How to Deal With Basin Modes When Generating Irregular Waves on Shallow Water

2016 ◽  
Author(s):  
Sanne van Essen ◽  
Willemijn Pauw ◽  
Joris van den Berg
Keyword(s):  
Shallow Water ◽  
Water Depth ◽  
Water Waves ◽  
Low Frequency ◽  
Effective Length ◽  
Irregular Waves ◽  
Natural Modes ◽  
Wave Basin ◽  
Basin Geometry ◽  
Basin Mode

Modeling shallow-water waves in a basin with a finite length and width introduces challenges related to low-frequency (LF) waves, especially for testing of moored vessels with long natural periods. Waves in this frequency range are also present in reality, as for instance bound set-down waves and unbound free waves formed by the geometry bathymetry. In model basins, additional unwanted LF wave components will be formed as a side-product of the wave generation and due to the basin geometry though. Standing waves over the basin length and width (basin modes) can generally be identified, which are difficult to dampen using beaches. This is the case for every wave basin, as they all have finite dimensions. Moored structures generally have natural frequencies in the LF range, which may be excited by basin modes with similar frequencies. It is therefore important to understand the natural modes of a basin before tests with moored structures in shallow water are done. The energy of these basin modes increases and their natural frequency decreases with decreasing water depth (waves travel slower in shallow water). Generally, it can be said that the issues with basin modes are present on very shallow water (typically ∼15–30 m water depth full-scale for structures with a length around 200 m at a scale around 1 to 40). The smaller the basin for the same water depth, the higher the basin mode frequencies and the higher the likelihood of resonance problems. The energy and frequencies of the basin modes and their relevance for specific tests depend on the effective length and width of the basin, the water depth, wave conditions and the (mooring stiffness of) the structure under consideration. The influence of these variables is evaluated in the current study. Tests were done in MARIN’s Offshore Basin (OB), but most of the results are also expected to be applicable to other basins. The observed basin mode frequencies during these tests were compared to the theoretical values, and an overview of the unwanted LF wave content as a function of water depth, wave height and period is presented. The energy and shape of individual basin modes is also discussed. Considering these results, a practical approach for future basin projects on shallow water is described.

Parametric Rolling in Regular Head Waves of the KRISO Container Ship: Numerical and Experimental Investigation in Shallow Water

2019 ◽  
Author(s):  
Manases Tello Ruiz ◽  
Jose Villagomez ◽  
Guillaume Delefortrie ◽  
Evert Lataire ◽  
Marc Vantorre
Keyword(s):  
Shallow Water ◽  
Water Depth ◽  
Water Waves ◽  
Failure Modes ◽  
Container Ship ◽  
Parametric Roll ◽  
Parametric Rolling ◽  
Wave Characteristics ◽  
Intact Stability ◽  
Head Waves

Abstract The IMO Intact Stability Code considers the parametric rolling phenomenon as one of the stability failure modes because of the larger roll angles attained. This hazardous condition of roll resonance can lead to loss of cargo, passenger discomfort, and even (in the extreme cases) the ship’s capsize. Studies as such are mostly conducted considering wave characteristics corresponding to wave lengths around one ship length (λ ≈ LPP) and wave amplitudes varying from moderate to rough values. These wave characteristics, recognised as main contributors to parametric rolling, are frequently encountered in deep water. Waves with lengths of such magnitudes are also met by modern container ships in areas in close proximity to ports, but with less significant wave amplitudes. In such areas, due to the limited water depth and the relatively large draft of the ships, shallow water effects influence the overall ship behaviour as well. Studies dedicated to parametric rolling occurrence in shallow water are scarce in literature. In spite of no accidents being yet reported in such scenarios, its occurrence and methods for its prediction require further attention; this in order to prevent any hazardous conditions. The present work investigates the parametric roll phenomenon numerically and experimentally in shallow water. The study is carried out with the KRISO container ship (KCS) hull. The numerical investigation uses methods available in literature to study the susceptibility and severity of parametric rolling. Their applicability to investigate this phenomenon in shallow water is also discussed. The experimental analysis was carried out at the Towing Tank for Manoeuvres in Confined Water at Flanders Hydraulics Research (in co-operation with Ghent University). Model tests comprised a variation of different forward speeds, wave amplitudes and wave lengths (around one LPP). The water depth was fixed to a condition equivalent to a gross under keel clearance (UKC) of 100% of the ship’s draft.

