scholarly journals On the limiting Stokes wave of extreme height in arbitrary water depth

2018 ◽  
Vol 843 ◽  
pp. 653-679 ◽  
Author(s):  
Xiaoxu Zhong ◽  
Shijun Liao
Keyword(s):  
Shallow Water ◽  
Solitary Waves ◽  
Water Depth ◽  
Stokes Wave ◽  
Analytic Approximation ◽  
Highly Nonlinear ◽  
Stokes Waves ◽  
Homotopy Analysis ◽  
Wave Models ◽  
Sharp Crest

Both Schwartz (J. Fluid Mech., vol. 62 (3), 1974, pp. 553–578) and Cokelet (Phil. Trans. R. Soc. Lond., vol. 286 (1335), 1977, pp. 183–230) failed to gain convergent results for limiting Stokes waves in extremely shallow water by means of perturbation methods, even with the aid of extrapolation techniques such as the Padé approximant. In particular, it is extremely difficult for traditional analytic/numerical approaches to present the wave profile of limiting waves with a sharp crest of$120^{\circ }$included angle first mentioned by Stokes in the 1880s. Thus, traditionally, different wave models are used for waves in different water depths. In this paper, by means of the homotopy analysis method (HAM), an analytic approximation method for highly nonlinear equations, we successfully gain convergent results (and especially the wave profiles) of the limiting Stokes waves with this kind of sharp crest in arbitrary water depth, even including solitary waves of extreme form in extremely shallow water, without using any extrapolation techniques. Therefore, in the frame of the HAM, the Stokes wave can be used as a unified theory for all kinds of waves, including periodic waves in deep and intermediate depths, cnoidal waves in shallow water and solitary waves in extremely shallow water.

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.

A high-order cnoidal wave theory

1979 ◽  
Vol 94 (1) ◽  
pp. 129-161 ◽  
Author(s):  
J. D. Fenton
Keyword(s):  
Shallow Water ◽  
Wave Height ◽  
Water Depth ◽  
Wave Theory ◽  
High Order ◽  
Stokes Wave ◽  
Cnoidal Wave ◽  
Expansion Parameter ◽  
Wave Solutions ◽  
Fifth Order

A method is outlined by which high-order solutions are obtained for steadily progressing shallow water waves. It is shown that a suitable expansion parameter for these cnoidal wave solutions is the dimensionless wave height divided by the parameter m of the cn functions: this explicitly shows the limitation of the theory to waves in relatively shallow water. The corresponding deep water limitation for Stokes waves is analysed and a modified expansion parameter suggested.Cnoidal wave solutions to fifth order are given so that a steady wave problem with known water depth, wave height and wave period or length may be solved to give expressions for the wave profile and fluid velocities, as well as integral quantities such as wave power and radiation stress. These series solutions seem to exhibit asymptotic behaviour such that there is no gain in including terms beyond fifth order. Results from the present theory are compared with exact numerical results and with experiment. It is concluded that the fifth-order cnoidal theory should be used in preference to fifth-order Stokes wave theory for wavelengths greater than eight times the water depth, when it gives quite accurate results.

Shallow Water Intercomparison of Wave Models — Part I Three Different Concepts to Model Surface Waves in Finite Water Depth

1985 ◽  
pp. 201-205 ◽  
Author(s):  
E. Bouws ◽  
J. J. Ephraums ◽  
J. A. Ewing ◽  
P. E. Francis ◽  
H. Günther ◽  
...  
Keyword(s):  
Surface Waves ◽  
Shallow Water ◽  
Water Depth ◽  
Model Surface ◽  
Finite Water Depth ◽  
Wave Models

Conditional Short-Crested Waves in Shallow Water and With Superimposed Current

2002 ◽  
Author(s):  
Jo̸rgen Juncher Jensen
Keyword(s):  
Shallow Water ◽  
Water Depth ◽  
Wave Spectrum ◽  
Wave Theory ◽  
Ocean Waves ◽  
Offshore Structures ◽  
Stokes Wave ◽  
Wave Crest ◽  
Non Linear ◽  
Drilling Rigs

For bottom-supported offshore structures like oil drilling rigs and oil production platforms, a deterministic design wave approach is often applied using a regular non-linear Stokes’ wave. Thereby, the procedure accounts for non-linear effects in the wave loading but the randomness of the ocean waves is poorly represented, as the shape of the wave spectrum does not enter the wave kinematics. To overcome this problem and still keep the simplicity of a deterministic approach, Tromans, Anaturk and Hagemeijer (1991) suggested the use of a deterministic wave, defined as the expected linear Airy wave, given the value of the wave crest at a specific point in time or space. In the present paper a derivation of the expected linear short-crested wave riding on a uniform current is given. The analysis is based on the conventional shallow water Airy wave theory and the direction of the main wind direction can make any direction with the current. A consistent derivation of the wave spectrum taking into account current and finite water depth is used. The numerical results show a significant effect of the water depth, the directional spreading and the current on the conditional mean wave profile. Extensions to higher order waves are finally discussed.

