Non-linear resonant wave–wave interaction (triad): Case studies based on rocket data and first application to satellite data

2006 ◽  
Vol 68 (9) ◽  
pp. 959-976 ◽  
Author(s):  
Sabine Wüst ◽  
Michael Bittner
Keyword(s):  
Case Studies ◽  
Satellite Data ◽  
Wave Interaction ◽  
Resonant Wave ◽  
Non Linear

scholarly journals Decay Rates of Internal Tides Estimated by an Improved Wave–Wave Interaction Analysis

2018 ◽  
Vol 48 (11) ◽  
pp. 2689-2701 ◽  
Author(s):  
Yohei Onuki ◽  
Toshiyuki Hibiya
Keyword(s):  
Kinetic Equation ◽  
Energy Loss ◽  
Interaction Analysis ◽  
Wave Interaction ◽  
Deep Ocean ◽  
Energy Decay ◽  
Decay Rates ◽  
Internal Tides ◽  
Global Ocean ◽  
Resonant Wave

AbstractRecent numerical and observational studies have reported that resonant wave–wave interaction may be a crucial process for the energy loss of internal tides and the associated vertical water mixing in the midlatitude deep ocean. Special attention has been directed to the remarkable latitudinal dependence of the resonant interaction intensity; semidiurnal internal tides promptly lose their energy to near-inertial motions through parametric subharmonic instability equatorward of the critical latitudes 29°N/S, where half the tidal frequency coincides with the local inertial frequency. This feature contradicts the classical theoretical prediction that resonant wave–wave interaction does not play a major role in the tidal energy loss in the open ocean. By reformulating the kinetic equation for long internal waves and developing its calculation method, we estimate the energy decay rates of the low-vertical-mode semidiurnal internal tides interacting with the “ubiquitous” oceanic internal wave field. The result shows rapid energy decay of the internal tides, typically within O(10) days for the lowest-mode component, near their critical latitudes. This decay time is severalfold shorter than those in the classical studies and, additionally, varies by a factor of 2 depending on the local depth and density structure. We suggest from this study that the numerical integration of the kinetic equation is a more effective approach than recognized to determine the decay parameter of wave energy, which is indispensable for the global ocean models.

scholarly journals Approximate Simulations for the Non-linear Long-Short Wave Interaction System

2020 ◽  
Vol 7 ◽  
Author(s):  
Haiyong Qin ◽  
Mostafa M. A. Khater ◽  
Raghda A. M. Attia ◽  
Dianchen Lu
Keyword(s):  
Wave Interaction ◽  
Short Wave ◽  
Interaction System ◽  
Non Linear

scholarly journals Evolution of a Random Directional Wave and Freak Wave Occurrence

2009 ◽  
Vol 39 (3) ◽  
pp. 621-639 ◽  
Author(s):  
Takuji Waseda ◽  
Takeshi Kinoshita ◽  
Hitoshi Tamura
Keyword(s):  
Wave Height ◽  
Wave Interaction ◽  
Northwest Pacific ◽  
Frequency Bandwidth ◽  
Extreme Wave ◽  
Spectral Parameters ◽  
Freak Wave ◽  
Resonant Wave ◽  
Directional Wave ◽  
Wind Sea

Abstract The evolution of a random directional wave in deep water was studied in a laboratory wave tank (50 m long, 10 m wide, 5 m deep) utilizing a directional wave generator. A number of experiments were conducted, changing the various spectral parameters (wave steepness 0.05 < ɛ < 0.11, with directional spreading up to 36° and frequency bandwidth 0.2 < δk/k < 0.6). The wave evolution was studied by an array of wave wires distributed down the tank. As the spectral parameters were altered, the wave height statistics change. Without any wave directionality, the occurrence of waves exceeding twice the significant wave height (the freak wave) increases as the frequency bandwidth narrows and steepness increases, due to quasi-resonant wave–wave interaction. However, the probability of an extreme wave rapidly reduces as the directional bandwidth broadens. The effective Benjamin–Feir index (BFIeff) is introduced, extending the BFI (the relative magnitude of nonlinearity and dispersion) to incorporate the effect of directionality, and successfully parameterizes the observed occurrence of freak waves in the tank. Analysis of the high-resolution hindcast wave field of the northwest Pacific reveals that such a directionally confined wind sea with high extreme wave probability is rare and corresponds mostly to a swell–wind sea mixed condition. Therefore, extreme wave occurrence in the sea as a result of quasi-resonant wave–wave interaction is a rare event that occurs only when the wind sea directionality is extremely narrow.