scholarly journals Far-Field Characteristics of Linear Water Waves Generated by a Submerged Landslide over a Flat Seabed

2020 ◽  
Vol 8 (3) ◽  
pp. 196
Author(s):  
Haixiao Jing ◽  
Yanyan Gao ◽  
Changgen Liu ◽  
Jingming Hou
Keyword(s):  
Shallow Water ◽  
Water Depth ◽  
Water Waves ◽  
Wave Model ◽  
Linear Wave ◽  
Far Field ◽  
Constant Depth ◽  
Low Froude Number ◽  
Dispersive Model ◽  
Wave Models

Understanding the propagation of landslide-generated water waves is of great help against tsunami hazards. In order to investigate the effects of landslide shapes on the far-field leading wave generated by a submerged landslide at a constant depth, three linear wave models with different degrees of dispersive properties are employed in this study. The linear fully dispersive model is then validated by comparing the results against the experimental data available for landslides with a low Froude number. Three simplified shapes of landslides with the same volume, which are unnatural for a body of incoherent material, are used to investigate the effects of landslide shapes on the far-field properties of the generated leading wave over a flat seabed. The results show that the far-field leading crest over a constant depth is independent of the exact landslide shape and is invalid at a shallow water depth. Therefore, the most popular non-dispersive model (also called the shallow water wave model) cannot be used to reproduce the phenomenon. The weakly dispersive wave model can predict this phenomenon well. If only the leading wave is considered, this model is accurate up to at least μ = h0/Lc = 0.6, where h0 is the water depth and Lc denotes the characteristic length of the landslide.

Low Frequency Wave Forces and Wave Induced Motions of a FPSO in Shallow Water

2007 ◽  
Author(s):  
Longfei Xiao ◽  
Jianmin Yang ◽  
Zhiqiang Hu
Keyword(s):  
Shallow Water ◽  
Wave Spectrum ◽  
Low Frequency ◽  
Wave Force ◽  
Wave Forces ◽  
Frequency Wave ◽  
Wave Basin ◽  
The Difference ◽  
The One ◽  
Wave Induced

The low frequency (LF) response of a soft yoke moored 160kDWT FPSO in shallow water is investigated by conducting frequency domain computations and wave basin model tests. An incident wave with Hs = 4.1m and Tp = 8.9s is applied. An obvious LF part appears in the measured wave spectrum at water depth of 16.7m. As a result, the 1st order LF wave force exists and is much larger than the 2nd one. The difference of the spectrums is about one hundred times. The LF wave drift force increases enormously. Consequently, much larger resonant surge response is induced. The LF surge amplitude at h = 16.7m is about 7 times the one at h = 29.0m and 9 times the one in deep water, although the 2nd order response changes a little. Therefore, in very shallow water, LF part of incident waves should be taken into account carefully and LF wave forces and wave induced motions will be very serious.

Application of a Hybrid Boussinesq-Panel Model for Motion Predictions of a Moored Sevan-Floater in Finite Water Depth

2017 ◽  
Author(s):  
Jikun You ◽  
Einar Bernt Glomnes
Keyword(s):  
Water Depth ◽  
Low Frequency ◽  
Boussinesq Equations ◽  
Wave Force ◽  
Irregular Waves ◽  
Wave Forces ◽  
Rankine Source ◽  
Panel Model ◽  
Finite Water Depth ◽  
Incident Waves

This paper presents the applications of an efficient hybrid time-domain simulation model for predicting moored Sevan-floater motions in irregular waves and finite water depth. The irregular incident waves are modeled by the extended Boussinesq equations, which can capture wave-wave interactions and the low-frequency long waves accurately in finite and shallow water depth. By imposing the incident wave kinematics on the surface of the floater, a panel model based on Rankine source method is applied for the calculation of wave forces and corresponding floater motions. The contributions from low-frequency components in incident waves as well as their diffraction effects are included in the wave force calculations. Validation of the irregular waves simulated by the present numerical model are performed against experimental data. Then, the simulated moored floater motions are compared with model test results and results based on Newman’s approximation. The general good agreements with experimental results demonstrate the present model can be used as an alternative for this problem while Newman’s approximation shows non-conservative results.

scholarly journals Airborne Electromagnetic Sea Ice Thickness Sounding in Shallow, Brackish Water Environments of the Caspian and Baltic Seas

