Analysis of Propagation of Long Waves in Shallow Water Using the KdV-Based Nonlinear Fourier Transform (KdV-NLFT)

2014 ◽  
Author(s):  
Markus Brühl ◽  
Hocine Oumeraci
Keyword(s):  
Fourier Transform ◽  
Free Surface ◽  
Water Resources ◽  
Shallow Water ◽  
Water Depth ◽  
Shallow Waters ◽  
Nonlinear Phenomenon ◽  
Undular Bore ◽  
Wave Maker ◽  
Nonlinear Fourier Transform

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.

New Approach for Assessment of Flexible Risers Interference in Shallow Waters

2013 ◽  
Author(s):  
Elton J. B. Ribeiro ◽  
Edson L. Labanca ◽  
Roberto Alvim ◽  
Otavio Veras
Keyword(s):  
Shallow Water ◽  
Water Depth ◽  
Critical Issue ◽  
Shallow Waters ◽  
Wake Effect ◽  
Hydrodynamic Coefficient ◽  
New Approach ◽  
Campos Basin ◽  
Internal Fluid ◽  
Flexible Risers

This paper presents a methodology to analyze the risers interference connected to an FPSO, which is using turret moored system in shallow water. It is not feasible in shallow water to use riser free hanging catenary configurations, since there is not enough length in order to dissipate FPSO dynamic response due to wave action, which can cause riser damage at TDP. Furthermore, FPSO static offset is very large, around 30% of water depth, when it is compared with deep water, around 11–12% of water depth. In order to become feasible a large number of risers connected to a FPSO using a turret moored system in shallow water are needed to use compliant configurations, such as: lazy wave, pliant wave and Lazy S. As mentioned above risers compliant configurations are capable to avoid riser damage at TDP, but they present a large lateral motion. Thus, riser interference becomes a critical issue to be overcome. As the applicable standards and rules are not entirely prescriptive about this issue, the riser analyst usually have to adopt independent criteria, such as load cases, internal fluid density, hydrodynamic coefficient considering or not wake effect and clashing criteria (allowable, partially allowable or not). Therefore, the proposed methodology is very robust and was used at FEED studies for FPSO OSX-2/3, both belong to OGX, which are planning to install them at the ending of 2013 in Campos Basin, offshore Brazil.

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
Keyword(s):  
Fourier Transform ◽  
Shallow Water ◽  
Frequency Domain Analysis ◽  
Spectral Structure ◽  
Rock Falls ◽  
Surface Data ◽  
Subaerial Landslide ◽  
Impulse Waves ◽  
Nonlinear Fourier Transform ◽  
The Impact

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.

Spilling breakers in shallow water: applications to Favre waves and to the shoaling and breaking of solitary waves

2016 ◽  
Vol 808 ◽  
pp. 441-468 ◽  
Author(s):  
S. L. Gavrilyuk ◽  
V. Yu. Liapidevskii ◽  
A. A. Chesnokov
Keyword(s):  
Experimental Data ◽  
Free Surface ◽  
Shallow Water ◽  
Froude Number ◽  
Fluid Velocity ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Undular Bore ◽  
Characteristic Wavelength ◽  
Good Agreement

A two-layer long-wave approximation of the homogeneous Euler equations for a free-surface flow evolving over mild slopes is derived. The upper layer is turbulent and is described by depth-averaged equations for the layer thickness, average fluid velocity and fluid turbulent energy. The lower layer is almost potential and can be described by Serre–Su–Gardner–Green–Naghdi equations (a second-order shallow water approximation with respect to the parameter $H/L$, where $H$ is a characteristic water depth and $L$ is a characteristic wavelength). A simple model for vertical turbulent mixing is proposed governing the interaction between these layers. Stationary supercritical solutions to this model are first constructed, containing, in particular, a local turbulent subcritical zone at the forward slope of the wave. The non-stationary model was then numerically solved and compared with experimental data for the following two problems. The first one is the study of surface waves resulting from the interaction of a uniform free-surface flow with an immobile wall (the water hammer problem with a free surface). These waves are sometimes called ‘Favre waves’ in homage to Henry Favre and his contribution to the study of this phenomenon. When the Froude number is between 1 and approximately 1.3, an undular bore appears. The characteristics of the leading wave in an undular bore are in good agreement with experimental data by Favre (Ondes de Translation dans les Canaux Découverts, 1935, Dunod) and Treske (J. Hydraul Res., vol. 32 (3), 1994, pp. 355–370). When the Froude number is between 1.3 and 1.4, the transition from an undular bore to a breaking (monotone) bore occurs. The shoaling and breaking of a solitary wave propagating in a long channel (300 m) of mild slope (1/60) was then studied. Good agreement with experimental data by Hsiao et al. (Coast. Engng, vol. 55, 2008, pp. 975–988) for the wave profile evolution was found.

scholarly journals The importance of Atmospheric Correction for Airborne Hyperspectral Remote Sensing of Shallow Waters. Application to Depth Estimation

