scholarly journals On the time-evolution of resonant triads in rotational capillary-gravity water waves

2019 ◽  
Vol 31 (11) ◽  
pp. 117103 ◽  
Author(s):  
Rossen I. Ivanov ◽  
Calin I. Martin
Keyword(s):  
Time Evolution ◽  
Water Waves ◽  
Resonant Triads

Experiments on ripple instabilities. Part 1. Resonant triads

1987 ◽  
Vol 184 ◽  
pp. 15-41 ◽  
Author(s):  
Diane M. Henderson ◽  
Joseph L. Hammack
Keyword(s):  
Water Waves ◽  
Selection Process ◽  
Interaction Coefficients ◽  
Initial Wave ◽  
Wide Range ◽  
Show Evidence ◽  
Wave Trains ◽  
Resonant Triads ◽  
Spatial Locations ◽  
Subharmonic Frequency

Water waves for which both gravitation and surface tension are important (ripples) exhibit a variety of instabilities. Here, experimental results are presented for ripple wavetrains on deep water with frequencies greater than 19.6 Hz where a continuum of resonant triad interactions are dynamically admissible. The experimental wave-trains are indeed unstable, and the instability becomes more pronounced as non-linearity is increased. The unstable wavefield is characterized by significant spatial disorder while temporal measurements at fixed spatial locations remain quite ordered. In fact, for most experiments temporal measurements suggest that a selection process exists in which a single triad dominates evolution. The dominant triad typically does not involve a subharmonic frequency of the generated wave and persists over a wide range of amplitudes for the initial wave. Viscosity does not appear to be important in the selection process; however, it may be responsible for the lack of subsequent triad production by the excited waves of the initial triad. The presence of a selection process contradicts previous conjecture, based on the form of the interaction coefficients, that a broad-banded spectrum of waves should occur. The general absence of subharmonic growth also contradicts previously reported experiments. Results are also presented for wavetrains at the parametric boundary of 19.6 Hz and a degenerate case of resonant triads at 9.8 Hz (Wilton's ripples). In addition to resonant triads, the experiments show evidence of (generally) weaker narrow-band interactions.

On the Exact Soliton Solutions of Some Nonlinear PDE by Tan-Cot Method

2018 ◽  
Vol 5 (1) ◽  
pp. 31-36
Author(s):  
Md Monirul Islam ◽  
Muztuba Ahbab ◽  
Md Robiul Islam ◽  
Md Humayun Kabir
Keyword(s):  
Solitary Wave ◽  
Acoustic Waves ◽  
Water Waves ◽  
Wave Equations ◽  
Rectangular Channel ◽  
Soliton Solutions ◽  
Boussinesq Equations ◽  
Travelling Wave ◽  
Ion Acoustic Waves ◽  
Analytical System

For many solitary wave applications, various approximate models have been proposed. Certainly, the most famous solitary wave equations are the K-dV, BBM and Boussinesq equations. The K-dV equation was originally derived to describe shallow water waves in a rectangular channel. Surprisingly, the equation also models ion-acoustic waves and magneto-hydrodynamic waves in plasmas, waves in elastic rods, equatorial planetary waves, acoustic waves on a crystal lattice, and more. If we describe all of the above situation, we must be needed a solution function of their governing equations. The Tan-cot method is applied to obtain exact travelling wave solutions to the generalized Korteweg-de Vries (gK-dV) equation and generalized Benjamin-Bona- Mahony (BBM) equation which are important equations to evaluate wide variety of physical applications. In this paper we described the soliton behavior of gK-dV and BBM equations by analytical system especially using Tan-cot method and shown in graphically. GUB JOURNAL OF SCIENCE AND ENGINEERING, Vol 5(1), Dec 2018 P 31-36

Extended F-Expansion Method for Solving the modified Korteweg-de Vries (mKdV) Equation

2020 ◽  
Vol 11 (1) ◽  
pp. 93-100
Author(s):  
Vina Apriliani ◽  
Ikhsan Maulidi ◽  
Budi Azhari
Keyword(s):  
Wave Equation ◽  
Exact Solutions ◽  
Internal Waves ◽  
Water Waves ◽  
Wave Equations ◽  
Elliptic Functions ◽  
Expansion Method ◽  
Mkdv Equation ◽  
Innovative Methods ◽  
De Vries

One of the phenomenon in marine science that is often encountered is the phenomenon of water waves. Waves that occur below the surface of seawater are called internal waves. One of the mathematical models that can represent solitary internal waves is the modified Korteweg-de Vries (mKdV) equation. Many methods can be used to construct the solution of the mKdV wave equation, one of which is the extended F-expansion method. The purpose of this study is to determine the solution of the mKdV wave equation using the extended F-expansion method. The result of solving the mKdV wave equation is the exact solutions. The exact solutions of the mKdV wave equation are expressed in the Jacobi elliptic functions, trigonometric functions, and hyperbolic functions. From this research, it is expected to be able to add insight and knowledge about the implementation of the innovative methods for solving wave equations. 

RESPONSE CHARACTERISTICS OF GRAVEL BEACH FROM THE VIEWPOINT OF SHALLOW WATER WAVES AND MOVEMENT OF GRAVELS

2020 ◽  
Vol 76 (2) ◽  
pp. I_565-I_570
Author(s):  
Shin-ichi AOKI ◽  
Tomoki HAMANO ◽  
Taishi NAKAYAMA ◽  
Eiichi OKETANI ◽  
Takahiro HIRAMATSU ◽  
...  
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Shallow Water Waves ◽  
Response Characteristics ◽  
Gravel Beach

A COMPARISON BETWEEN ZIRCON-RUTILE THERMOMETRY OF ECLOGITES: IMPLICATIONS FOR TEMPERATURE-TIME EVOLUTION OF THE NORTH QAIDAM UHP TERRANE, CHINA

2017 ◽  
Author(s):  
David Hernández-Uribe ◽  
◽  
Chris G. Mattinson ◽  
Owen K. Neill ◽  
Andrew Kylander-Clark ◽  
...  
Keyword(s):  
Time Evolution ◽  
The North ◽  
North Qaidam ◽  
Temperature Time
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