Lagrangian approach to non-linear wave interactions in a warm plasma

1971 ◽  
Vol 6 (1) ◽  
pp. 53-72 ◽  
Author(s):  
J. J. Galloway ◽  
H. Kim
Keyword(s):  
Linear Equations ◽  
Wave Interaction ◽  
Lagrangian Approach ◽  
Linear Wave ◽  
Coupling Coefficients ◽  
Direct Expansion ◽  
Wave Interactions ◽  
Electrostatic Waves ◽  
Non Linear ◽  
Warm Plasma

In this paper, the coupled-mode equations and coupling coefficients for three-wave interaction are derived by a Lagrangian approach for a general medium. A derivation of the Low Lagrangian for a warm plasma is then given, which avoids certain problems associated with the original analysis. An application of the Lagrangian method is made to interaction between collinearly-propagating electrostatic waves, and a coupling coefficient is derived which agrees with a previous result obtained by direct expansion of the non-linear equations. The paper serves primarily to present and demonstrate a conceptually useful and efficient theoretical approach to non-linear wave interactions.

Non-Linear Corrosion Growth: A More Appropriate and Accurate Model for Predicting Corrosion Growth Rate

2016 ◽  
Author(s):  
M. Al-Amin ◽  
S. Kariyawasam ◽  
S. Zhang ◽  
W. Zhou
Keyword(s):  
Growth Rate ◽  
Case Studies ◽  
Growth Model ◽  
Measurement Errors ◽  
Linear Growth ◽  
Management Program ◽  
Linear Growth Rate ◽  
Metal Loss ◽  
Contributing Factors ◽  
Non Linear

External metal-loss corrosion is one of the major contributing factors for pipeline failures in North America. Corrosion growth rate plays a crucial role in managing corrosion hazard for gas and liquid pipelines. Quantifying the growth of corrosion over time is critically important for the risk and reliability analysis of pipelines, planning for corrosion mitigation and repair, and determination of time intervals for corrosion inspections. Conservatism in predicting the growth rate has significant engineering implication as non-conservatism can lead to critical anomalies being missed by mitigation actions and may cause pipeline failure; whereas, over conservatism can lead to unnecessary inspections and anomaly mitigations that may result in significant unnecessary cost to pipeline operators. As more and more pipelines are now being inspected by in-line inspection (ILI) tools on a regular basis, the ILI data from multiple inspections provide valuable information about the growth of corrosion anomalies on the pipeline. Although the application of linear growth rate calculated by comparing depths from two successive ILI is a common practice in the pipeline industry, research has shown that the growth of corrosion anomaly is non-linear and anomaly-specific. The authors of this paper have previously developed anomaly-specific non-linear corrosion growth model based on multiple ILI data. The objectives of this paper are to demonstrate the appropriateness of anomaly-specific non-linear corrosion growth model, and to illustrate the advantages of using non-linear corrosion growth model in the integrity management program. Two case studies were performed to illustrate the application of non-linear growth model by incorporating the measurement errors associated with the ILI tools, which include both the bias (constant and non-constant) and random scattering error. The findings of these case studies are presented in this paper.

Resonant Wave Interaction with Random Forcing and Dissipation

2002 ◽  
Vol 108 (1) ◽  
pp. 123-144 ◽  
Author(s):  
Paul A. Milewski ◽  
Esteban G. Tabak ◽  
Eric Vanden-Eijnden
Keyword(s):  
Wave Interaction ◽  
Random Forcing ◽  
Resonant Wave
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