Oblique interactions of weakly nonlinear long waves in dispersive systems

2006 ◽  
Vol 38 (12) ◽  
pp. 868-898 ◽  
Author(s):  
Masayuki Oikawa ◽  
Hidekazu Tsuji
Keyword(s):  
Long Waves ◽  
Weakly Nonlinear ◽  
Dispersive Systems

scholarly journals Focusing of long waves with finite crest over constant depth

2013 ◽  
Vol 469 (2153) ◽  
pp. 20130015 ◽  
Author(s):  
Utku Kânoğlu ◽  
Vasily V. Titov ◽  
Baran Aydın ◽  
Christopher Moore ◽  
Themistoklis S. Stefanakis ◽  
...  
Keyword(s):  
Source Region ◽  
Wave Theory ◽  
Long Waves ◽  
Constant Depth ◽  
Large Wave ◽  
Weakly Nonlinear ◽  
Scaling Relationships ◽  
2011 Japan Tsunami ◽  
Wave Heights ◽  
Run Up

Tsunamis are long waves that evolve substantially, through spatial and temporal spreading from their source region. Here, we introduce a new analytical solution to study the propagation of a finite strip source over constant depth using linear shallow-water wave theory. This solution is not only exact, but also general and allows the use of realistic initial waveforms such as N -waves. We show the existence of focusing points for N -wave-type initial displacements, i.e. points where unexpectedly large wave heights may be observed. We explain the effect of focusing from a strip source analytically, and explore it numerically. We observe focusing points using linear non-dispersive and linear dispersive theories, analytically; and nonlinear non-dispersive and weakly nonlinear weakly dispersive theories, numerically. We discuss geophysical implications of our solutions using the 17 July 1998 Papua New Guinea and the 17 July 2006 Java tsunamis as examples. Our results may also help to explain high run-up values observed during the 11 March 2011 Japan tsunami, which are otherwise not consistent with existing scaling relationships. We conclude that N -waves generated by tectonic displacements feature focusing points, which may significantly amplify run-up beyond what is often assumed from widely used scaling relationships.

scholarly journals Nonlinear long waves over a muddy beach

2013 ◽  
Vol 718 ◽  
pp. 371-397 ◽  
Author(s):  
Erell-Isis Garnier ◽  
Zhenhua Huang ◽  
Chiang C. Mei
Keyword(s):  
Boundary Layer ◽  
Thin Layer ◽  
Surface Waves ◽  
Nonlinear Waves ◽  
Water Waves ◽  
Long Waves ◽  
Fluid Mud ◽  
Weakly Nonlinear ◽  
Sea Bottom ◽  
Oscillatory Boundary Layer

AbstractWe analyse theoretically the interaction between water waves and a thin layer of fluid mud on a sloping seabed. Under the assumption of long waves in shallow water, weakly nonlinear and dispersive effects in water are considered. The fluid mud is modelled as a thin layer of viscoelastic continuum. Using the constitutive coefficients of mud samples from two field sites, we examine the interaction of nonlinear waves and the mud motion. The effects of attenuation on harmonic evolution of surface waves are compared for two types of mud with distinct rheological properties. In general mud dissipation is found to damp out surface waves before they reach the shore, as is known in past observations. Similar to the Eulerian current in an oscillatory boundary layer in a Newtonian fluid, a mean displacement in mud is predicted which may lead to local rise of the sea bottom.

Another possible model equation for long waves in nonlinear dispersive systems

1977 ◽  
Vol 61 (7) ◽  
pp. 429-430 ◽  
Author(s):  
Richard I. Joseph ◽  
Robert Egri
Keyword(s):  
Model Equation ◽  
Long Waves ◽  
Dispersive Systems
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