2006 ◽  
Author(s):  
Christian Haas
Keyword(s):  
Shallow Water ◽  
Water Depth ◽  
Brackish Water ◽  
Low Frequency ◽  
Ice Thickness ◽  
Sea Ice Thickness ◽  
Sea Floor ◽  
Airborne Electromagnetic ◽  
The Baltic ◽  
Engineering Projects

Ice engineering projects often rely on the knowledge of ice thickness in shallow, brackish water like in the Baltic and Caspian Seas. By means of field data and model results, the paper shows that helicopter-borne electromagnetic induction measurements using frequencies of 3.68 and 112 kHz can yield accurate thickness estimates with salinities as low as 3 ppt. The higher frequency yields the strongest EM signals. In addition, in shallow water the higher frequency is less sensitive to the sea floor signal, and can thus be used in water depths as shallow as 4 to 6 m, depending on flying altitude. Because the low frequency signal is very sensitive on shallow water depth, a combination of both signals will allow the retrieval of both ice thickness and water depth.

Laboratory Wave Modelling for Floating Structures in Shallow Water

2006 ◽  
Author(s):  
Carl Trygve Stansberg
Keyword(s):  
Shallow Water ◽  
Low Frequency ◽  
Second Order ◽  
Wave Groups ◽  
Large Wave ◽  
Frequency Wave ◽  
Wave Modelling ◽  
Floating Structures ◽  
Wave Basin ◽  
Wave Drift Forces

The analysis of moored floating vessels in shallow water requires special attention, when compared to similar problems in deep water. In particular, low-frequency wave drift forces need to be studied. Model testing is essential in validation of numerical prediction tools for these problems. Wave-group induced low-frequency wave components is an important part of the problem. Their reproduction in laboratories needs special attention. In general, two types of low-frequency waves are present: “bound” waves following the wave groups, and “free” waves propagating with their own speed. The former is included in second-order numerical codes for floater is included in second-order numerical codes for floaters, while the latter is normally not. Therefore, identification and possible reduction of the free components is of interest. A practical way to do this in a large wave basin is described in this paper. Results from generation of bi-chromatic waves without and with correction are presented. Corrected results show a clear reduction of the free wave component.

scholarly journals Long Rossby Wave Basin-Crossing Time and the Resonance of Low-Frequency Basin Modes

2002 ◽  
Vol 32 (9) ◽  
pp. 2652-2665 ◽  
Author(s):  
François Primeau
Keyword(s):  
Ocean Circulation ◽  
Rossby Wave ◽  
Low Frequency ◽  
Western Boundary ◽  
Singular Case ◽  
Long Wave ◽  
Eastern Boundary ◽  
Wave Basin ◽  
Crossing Time ◽  
Basin Geometry

Abstract The ability of long-wave low-frequency basin modes to be resonantly excited depends on the efficiency with which energy fluxed onto the western boundary can be transmitted back to the eastern boundary. This efficiency is greatly reduced for basins in which the long Rossby wave basin-crossing time is latitude dependent. In the singular case where the basin-crossing time is independent of latitude, the amplitude of resonantly excited long-wave basin modes grows without bound except for the effects of friction. The speed of long Rossby waves is independent of latitude for quasigeostrophic dynamics, and the rectangular basin geometry often used for theoretical studies of the wind-driven ocean circulation is such a singular case for quasigeostrophic dynamics. For more realistic basin geometries, where only a fraction of the energy incident on the western boundary can be transmitted back to the eastern boundary, the modes have a finite decay rate that in the limit of weak friction is independent of the choice of frictional parameters. Explicit eigenmode computations for a basin geometry similar to the North Pacific but closed along the equator yield basin modes sufficiently weakly damped that they could be resonantly excited.

