies

This chapter on assessing student learning and Orff Schulwerk examines the foundations of this approach, its focus on creativity, and practical applications of this pedagogy. By reviewing current research literature and international adoptions of the Schulwerk, the chapter focuses on three assessment-related challenges: a lack of clearly defined teaching practices, a de-emphasis of evaluation in the Orff process, and inherent challenges related to assessing creativity. An examination of professional resource documents and recent developments in national standards provides ways to address each of these assessment challenges in Orff-based instruction. A discussion of curricular levels offers more possibilities for enhancing authentic assessment strategies. Practical recommendations for Orff Schulwerk teachers to improve their assessment protocols and implications for teacher-educators conclude this chapter.

scholarly journals An alternative approach to study irrotational periodic gravity water waves

2021 ◽  
Vol 72 (4) ◽  
Author(s):  
Biswajit Basu ◽  
Calin I. Martin
Keyword(s):  
Free Surface ◽  
Water Waves ◽  
Water Wave ◽  
Wave Problem ◽  
Water Wave Problem ◽  
Stagnation Points ◽  
Alternative Approach ◽  
New Formulation ◽  
Bounded Below ◽  
Surface Dynamic

AbstractWe are concerned here with an analysis of the nonlinear irrotational gravity water wave problem with a free surface over a water flow bounded below by a flat bed. We employ a new formulation involving an expression (called flow force) which contains pressure terms, thus having the potential to handle intricate surface dynamic boundary conditions. The proposed formulation neither requires the graph assumption of the free surface nor does require the absence of stagnation points. By way of this alternative approach we prove the existence of a local curve of solutions to the water wave problem with fixed flow force and more relaxed assumptions.

scholarly journals A Broadband High-Diffraction-Efficiency Electro-Optic Bragg Deflector Based on Monolithic Dual-Grating Periodically-Poled Lithium Niobate

Photonics ◽  
2021 ◽  
Vol 8 (7) ◽  
pp. 242
Author(s):  
An-Chung Chiang ◽  
Yuan-Yao Lin ◽  
Shou-Tai Lin ◽  
Yen-Yin Lin
Keyword(s):  
Lithium Niobate ◽  
Wave Theory ◽  
Beam Radius ◽  
Acceptance Angle ◽  
Periodically Poled ◽  
Periodically Poled Lithium Niobate ◽  
Electro Optic ◽  
Recent Developments ◽  
Strong Focusing ◽  
Grating Design

Electro-optic (EO) Bragg deflectors have been extensively used in a variety of applications. Recent developments show that bandwidths and deflection efficiencies, as well as angular bandwidths, would significantly limit the utilization of EO Bragg deflectors, especially for applications which need strong focusing, such as intra-cavity applications. In this paper, we introduce a broadband EO Bragg deflector based on periodically-poled lithium niobate with a monolithic dual-grating design. We analyzed the deflection properties of this device by using a modified coupled wave theory and showed that this device can be still efficient for a small beam radius under strong focusing, whereas a single-grating one becomes very inefficient. Using a 1064-nm laser beam with a 100-μm beam radius, we obtained a 74% deflection efficiency with a 190-V bias voltage with a 0.5-mm-thick and 7.5-mm-long dual-grating sample. The acceptance angle for the Bragg condition of this device is as large as a few tens of mrad. The potential bandwidth of this device exceeds 500 nm if the proper operation region is chosen.

DISPERSION IN SEISMIC SURFACE WAVES

Geophysics ◽  
1951 ◽  
Vol 16 (1) ◽  
pp. 63-80 ◽  
Author(s):  
Milton B. Dobrin
Keyword(s):  
Surface Waves ◽  
Water Waves ◽  
Seismic Refraction ◽  
Wave Theory ◽  
Wave Dispersion ◽  
Surface Zone ◽  
Surface Wave Dispersion ◽  
Near Surface ◽  
Arrival Times ◽  
Ground Roll

A non‐mathematical summary is presented of the published theories and observations on dispersion, i.e., variation of velocity with frequency, in surface waves from earthquakes and in waterborne waves from shallow‐water explosions. Two further instances are cited in which dispersion theory has been used in analyzing seismic data. In the seismic refraction survey of Bikini Atoll, information on the first 400 feet of sediments below the lagoon bottom could not be obtained from ground wave first arrival times because shot‐detector distances were too great. Dispersion in the water waves, however, gave data on speed variations in the bottom sediments which made possible inferences on the recent geological history of the atoll. Recent systematic observations on ground roll from explosions in shot holes have shown dispersion in the surface waves which is similar in many ways to that observed in Rayleigh waves from distant earthquakes. Classical wave theory attributes Rayleigh wave dispersion to the modification of the waves by a surface layer. In the case of earthquakes, this layer is the earth’s crust. In the case of waves from shot‐holes, it is the low‐speed weathered zone. A comparison of observed ground roll dispersion with theory shows qualitative agreement, but it brings out discrepancies attributable to the fact that neither the theory for liquids nor for conventional solids applies exactly to unconsolidated near‐surface rocks. Additional experimental and theoretical study of this type of surface wave dispersion may provide useful information on the properties of the surface zone and add to our knowledge of the mechanism by which ground roll is generated in seismic shooting.

Shallow water wave generation by unsteady flow

1968 ◽  
Vol 31 (4) ◽  
pp. 779-788 ◽  
Author(s):  
J. E. Ffowcs Williams ◽  
D. L. Hawkings
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Water Wave ◽  
Small Amplitude ◽  
Point Of View ◽  
Sound Waves ◽  
Aerodynamic Sound ◽  
Shallow Layer ◽  
Sound Theory ◽  
Water Simulation

Small amplitude waves on a shallow layer of water are studied from the point of view used in aerodynamic sound theory. It is shown that many aspects of the generation and propagation of water waves are similar to those of sound waves in air. Certain differences are also discussed. It is concluded that shallow water simulation can be employed in the study of some aspects of aerodynamically generated sound.

scholarly journals Nonlinear water waves

2012 ◽  
Vol 370 (1964) ◽  
pp. 1501-1504 ◽  
Author(s):  
Adrian Constantin
Keyword(s):  
Water Waves ◽  
Theme Issue ◽  
Nonlinear Water Waves ◽  
Recent Developments

This introduction to the issue provides a review of some recent developments in the study of water waves. The content and contributions of the papers that make up this Theme Issue are also discussed.

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