Ship Springing Response in Finite Water Depth

2012 ◽  
Vol 56 (02) ◽  
pp. 80-90
Author(s):  
Jelena Vidic-Perunovic
Keyword(s):  
Relative Motion ◽  
Water Depth ◽  
Deep Water ◽  
Bending Moment ◽  
Intermediate Water ◽  
Short Term ◽  
Strip Theory ◽  
Influence Of Water ◽  
Finite Water Depth ◽  
Wave Induced

The influence of water depth on the vertical wave induced bending moment acting on a hull has been studied. The deep-water second-order nonlinear hydroelastic strip theory, which is based on the relative motion concept, has been generalized to account for a finite water depth. Results for an analytical beam and for a tanker ship are presented and discussed. Short-term load predictions that account for a range of different sea states are given for a tanker ship. As seen from the present study, the effect of intermediate water depth may be a significant factor in calculations of ship springing response.

Influence of Whipping on Long-term Vertical Bending Moment

2004 ◽  
Vol 48 (04) ◽  
pp. 261-272
Author(s):  
Gro Sagli Baarholm ◽  
Jørgen Juncher Jensen
Keyword(s):  
Nonlinear Response ◽  
Extreme Values ◽  
Bending Moment ◽  
Sea Waves ◽  
Short Term ◽  
Strip Theory ◽  
Long Time ◽  
Wave Induced ◽  
Vertical Bending Moment

This paper is concerned with estimating the response value corresponding to a long return period, say 20 years. Time domain simulation is required to obtain the nonlinear response, and long time series are required to limit the statistical uncertainty in the simulations. It is crucial to introduce ways to improve the efficiency in the calculation. A method to determine the long-term extremes by considering only a few short-term sea states is applied. Long-term extreme values are estimated using a set of sea states that have a certain probability of occurrence, known as the contour line approach. Effect of whipping is included by assuming that the whipping and wave-induced responses are independent, but the effect of correlation of the long-term extreme value is also studied. Numerical calculations are performed using a nonlinear, hydroelastic strip theory as suggested by Xia et al (1998). Results are presented for the S-175 containership (ITTC 1983) in head sea waves. The analysis shows that whipping increases the vertical bending moment and that the correlation is significant.

scholarly journals Effects of Water Depth on the Growth of the Submerged Macrophytes Vallisneria natans and Hydrilla verticillata: Implications for Water Level Management

Water ◽  
2021 ◽  
Vol 13 (18) ◽  
pp. 2590
Author(s):  
Qisheng Li ◽  
Yanqing Han ◽  
Kunquan Chen ◽  
Xiaolong Huang ◽  
Kuanyi Li ◽  
...  
Keyword(s):  
Water Level ◽  
Water Depth ◽  
Deep Water ◽  
Submerged Macrophytes ◽  
Hydrilla Verticillata ◽  
Water Level Fluctuations ◽  
Total Biomass ◽  
Intermediate Water ◽  
Factors Affecting ◽  
Vallisneria Natans

Water level is one of the most important factors affecting the growth of submerged macrophytes in aquatic ecosystems. The rosette plant Vallisneria natans and the erect plant Hydrilla verticillata are two common submerged macrophytes in lakes of the middle and lower reaches of the Yangtze River, China. How water level fluctuations affect their growth and competition is still unknown. In this study, three water depths (50 cm, 150 cm, and 250 cm) were established to explore the responses in growth and competitive patterns of the two plant species to water depth under mixed planting conditions. The results show that, compared with shallow water conditions (50 cm), the growth of both submerged macrophytes was severely suppressed in deep water depth (250 cm), while only V. natans was inhibited under intermediate water depth (150 cm). Moreover, the ratio of biomass of V. natans to H. verticillata gradually increased with increasing water depth, indicating that deep water enhanced the competitive advantage of V. natans over H.verticillata. Morphological adaptation of the two submerged macrophytes to water depth was different. With increasing water depth, H. verticillata increased its height, at the cost of reduced plant numbers to adapt to poor light conditions. A similar strategy was also observed in V. natans, when water depth increased from 50 cm to 150 cm. However, both the plant height and number were reduced at deep water depth (250 cm). Our study suggests that water level reduction in lake restoration efforts could increase the total biomass of submerged macrophytes, but the domination of key plants, such as V. natans, may decrease.

Bending Moments and Shear Forces in Ships Sailing in Irregular Waves

1981 ◽  
Vol 25 (04) ◽  
pp. 243-251
Author(s):  
J. Juncher Jensen ◽  
P. Terndrup Pedersen
Keyword(s):  
Linear Part ◽  
Vertical Motion ◽  
Bending Moment ◽  
Irregular Waves ◽  
Bending Moments ◽  
Shear Forces ◽  
Strip Theory ◽  
Wave Heights ◽  
Exciting Forces ◽  
Wave Induced

This paper presents some results concerning the vertical response of two different ships sailing in regular and irregular waves. One ship is a containership with a relatively small block coefficient and with some bow flare while the other ship is a tanker with a large block coefficient. The wave-induced loads are calculated using a second-order strip theory, derived by a perturbational procedure in which the linear part is identical to the usual strip theory. The additional quadratic terms are determined by taking into account the nonlinearities of the exiting waves, the nonvertical sides of the ship, and, finally, the variations of the hydrodynamic forces during the vertical motion of the ship. The flexibility of the hull is also taken into account. The numerical results show that for the containership a substantial increase in bending moments and shear forces is caused by the quadratic terms. The results also show that for both ships the effect of the hull flexibility (springing) is a fair increase of the variance of the wave-induced midship bending moment. For the tanker the springing is due mainly to exciting forces which are linear with respect to wave heights whereas for the containership the nonlinear exciting forces are of importance.