2017 ◽  
Author(s):  
Elena Castillo-López ◽  
Jose Antonio Dominguez ◽  
Raúl Pereda ◽  
Julio Manuel de Luis ◽  
Ruben Pérez ◽  
...  
Keyword(s):  
Shallow Water ◽  
Water Depth ◽  
Accurate Determination ◽  
Atmospheric Correction ◽  
Principal Component ◽  
Depth Estimation ◽  
Correction Method ◽  
Shallow Waters ◽  
Depth Information ◽  
Cross Track

Abstract. Abstract. Accurate determination of water depth is indispensable in multiple aspects of civil engineering (dock construction, dikes, submarines outfalls, trench control, etc.). According to the final objective, different accuracies will be required. Accuracy in bathymetric information is highly dependent on the atmospheric correction made to the imagery. The reduction of effects such as glint and cross track illumination in shallow-water areas with homogeneous improves the results of the depth estimations. The aim of this work is to assess the best atmospheric correction method for the estimation of depth in shallow waters. This paper addresses the use of hyperspectral imagery to quantitative bathymetric mapping, and explores one of the most common problems when attempting to extract depth information in conditions of variable water types and bottom reflectances. The current work assesses the accuracy of some classical bathymetric algorithms (Polcyn-Lyzenga, Philpot, Benny-Dawson, Hamilton, Principal Component Analysis) when four different atmospheric correction methods are applied and water depth is derived. This work shows the importance of atmospheric correction in order to depth estimation in shallow waters. None atmospheric correction is valid for all type of coastal waters but in heterogeneous shallow water, the model of atmospheric correction 6S offers good results.

scholarly journals The importance of atmospheric correction for airborne hyperspectral remote sensing of shallow waters: application to depth estimation

2017 ◽  
Vol 10 (10) ◽  
pp. 3919-3929 ◽  
Author(s):  
Elena Castillo-López ◽  
Jose Antonio Dominguez ◽  
Raúl Pereda ◽  
Julio Manuel de Luis ◽  
Ruben Pérez ◽  
...  
Keyword(s):  
Shallow Water ◽  
Water Depth ◽  
Accurate Determination ◽  
Atmospheric Correction ◽  
Principal Component ◽  
Depth Estimation ◽  
Correction Method ◽  
Shallow Waters ◽  
Depth Information ◽  
Cross Track

Abstract. Accurate determination of water depth is indispensable in multiple aspects of civil engineering (dock construction, dikes, submarines outfalls, trench control, etc.). To determine the type of atmospheric correction most appropriate for the depth estimation, different accuracies are required. Accuracy in bathymetric information is highly dependent on the atmospheric correction made to the imagery. The reduction of effects such as glint and cross-track illumination in homogeneous shallow-water areas improves the results of the depth estimations. The aim of this work is to assess the best atmospheric correction method for the estimation of depth in shallow waters, considering that reflectance values cannot be greater than 1.5 % because otherwise the background would not be seen. This paper addresses the use of hyperspectral imagery to quantitative bathymetric mapping and explores one of the most common problems when attempting to extract depth information in conditions of variable water types and bottom reflectances. The current work assesses the accuracy of some classical bathymetric algorithms (Polcyn–Lyzenga, Philpot, Benny–Dawson, Hamilton, principal component analysis) when four different atmospheric correction methods are applied and water depth is derived. No atmospheric correction is valid for all type of coastal waters, but in heterogeneous shallow water the model of atmospheric correction 6S offers good results.

Nonlinear Decomposition of Transmitted Wave Trains Behind Submerged Reef Structures Using “Nonlinear Fourier Transform”: The Nonlinear Spectral Basic Components

2012 ◽  
Author(s):  
Markus Bruehl ◽  
Hocine Oumeraci
Keyword(s):  
Fourier Transform ◽  
Shallow Water ◽  
Water Waves ◽  
Kdv Equation ◽  
Ocean Engineering ◽  
Alternative Analysis ◽  
Wave Interactions ◽  
Nonlinear Decomposition ◽  
Nonlinear Fourier Transform ◽  
Soliton Fission

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.

Experimental Study of a Tanker Ship Squat in Shallow Water

2014 ◽  
Vol 66 (2) ◽  
Author(s):  
Mohammadreza Fathi Kazerooni ◽  
Mohammad Saeed Seif
Keyword(s):  
Experimental Study ◽  
Shallow Water ◽  
Experimental Approach ◽  
Model Tests ◽  
Ship Hull ◽  
Experimental Results ◽  
Shallow Waters ◽  
Towing Tank ◽  
Ship Model

One of the phenomena restricting the tanker navigation in shallow waters is reduction of under keel clearance in the terms of sinkage and dynamic trim that is called squatting. According to the complexity of flow around ship hull, one of the best methods to predict the ship squat is experimental approach based on model tests in the towing tank. In this study model tests for tanker ship model had been held in the towing tank and squat of the model are measured and analyzed. Based on experimental results suitable formulae for prediction of these types of ship squat in fairways are obtained.

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