Dynamics of Combined Solitary-waves in the General Shallow Water Wave Models

2003 ◽  
Vol 58 (9-10) ◽  
pp. 520-528
Author(s):  
Woo-Pyo Hong
Keyword(s):  
Solitary Wave ◽  
Shallow Water ◽  
Solitary Waves ◽  
Water Wave ◽  
Hyperbolic Function ◽  
Ansatz Method ◽  
Shallow Water Wave ◽  
Wave Models ◽  
Fifth Order ◽  
52.35 Mw

We find new analytic solitary-wave solutions, having a nonzero background at infinity, of the general fifth-order shallow water wave models using the hyperbolic function ansatz method. We study the dynamical properties of the solutions in the combined form of a bright and a dark solitary-wave by using numerical simulations. It is shown that the solitary-waves can be stable or marginally stable, depending on the coefficients of the model.We study the interaction dynamics by using the combined solitary-waves as the initial profiles to show the formation of sech2-type solitary-waves in the presence of a strong nonlinear dispersion term. - PACS: 03.40.Kf, 02.30.Jr, 47.20.Ky, 52.35.Mw

Resistance Tests of an Articulated Pusher Barge System in Deep and Shallow Water

2021 ◽  
Author(s):  
Li Zhang ◽  
Lei Xing ◽  
Mingyu Dong ◽  
Weimin Chen
Keyword(s):  
Shallow Water ◽  
Water Depth ◽  
Deep Water ◽  
Water Resistance ◽  
Model Tests ◽  
System 2 ◽  
Changing Trend ◽  
The Difference ◽  
Transport Vessel ◽  
Resistance Performance

Abstract Articulated pusher barge vessel is a short-distance transport vessel with good economic performance and practicability, which is widely used in the Yangtze River of China. In this present work, the resistance performance of articulated pusher barge vessel in deep water and shallow water was studied by model tests in the towing tank and basin of Shanghai Ship and Shipping Research Institute. During the experimental investigation, the articulated pusher barge vessel was divided into three parts: the pusher, the barge and the articulated pusher barge system. Firstly, the deep water resistance performance of the articulated pusher barge system, barge and the pusher at design draught T was studied, then the water depth h was adjusted, and the shallow water resistance at h/T = 2.0, 1.5 and 1.2 was tested and studied respectively, and the difference between deep water resistance and shallow water resistance at design draught were compared. The results of model tests and analysis show that: 1) in the study of deep water resistance, the total resistance of the barge was larger than that of the articulated pusher barge system. 2) for the barge, the shallow water resistance increases about 0.4–0.7 times at h/T = 2.0, 0.5–1.1 times at h/T = 1.5, and 0.7–2.3 times at h/T = 1.2. 3) for the pusher, the shallow water resistance increases about 1.0–0.4 times at h/T = 2.7, 1.2–0.9 times at h/T = 2.0, and 1.7–2.4 times at h/T = 1.6. 4) for the articulated pusher barge system, the shallow water resistance increases about 0.2–0.3 times at h/T = 2.0, 0.5–1.3 times at h/T = 1.5, and 1.0–3.5 times at h/T = 1.2. Furthermore, the water depth Froude number Frh in shallow water was compared with the changing trend of resistance in shallow water.