Steep Wave Effects on Wave Induced Vertical Bending Moment Using a 3D Numerical Wave Tank

2017 ◽  
Author(s):  
Shivaji Ganesan Thirunaavukarasu ◽  
Debabrata Sen ◽  
Yogendra Parihar
Keyword(s):  
Comparative Study ◽  
Incident Wave ◽  
Bending Moment ◽  
Wave Steepness ◽  
Numerical Wave Tank ◽  
Wave Tank ◽  
Strip Theory ◽  
Numerical Wave ◽  
Wave Induced ◽  
Vertical Bending Moment

This paper presents a detail comparative study on wave induced vertical bending moment (VBM) between linear and approximate nonlinear calculations using a 3D numerical wave tank (NWT) method. The developed numerical approach is in time domain where the ambient incident waves can be defined by any suitable wave theory. Certain justifying approximations employed in the solution of the interaction hydrodynamics (diffraction and radiation) enabling the NWT to generate stable long duration time histories of all parameters of interest. This is an extension of our earlier works towards the development of a practical NWT based solution for wave-structure interactions [1]. After a brief outline of the implemented numerical details, a comprehensive validation and verification of vertical shear force (VSF) and bending moment RAOs computed using the linearized version of the NWT against the usual linear results of strip theory and 3D panel codes are presented. Next we undertake the comparative study between the fully linear and approximate nonlinear versions of the present code for different incident wave steepness. In the approximate nonlinear formulation, the ambient incident wave is defined by the full nonlinear numerical wave model based on Fourier approximation method which can generate very steep steady periodic nonlinear waves up to the near wave breaking limit. The nonlinearities associated with the incident Froude Krylov and hydrostatic restoring forces/moments are exact up to the instantaneous wetted surface at the displaced location, but the hydrodynamic diffraction and radiation effects are linearized around the mean wetted surface. The standard S175 container hull is considered for the comparative studies because of its geometric nonlinearities. Numerical simulations are performed for four different wave lengths with increasing wave steepness. It is observed that the computed wave induced VBM amidships from the approximate nonlinear results can be almost 30% higher compared to the results from a purely linear solution, which can be a critical issue from the safety point. Significant higher harmonics are also observed in the approximate nonlinear results which at some times may be responsible for exciting the undesirable whipping/springing responses.

scholarly journals Modulational instability and wave amplification in finite water depth

2014 ◽  
Vol 14 (3) ◽  
pp. 705-711 ◽  
Author(s):  
L. Fernandez ◽  
M. Onorato ◽  
J. Monbaliu ◽  
A. Toffoli
Keyword(s):  
Plane Wave ◽  
Water Depth ◽  
Modulational Instability ◽  
Wave Train ◽  
Rogue Waves ◽  
Side Band ◽  
Sea Floor ◽  
Wave Amplification ◽  
Finite Water Depth ◽  
Wave Induced

Abstract. The modulational instability of a uniform wave train to side band perturbations is one of the most plausible mechanisms for the generation of rogue waves in deep water. In a condition of finite water depth, however, the interaction with the sea floor generates a wave-induced current that subtracts energy from the wave field and consequently attenuates the instability mechanism. As a result, a plane wave remains stable under the influence of collinear side bands for relative depths kh &amp;leq; 1.36 (where k is the wavenumber of the plane wave and h is the water depth), but it can still destabilise due to oblique perturbations. Using direct numerical simulations of the Euler equations, it is here demonstrated that oblique side bands are capable of triggering modulational instability and eventually leading to the formation of rogue waves also for kh &amp;leq; 1.36. Results, nonetheless, indicate that modulational instability cannot sustain a substantial wave growth for kh < 0.8.

