Reviews and abstracts - Geometrical optics in non-linear wave theory

1978 ◽  
Vol 20 (4) ◽  
pp. 11-11
Author(s):  
A. Shvartsburg
Keyword(s):  
Wave Theory ◽  
Geometrical Optics ◽  
Linear Wave ◽  
Linear Wave Theory ◽  
Non Linear

scholarly journals EFFECT OF WAVE-CURRENT INTERACTION ON THE WAVE PARAMETER

1982 ◽  
Vol 1 (18) ◽  
pp. 28
Author(s):  
Yu-Cheng Li ◽  
John B. Herbich
Keyword(s):  
Wave Height ◽  
Wave Length ◽  
Wave Theory ◽  
Length Change ◽  
Numerical Calculations ◽  
Wave Parameter ◽  
Linear Wave ◽  
Linear Wave Theory ◽  
Wide Range ◽  
Non Linear

The interaction of a gravity wave with a steady uniform current is described in this paper. Numerical calculations of the wave length change by different non-linear wave theories show that errors in the results computed by the linear wave theory are less than 10 percent within the range of 0.15 < d/Ls s 0.40, 0.01 < Hs/Ls < 0.07 and -0.15 < U/Cs i 0.30. Numerical calculations of wave height change employing different wave theories show that errors in the results obtained by the linear wave theory in comparison with the non-linear theories are greater when the opposing relative current and wave steepness become larger. However, within range of the following currents such errors will not be significant. These results were verified by model tests. Nomograms for the modification of wave length and wave height by the linear wave theory and Stokes1 third order theory are presented for a wide range of d/Ls, Hs/Ls and U/C. These nomograms provide the design engineer with a practical guide for estimating wave lengths and heights affected by currents.

The Average Shape of Large Waves in the Norwegian Sea: Is Non-Linear Physics Important?

2019 ◽  
Author(s):  
Tianning Tang ◽  
Margaret J. Yelland ◽  
Thomas A. A. Adcock
Keyword(s):  
Field Data ◽  
Wave Theory ◽  
Linear Wave ◽  
Wave Problem ◽  
Linear Dispersion ◽  
Norwegian Sea ◽  
Linear Wave Theory ◽  
Average Shape ◽  
Non Linear ◽  
Average Wave

Abstract Linear wave theory predicts that in a random sea, the shape of the average wave is given by the scaled autocorrelation function — the “NewWave”. However, the gravity wave problem is non-linear. Numerical simulations of waves on deep water have suggested that their average shape can become modified in a number of ways, including the largest wave in a group tending to move to the front of the group through non-linear dispersion. In this paper we examine whether this occurs for waves in the Norwegian Sea. Field data measured from the weather ship Polarfront is analysed for the period 2000 to 2009. We find that, at this location, the effect of non-linearity is small due to the moderate steepness of the sea-states.

Schumpeterian dynamics as a non-linear wave theory

1991 ◽  
Vol 20 (6) ◽  
pp. 551-590 ◽  
Author(s):  
Gennadi M. Henkin ◽  
Victor M. Polterovich
Keyword(s):  
Wave Theory ◽  
Linear Wave ◽  
Linear Wave Theory ◽  
Non Linear ◽  
Schumpeterian Dynamics

Nonlinear Waves in Strings: The Barrage Balloon Problem

1998 ◽  
Vol 65 (1) ◽  
pp. 141-149
Author(s):  
J. F. Hall
Keyword(s):  
World War Ii ◽  
Nonlinear Waves ◽  
Wave Reflection ◽  
Wave Theory ◽  
P Wave ◽  
Linear Wave ◽  
Geometrically Nonlinear ◽  
World War ◽  
Linear Wave Theory ◽  
Important Solution

This paper develops a theory for geometrically nonlinear waves in strings and presents analytical solutions for a traveling kink, generation of a geometric wave with its accompanying P wave, reflection of a kink at a fixed support and at a smooth sliding support, and interaction of a P wave and a kink. Conditions that must be satisfied for linear wave theory to hold are derived. The nonlinear theory is demonstrated by extending an historically important solution of the barrage balloon problem that was obtained during World War II.

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