Cnoidal Wave-Induced Residual Liquefaction in Loosely Deposited Seabed under Coastal Shallow Water

2021 ◽  
Vol 11 (24) ◽  
pp. 11631
Author(s):  
Xiuwei Chai ◽  
Jingyuan Liu ◽  
Yu Zhou
Keyword(s):  
Shallow Water ◽  
Pore Pressure ◽  
Water Environment ◽  
Lateral Spreading ◽  
Stokes Wave ◽  
Cnoidal Wave ◽  
Liquefaction Resistance ◽  
Liquefaction Process ◽  
Wave Induced ◽  
Seabed Soil

This study is aimed at numerically investigating the cnoidal wave-induced dynamics characteristics and the liquefaction process in a loosely deposited seabed floor in a shallow water environment. To achieve this goal, the integrated model FSSI-CAS 2D is taken as the computational platform, and the advanced soil model Pastor–Zienkiewicz Mark III is utilized to describe the complicated mechanical behavior of loose seabed soil. The computational results show that a significant lateral spreading and vertical subsidence could be observed in the loosely deposited seabed floor due to the gradual loss of soil skeleton stiffness caused by the accumulation of pore pressure. The accumulation of pore pressure in the loose seabed is not infinite but limited by the liquefaction resistance line. The seabed soil at some locations could be reached to the full liquefaction state, becoming a type of heavy fluid with great viscosity. Residual liquefaction is a progressive process that is initiated at the upper part of the seabed floor and then enlarges downward. For waves with great height in shallow water, the depth of the liquefaction zone will be greatly overestimated if the Stokes wave theory is used. This study can enhance the understanding of the characteristics of the liquefaction process in a loosely deposited seabed under coastal shallow water and provide a reference for engineering activities.

Stability of offshore structures in shallow water depth

2011 ◽  
Vol 2 (2) ◽  
pp. 320-333
Author(s):  
F. Van den Abeele ◽  
J. Vande Voorde
Keyword(s):  
Shallow Water ◽  
Water Depth ◽  
Fossil Fuels ◽  
Oil And Gas ◽  
Structural Response ◽  
Offshore Structures ◽  
Exploration And Production ◽  
Subsea Pipelines ◽  
Wave Induced ◽  
Shallow Water Depth

The worldwide demand for energy, and in particular fossil fuels, keeps pushing the boundaries of offshoreengineering. Oil and gas majors are conducting their exploration and production activities in remotelocations and water depths exceeding 3000 meters. Such challenging conditions call for enhancedengineering techniques to cope with the risks of collapse, fatigue and pressure containment.On the other hand, offshore structures in shallow water depth (up to 100 meter) require a different anddedicated approach. Such structures are less prone to unstable collapse, but are often subjected to higherflow velocities, induced by both tides and waves. In this paper, numerical tools and utilities to study thestability of offshore structures in shallow water depth are reviewed, and three case studies are provided.First, the Coupled Eulerian Lagrangian (CEL) approach is demonstrated to combine the effects of fluid flowon the structural response of offshore structures. This approach is used to predict fluid flow aroundsubmersible platforms and jack-up rigs.Then, a Computational Fluid Dynamics (CFD) analysis is performed to calculate the turbulent Von Karmanstreet in the wake of subsea structures. At higher Reynolds numbers, this turbulent flow can give rise tovortex shedding and hence cyclic loading. Fluid structure interaction is applied to investigate the dynamicsof submarine risers, and evaluate the susceptibility of vortex induced vibrations.As a third case study, a hydrodynamic analysis is conducted to assess the combined effects of steadycurrent and oscillatory wave-induced flow on submerged structures. At the end of this paper, such ananalysis is performed to calculate drag, lift and inertia forces on partially buried subsea pipelines.

Experimental Investigation of Trimaran Models in Shallow Water

2014 ◽  
Vol 30 (02) ◽  
pp. 66-78
Author(s):  
Mark Pavkov ◽  
Morabito Morabitob
Keyword(s):  
Shallow Water ◽  
Water Depth ◽  
Critical Speed ◽  
Water Effect ◽  
Finite Water Depth ◽  
Speed Regime ◽  
Displacement Speed ◽  
Littoral Combat Ship ◽  
Shallow Water Effect ◽  
The U.S

Experiments were conducted at the U.S. Naval Academy's Hydromechanics Laboratory to determine the effect of finite water depth on the resistance, heave, and trim of two different trimaran models. The models were tested at the same length to water depth ratios over a range of Froude numbers in the displacement speed regime. The models were also towed in deep water for comparison. Additionally, the side hulls were adjusted to two different longitudinal positions to investigate possible differences resulting from position. Near critical speed, a large increase in resistance and sinkage was observed, consistent with observations of conventional displacement hulls. The data from the two models are scaled up to a notional 125-m length to illustrate the effects that would be observed for actual ships similar in size to the U.S. Navy's Independence Class Littoral Combat Ship. Faired plots are developed to allow for rapid estimation of shallow water effect on trimaran resistance and under keel clearance. An example is provided.

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