Analysis of wave induced drift forces acting on a submerged sphere in finite water depth

1994 ◽  
Vol 16 (6) ◽  
pp. 353-361 ◽  
Author(s):  
G.X. Wu ◽  
J.A. Witz ◽  
Q. Ma ◽  
D.T. Brown
Keyword(s):  
Water Depth ◽  
Submerged Sphere ◽  
Finite Water Depth ◽  
Wave Induced ◽  
Drift Forces

An Advanced Salvage Method for Damaged Ship Structures

2021 ◽  
Author(s):  
Alessandro La Ferlita ◽  
Helge Rathje ◽  
Thomas Lindemann ◽  
Patrick Kaeding ◽  
Robert Bronsart
Keyword(s):  
Decision Making ◽  
Environmental Conditions ◽  
Bending Moment ◽  
Decision Making Process ◽  
Iterative Approach ◽  
Short Term ◽  
Smith Method ◽  
Longitudinal Strength ◽  
Wave Induced ◽  
Damaged Ship

An advanced salvage method is proposed for damaged ships to ensure a short-term decision-making process for a safe ocean towage to the repair yard. The residual longitudinal strength must be greater than the sum of the still water and the maximum vertical wave bending moment. The ultimate bending moment is determined numerically for a container vessel by using an incremental iterative approach (Smith method) and wave-induced loads are predicted by means of hydrodynamic analyses. Successful applicability of the advanced salvage method is demonstrated for a damaged container vessel, which was towed from La Libertad, Ecuador, via Panama to the repair yard in Zhoushan, China, in restricted environmental conditions.

scholarly journals Ship waves on uniform shear current at finite depth: wave resistance and critical velocity

2016 ◽  
Vol 791 ◽  
pp. 539-567 ◽  
Author(s):  
Yan Li ◽  
Simen Å Ellingsen
Keyword(s):  
Froude Number ◽  
Critical Velocity ◽  
Water Depth ◽  
Deep Water ◽  
Wave Resistance ◽  
Ship Motion ◽  
Ship Waves ◽  
Lateral Wave ◽  
Shear Current ◽  
Finite Water Depth

We present a comprehensive theory for linear gravity-driven ship waves in the presence of a shear current with uniform vorticity, including the effects of finite water depth. The wave resistance in the presence of shear current is calculated for the first time, containing in general a non-zero lateral component. While formally apparently a straightforward extension of existing deep water theory, the introduction of finite water depth is physically non-trivial, since the surface waves are now affected by a subtle interplay of the effects of the current and the sea bed. This becomes particularly pronounced when considering the phenomenon of critical velocity, the velocity at which transversely propagating waves become unable to keep up with the moving source. The phenomenon is well known for shallow water, and was recently shown to exist also in deep water in the presence of a shear current (Ellingsen, J. Fluid Mech., vol. 742, 2014, R2). We derive the exact criterion for criticality as a function of an intrinsic shear Froude number $S\sqrt{b/g}$ ($S$ is uniform vorticity, $b$ size of source), the water depth and the angle between the shear current and the ship’s motion. Formulae for both the normal and lateral wave resistance forces are derived, and we analyse their dependence on the source velocity (or Froude number $Fr$) for different amounts of shear and different directions of motion. The effect of the shear current is to increase wave resistance for upstream ship motion and decrease it for downstream motion. Also the value of $Fr$ at which $R$ is maximal is lowered for upstream and increased for downstream directions of ship motion. For oblique angles between ship motion and current there is a lateral wave resistance component which can amount to 10–20 % of the normal wave resistance for side-on shear and $S\sqrt{b/g}$ of order unity. The theory is fully laid out and far-field contributions are carefully separated off by means of Cauchy’s integral theorem, exposing potential pitfalls associated with a slightly different method (Sokhotsky–Plemelj) used in several previous works.

Estimation of hull girder vertical bending moments including non-linear and flexibility effects using closed form expressions

2009 ◽  
Vol 223 (3) ◽  
pp. 377-390 ◽  
Author(s):  
P T Pedersen ◽  
J J Jensen
Keyword(s):  
Closed Form ◽  
Linear Response ◽  
Bending Moment ◽  
Phase Lag ◽  
Bending Moments ◽  
Hull Girder ◽  
Strip Theory ◽  
Non Linear ◽  
Bow Flare ◽  
Wave Induced

A simple but rational procedure for prediction of extreme wave-induced hull girder bending moment in slender mono-hull displacement vessels is presented. The procedure takes into account main ship hull characteristics such as length, breadth, draught, block coefficient, bow flare coefficient, forward speed, and hull flexibility. The wave-induced loads are evaluated for specific operational profiles. Non-linearity in the wave bending moment is modelled using results derived from a second-order strip theory and water entry solutions for wedge-type sections. Hence, bow flare slamming is accounted for through a momentum type of approach. The stochastic properties of this non-linear response are calculated through a monotonic Hermite transformation. In addition, the impulse loading attributable to, for example, bottom slamming or a rapid change in bow flare is included using a modal expansion in the two lowest vertical vibration modes. These whipping vibrations are added to the wave frequency non-linear response, taking into account the rise time of the impulse response as well as the phase lag between the occurrence of the maximum non-linear load and the maximum impulse load. Previous results for the sagging bending moment are validated by comparison with fully non-linear strip theory calculations and supplemented with new closed form results for the hogging bending moment. Focus is on the extreme hull girder hogging bending moment. Owing to the few input parameters, this procedure can be used to estimate the wave-induced bending moments at the conceptual design phase. Another application area is for novel single-hull ship types not presently covered by the rules of the classification societies. As one application example the container ship MSC Napoli is considered. Further validations are needed, however, in order to select proper values of the parameters entering the analytical form of the slamming impulse.

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