Analysis of long-period cosine-wave dispersion in very shallow water using nonlinear Fourier transform based on KdV equation

2016 ◽  
Vol 61 ◽  
pp. 81-91 ◽  
Author(s):  
Markus Brühl ◽  
Hocine Oumeraci
Author(s):  
Markus Bruehl ◽  
Hocine Oumeraci

The nonlinear Fourier transform (NLFT) is introduced as an alternative analysis method for nonlinear waves in shallow water. In physics the NLFT is the application of the inverse scattering transform (IST) for the solution of the Korteweg-deVries (KdV) equation that gouverns the evolution of waves in shallow water. In coastal and ocean engineering the NLFT can be regarded as an extension of the conventional Fourier transform (FT) as it uses nonlinear shallow water waves (cnoidal waves) as basic components for the spectral decomposition and explicitly considers the nonlinear wave-wave interactions during the analysis. A first description of the numerical implementation and its application for the analysis of soliton fission over and behind submerged reefs is given in a former paper [1]. This paper presents a closer view on the interpretation of both types of spectral basic components of the nonlinear decomposition: solitons and nonlinear oscillatory waves.


2018 ◽  
Vol 12 (02) ◽  
pp. 1840002 ◽  
Author(s):  
Markus Brühl ◽  
Matthias Becker

Subaerial and underwater landslides, rock falls and glacier calvings can generate impulse waves in lakes, fjords and the open sea. Experiments with subaerial landslides have shown that, depending on the slide characteristics, different wave types (Stokes, cnoidal or bore-like waves) are generated. Each of these wave types shows different wave height decay with increasing distance from the impact position. Furthermore, in very shallow water, the first impulse wave shows characteristic properties of a solitary wave. The nonlinear Fourier transform based on the Korteweg–deVries equation (KdV-NLFT) is a frequency-domain analysis method that decomposes shallow-water free-surface data into nonlinear cnoidal waves instead of linear sinusoidal waves. This method explicitly identifies solitons as spectral components within the given data. In this study, we apply the KdV-NLFT for the very first time to available 2D and 3D landslide-test data. The objective of the nonlinear decomposition is to identify the hidden nonlinear spectral structure of the impulse waves, including solitons. Furthermore, we analyze the determined solitons at different downstream positions from the impact point with respect to soliton propagation and modification. Finally, we draw conclusions for the prediction of the expected landslide-generated downstream solitons in the far-field.


Author(s):  
Markus Brühl ◽  
Hocine Oumeraci

Hydraulic model tests and numerical simulations show that long sinusoidal waves that are generated in very shallow waters are not stable but show modifications of the free surface as function of propagation in time and space. First, with increasing distance from the wave maker the wave becomes asymmetric and develops into a bore-shaped wave. Second, with further increasing distance more and more additional wave crests appear from the front of the bore (undular bore). The shallower the water depth, the more additional wave components can be observed. In extremely shallow water, the periodic sine waves completely disintegrate into periodic trains of solitons. At Leichtweiss-Institute for Hydraulic Engineering and Water Resources (LWI), TU Braunschweig, a nonlinear Fourier transform based on the Korteweg-deVries equation (KdV-NLFT) is implemented and successfully applied in Brühl [1] that provides an explanation for this nonlinear phenomenon and allows the prediction of the dispersion and propagation of long sinusoidal waves in shallow water.


2019 ◽  
Vol 9 (9) ◽  
pp. 1855
Author(s):  
Youn-Ju Jeong ◽  
Min-Su Park ◽  
Jeongsoo Kim ◽  
Sung-Hoon Song

This paper presents the results of wave force tests conducted on three types of offshore support structures considering eight waves and three sea levels to investigate the corresponding wave forces. As a result of this study, it is found that the occurrence of shoaling in shallow water induces a significant increase of the wave force. Most of the test models at the shallow water undergo a nonlinear increase of the wave force with higher wave height increasing. In addition, the larger the diameter of the support structure within the range of this study, the larger the diffraction effect is, and the increase in wave force due to shoaling is suppressed. Under an irregular wave at the shallow water, the wave force to the long-period wave tends to be slightly higher than that of the short period wave since the higher wave height component included in the irregular wave has an influence on the shoaling. In addition, it is found that the influence of shoaling under irregular wave becomes more apparent in the long period.


2021 ◽  
Author(s):  
Yutian Wang ◽  
Songnian Fu ◽  
Chi Zhang ◽  
Xiahui Tang ◽  
Jian Kong ◽  
...  

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