Analysis of Subaerial Landslide Data Using Nonlinear Fourier Transform Based on Korteweg-deVries Equation (KdV-NLFT)

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 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.


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.


Minerals ◽  
2021 ◽  
Vol 11 (7) ◽  
pp. 659
Author(s):  
Mingyang Wei ◽  
Zhidong Bao ◽  
Axel Munnecke ◽  
Wei Liu ◽  
G. William M. Harrison ◽  
...  

Just as in deep-water sedimentary environments, productive source rocks can be developed in an evaporitic platform, where claystones are interbedded with evaporites and carbonates. However, the impact of the paleoenvironment on the organic matter enrichment of shallow water source rocks in an evaporite series has not been well explored. In this study, two wells in the central uplift of the Tarim Basin were systematically sampled and analyzed for a basic geochemical study, including major elements, trace elements, and total organic carbon (TOC), to understand the relationship between TOC and the paleoenvironmental parameters, such as paleosalinity, redox, paleoclimate, paleo-seawater depth, and paleoproductivity. The results show that the Lower–Middle Cambrian mainly developed in a fluctuating salinity, weak anoxic to anoxic, continuous dry and hot, and proper shallow water environment. The interfingering section of evaporites, carbonates, and claystones of the Awatag Fm. have higher paleoproductivity and higher enrichment of organic matter. Paleosalinity, redox, paleoclimate, paleo-seawater depth, and paleoproductivity jointly control the organic matter enrichment of shallow water source rocks in the evaporite series. The degree of enrichment of organic matter in shallow water source rocks first increases and then decreases with the increase in paleosalinity. All the samples with high content of organic matter come from the shallower environment of the Awatag Fm.


Author(s):  
Sen Zhang ◽  
Dingxi Wang ◽  
Yi Li ◽  
Hangkong Wu ◽  
Xiuquan Huang

Abstract The time spectral method is a very popular reduced order frequency method for analyzing unsteady flow due to its advantage of being easily extended from an existing steady flow solver. Condition number of the inverse Fourier transform matrix used in the method can affect the solution convergence and stability of the time spectral equation system. This paper aims at evaluating the effect of the condition number of the inverse Fourier transform matrix on the solution stability and convergence of the time spectral method from two aspects. The first aspect is to assess the impact of condition number using a matrix stability analysis based upon the time spectral form of the scalar advection equation. The relationship between the maximum allowable Courant number and the condition number will be derived. Different time instant groups which lead to the same condition number are also considered. Three numerical discretization schemes are provided for the stability analysis. The second aspect is to assess the impact of condition number for real life applications. Two case studies will be provided: one is a flutter case, NASA rotor 67, and the other is a blade row interaction case, NASA stage 35. A series of numerical analyses will be performed for each case using different time instant groups corresponding to different condition numbers. The conclusion drawn from the two real life case studies will corroborate the relationship derived from the matrix stability analysis.


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

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