Well-posedness and the small time large deviations of the stochastic integrable equation governing short-waves in a long-wave model

2016 ◽  
Vol 29 ◽  
pp. 38-57 ◽  
Author(s):  
Yong Chen ◽  
Hongjun Gao ◽  
Lili Fan
Keyword(s):  
Large Deviations ◽  
Wave Model ◽  
Integrable Equation ◽  
Small Time ◽  
Well Posedness ◽  
Short Waves ◽  
Long Wave

An integrable equation governing short waves in a long-wave model

2007 ◽  
Vol 463 (2084) ◽  
pp. 1939-1954 ◽  
Author(s):  
M Faquir ◽  
M.A Manna ◽  
A Neveu
Keyword(s):  
Surface Tension ◽  
Gordon Equation ◽  
Wave Model ◽  
Short Wave ◽  
Lax Pair ◽  
Integrable Equation ◽  
Conserved Quantities ◽  
Long Wave ◽  
Tension Term ◽  
Wave Limit

The dynamics of a nonlinear and dispersive long surface capillary-gravity wave model equation is studied analytically in its short-wave limit. We exhibit its Lax pair and some non-trivial conserved quantities. Through a change of functions, an unexpected connection between this classical surface water-wave model and the sine-Gordon (or sinh-Gordon) equation is established. Numerical and analytical studies show that in spite of integrability their solutions can develop singularities and multivaluedness in finite time. These features can be traced to the fact that the surface tension term in the energy involves second-order derivatives. It would be interesting to see in an experiment whether such singularities actually appear, for which surface tension would be specifically responsible.

Local well-posedness of a new integrable equation

2006 ◽  
Vol 64 (11) ◽  
pp. 2516-2526
Author(s):  
Yongqin Liu ◽  
Weike Wang
Keyword(s):  
Integrable Equation ◽  
Well Posedness

A Whitham–Boussinesq long-wave model for variable topography

Wave Motion ◽  
2016 ◽  
Vol 65 ◽  
pp. 156-174 ◽  
Author(s):  
R.M. Vargas-Magaña ◽  
P. Panayotaros
Keyword(s):  
Wave Model ◽  
Long Wave ◽  
Variable Topography

Wave breaking in the presence of wind drift and swell

1974 ◽  
Vol 66 (4) ◽  
pp. 625-640 ◽  
Author(s):  
O. M. Phillips ◽  
M. L. Banner
Keyword(s):  
Wind Speed ◽  
Wave Breaking ◽  
Wind Wave ◽  
Maximum Amplitude ◽  
Velocity Difference ◽  
Wind Drift ◽  
Short Waves ◽  
Long Wave ◽  
Molecular Viscosity ◽  
Surface Drift

Wind, blowing over a water surface, induces a thin layer of high vorticity in which the wind stress is supported by molecular viscosity; the magnitude of the surface drift, the velocity difference across the layer, being of the order of 3% of the wind speed. When long waves move across the surface, there is a nonlinear augmentation of the surface drift near the long-wave crests, so that short waves, superimposed on the longer ones, experience an augmented drift in these regions. This is shown to reduce the maximum amplitude that the short waves can attain when they are at the point of incipient breaking.Theoretical estimates of the reduction are compared with measurements in wind-wave tanks by the authors and by Mitsuyasu (1966) in which long mechanically generated waves are superimposed on short wind-generated waves. The reductions measured in the energy density of the short waves by increasing the slope of the longer ones at constant wind speed are generally consistent with the predictions of the theory in a variety of cases.

Radiation of short waves from the resonantly excited capillary–gravity waves

2016 ◽  
Vol 810 ◽  
pp. 5-24 ◽  
Author(s):  
M. Hirata ◽  
S. Okino ◽  
H. Hanazaki
Keyword(s):  
Solitary Wave ◽  
Solitary Waves ◽  
Gravity Waves ◽  
Wave Pattern ◽  
Short Wave ◽  
Bond Number ◽  
Linear Wave ◽  
Cnoidal Wave ◽  
Short Waves ◽  
Long Wave

Capillary–gravity waves resonantly excited by an obstacle (Froude number: $Fr=1$) are investigated by the numerical solution of the Euler equations. The radiation of short waves from the long nonlinear waves is observed when the capillary effects are weak (Bond number: $Bo<1/3$). The upstream-advancing solitary wave radiates a short linear wave whose phase velocity is equal to the solitary waves and group velocity is faster than the solitary wave (soliton radiation). Therefore, the short wave is observed upstream of the foremost solitary wave. The downstream cnoidal wave also radiates a short wave which propagates upstream in the depression region between the obstacle and the cnoidal wave. The short wave interacts with the long wave above the obstacle, and generates a second short wave which propagates downstream. These generation processes will be repeated, and the number of wavenumber components in the depression region increases with time to generate a complicated wave pattern. The upstream soliton radiation can be predicted qualitatively by the fifth-order forced Korteweg–de Vries equation, but the equation overestimates the wavelength since it is based on a long-wave approximation. At a large Bond number of $Bo=2/3$, the wave pattern has the rotation symmetry against the pattern at $Bo=0$, and the depression solitary waves propagate downstream.

scholarly journals Far-infrared bands in plasmonic metal-insulator-metal absorbers optimized for long-wave infrared

MRS Advances ◽  
2019 ◽  
Vol 4 (11-12) ◽  
pp. 667-674 ◽  
Author(s):  
Rachel N. Evans ◽  
Seth R. Calhoun ◽  
Jonathan R. Brescia ◽  
Justin W. Cleary ◽  
Evan M. Smith ◽  
...  
Keyword(s):  
Ground Plane ◽  
Wavelength Region ◽  
Wave Model ◽  
Far Infrared ◽  
Resonance Wavelength ◽  
Surface Structures ◽  
Metal Insulator ◽  
Long Wave ◽  
Metal Insulator Metal ◽  
Long Wave Infrared

ABSTRACTMetal–insulator–metal (MIM) resonant absorbers comprise a conducting ground plane, a dielectric of thickness t, and thin separated metal top-surface structures of dimension l. The fundamental resonance wavelength is predicted by an analytic standing-wave model based on t, l, and the dielectric refractive index spectrum. For the dielectrics SiO2, AlN, and TiO2, values for l of a few microns give fundamental resonances in the 8-12 μm long-wave infrared (LWIR) wavelength region. Agreement with theory is better for t/l exceeding 0.1. Harmonics at shorter wavelengths were already known, but we show that there are additional resonances in the far-infrared 20 - 50 μm wavelength range in MIM structures designed to have LWIR fundamental resonances. These new resonances are consistent with the model if far-IR dispersion features in the index spectrum are considered. LWIR fundamental absorptions are experimentally shown to be optimized for a ratio t/l of 0.1 to 0.3 for SiO2- and AlN-based MIM absorbers, respectively, with TiO2-based MIM optimized at an intermediate ratio.

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