Experimental and Numerical Study on Large Truncation of Deepwater Mooring Line

2009 ◽  
Author(s):  
Yihua Su ◽  
Jianmin Yang ◽  
Longfei Xiao ◽  
Gang Chen
Keyword(s):  
Dynamic Response ◽  
Water Depth ◽  
Numerical Study ◽  
Unit Length ◽  
Low Frequency ◽  
Model Tests ◽  
Mooring Line ◽  
Mooring System ◽  
Mooring Lines ◽  
Wave Basin

Modeling the deepwater mooring system in present available basin using standard Froude scaling at an acceptable scale presents new challenges. A prospective method is to truncate the full-depth mooring lines and find an equivalent truncated mooring system that can reproduce both static and dynamic response of the full-depth mooring system, but large truncation arise if the water depth where the deepwater platform located is very deep or the available water depth of the basin is shallow. A Cell-Truss Spar operated in 1500m water depth is calibrated in a wave basin with 4m water depth. Large truncation arises even though a small model scale 1:100 is chosen. A series of truncated mooring lines are designed and investigated through numerical simulations, single line model tests and coupled wave basin model tests. It is found that dynamic response of the truncated mooring line can be enlarged by using larger diameter and mass per unit length in air. Although the truncated mooring line with clump presents a “taut” shape, its dynamic characteristics is dominated by the geometry stiffness and it underestimates dynamic response of the full-depth mooring line, even induces high-frequency dynamic response. There are still two obstacles in realizing dynamic similarity for the largely truncated mooring system: lower mean value of the top tension of upstream mooring lines, and smaller low-frequency mooring-induced damping.

Cloaking in shallow-water waves via nonlinear medium transformation

2015 ◽  
Vol 778 ◽  
pp. 273-287 ◽  
Author(s):  
Ahmad Zareei ◽  
Mohammad-Reza Alam
Keyword(s):  
Shallow Water ◽  
Water Depth ◽  
Governing Equation ◽  
Water Waves ◽  
Electromagnetic Waves ◽  
Nonlinear Transformation ◽  
Gravitational Acceleration ◽  
Shallow Water Waves ◽  
Variable Permeability ◽  
Single Polarization

A major obstacle in designing a perfect cloak for objects in shallow-water waves is that the linear transformation media scheme (also known as transformation optics) requires spatial variations of two independent medium properties. In the Maxwell’s equation and for the well-studied problem of electromagnetic cloaking, these two properties are permittivity and permeability. Designing an anisotropic material with both variable permittivity and variable permeability, while challenging, is achievable. On the other hand, for long gravity waves, whose governing equation maps one-to-one to the single polarization Maxwell’s equations, the two required spatially variable properties are the water depth and the gravitational acceleration; in this case changing the gravitational acceleration is simply impossible. Here we present a nonlinear transformation that only requires the change in one of the medium properties, which, in the case of shallow-water waves, is the water depth, while keeping the gravitational acceleration constant. This transformation keeps the governing equation perfectly intact and, if the cloak is large enough, asymptotically satisfies the necessary boundary conditions. We show that with this nonlinear transformation an object can be cloaked from any wave that merely satisfies the long-wave assumption. The presented transformation can be applied as well for the design of non-magnetic optical cloaks for electromagnetic waves.

Viscous Drift Forces and Responses on a Semisubmersible Platform in High Waves

2009 ◽  
Author(s):  
Petter Andreas Berthelsen ◽  
Rolf Baarholm ◽  
Csaba Pa´kozdi ◽  
Carl Trygve Stansberg ◽  
Amany Hassan ◽  
...  
Keyword(s):  
Low Frequency ◽  
Irregular Waves ◽  
Wave Zone ◽  
Free Surface Elevation ◽  
Viscous Effects ◽  
Sea State ◽  
Viscous Forces ◽  
Wave Basin ◽  
Drift Forces ◽  
Drag Term

In this paper the significance of viscous effects on a moored semisubmersible platform in various sea state conditions is explored. Experimental data from a 1:50 model scale tests in a 50m × 80m wave basin are compared with numerical time domain simulations. Both regular and irregular waves are included, and some tests are also run with current. This paper presents results from a horizontally moored semisubmersible, where we focus on the hull hydrodynamics alone. The emphasis here is low frequency surge responses. Use of conventional potential theory shows large discrepancies when compared with experimental results in high sea states. For surge motion, they are believed to be due to viscous forces in the wave zone. Viscous forces and damping in the numerical model are included by the drag term of Morison’s equation using a total relative velocity approach, which is integrated up to the instantaneous free surface elevation. A common challenge is to choose a suitable Cd coefficient which provides for sufficient excitation force without introducing excessive motion damping. It is found that using a larger Cd coefficient in the wave zone gives larger excitation without influencing the total damping significantly. This way, applying the drag term of Morison’s equation can give results that compare well with measurements. Also, the coefficient is found to be lower in waves with current than in waves only.

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