Forcing of a bottom-mounted circular cylinder by steep regular water waves at finite depth

2014 ◽  
Vol 755 ◽  
pp. 1-34 ◽  
Author(s):  
Bo T. Paulsen ◽  
H. Bredmose ◽  
H. B. Bingham ◽  
N. G. Jacobsen
Keyword(s):  
Free Surface ◽  
Circular Cylinder ◽  
Water Waves ◽  
Finite Depth ◽  
Load Cycle ◽  
Harmonic Force ◽  
Third Harmonic ◽  
The Third ◽  
Nonlinear Motion ◽  
Secondary Load

AbstractForcing by steep regular water waves on a vertical circular cylinder at finite depth was investigated numerically by solving the two-phase incompressible Navier–Stokes equations. Consistently with potential flow theory, boundary layer effects were neglected at the sea bed and at the cylinder surface, but the strong nonlinear motion of the free surface was included. The numerical model was verified and validated by grid convergence and by comparison to relevant experimental measurements. First-order convergence towards an analytical solution was demonstrated and an excellent agreement with the experimental data was found. Time-domain computations of the normalized inline force history on the cylinder were analysed as a function of dimensionless wave height, water depth and wavelength. Here the dependence on depth was weak, while an increase in wavelength or wave height both lead to the formation of secondary load cycles. Special attention was paid to this secondary load cycle and the flow features that cause it. By visual observation and a simplified analytical model it was shown that the secondary load cycle was caused by the strong nonlinear motion of the free surface which drives a return flow at the back of the cylinder following the passage of the wave crest. The numerical computations were further analysed in the frequency domain. For a representative example, the secondary load cycle was found to be associated with frequencies above the fifth- and sixth-harmonic force component. For the third-harmonic force, a good agreement with the perturbation theories of Faltinsen, Newman & Vinje (J. Fluid Mech., vol. 289, 1995, pp. 179–198) and Malenica & Molin (J. Fluid Mech., vol. 302, 1995, pp. 203–229) was found. It was shown that the third-harmonic forces were estimated well by a Morison force formulation in deep water but start to deviate at decreasing depth.

EFFECTS OF SURFACE TENSION ON TRAPPED MODES IN A TWO-LAYER FLUID

2015 ◽  
Vol 57 (2) ◽  
pp. 189-203 ◽  
Author(s):  
S. SAHA ◽  
S. N. BORA
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Circular Cylinder ◽  
Boundary Value Problems ◽  
Finite Depth ◽  
Trapped Modes ◽  
Trapped Waves ◽  
Linearized Theory ◽  
Horizontal Circular Cylinder ◽  
Effect Of Surface

We consider a two-layer fluid of finite depth with a free surface and, in particular, the surface tension at the free surface and the interface. The usual assumptions of a linearized theory are considered. The objective of this work is to analyse the effect of surface tension on trapped modes, when a horizontal circular cylinder is submerged in either of the layers of a two-layer fluid. By setting up boundary value problems for both of the layers, we find the frequencies for which trapped waves exist. Then, we numerically analyse the effect of variation of surface tension parameters on the trapped modes, and conclude that realistic changes in surface tension do not have a significant effect on the frequencies of these.

scholarly journals Resonance of a tension leg platform exited by third-harmonic force in nonlinear regular waves

2015 ◽  
Vol 373 (2033) ◽  
pp. 20140105 ◽  
Author(s):  
B. Z. Zhou ◽  
G. X. Wu
Keyword(s):  
Harmonic Wave ◽  
The Body ◽  
Initial Time ◽  
Wave Forces ◽  
Regular Waves ◽  
Harmonic Force ◽  
Tension Leg Platform ◽  
Incoming Wave ◽  
Third Harmonic ◽  
The Third

The resonance of a floating tension leg platform (TLP) excited by the third-harmonic force of a regular wave is investigated based on fully nonlinear theory with a higher order boundary element method (BEM). The total wave elevation and the total velocity potential are separated into two parts, based on the incoming wave from infinity and the disturbed potential by the body. A numerical radiation condition is then applied at the far field to absorb the disturbed potential without affecting the incident potential. The BEM mesh on the free surface is generated only once at the initial time and the element nodes are rearranged subsequently without changing their connectivity by using a spring analysis method. Through some auxiliary functions, the mutual dependence of fluid/structure motions is decoupled, which allows the body acceleration to be obtained without the knowledge of the pressure distribution. Numerical simulation is carried out for the interaction of a floating TLP with waves. The focus is on the motion principally excited by higher harmonic wave forces. In particular, the resonance of the ISSC TLP generated by the third-order force at the triple wave frequency in regular waves is investigated, together with the tensions of the tendons.

scholarly journals Flow from a source above a sloping base

2020 ◽  
Vol 61 ◽  
pp. C75-C88
Author(s):  
Shaymaa Mukhlif Shraida ◽  
Graeme Hocking
Keyword(s):  
Free Surface ◽  
Flow Rate ◽  
Water Waves ◽  
Line Source ◽  
Free Surface Flow ◽  
Finite Depth ◽  
Free Surface Flows ◽  
Surface Flow ◽  
Theoretical Research ◽  
Line Sink

We consider the outflow of water from the peak of a triangular ridge into a channel of finite depth. Solutions are computed for different flow rates and bottom angles. A numerical method is used to compute the flow from the source for small values of flow rate and it is found that there is a maximum flow rate beyond which steady solutions do not seem to exist. Limiting flows are computed for each geometrical configuration. One application of this work is as a model of saline water being returned to the ocean after desalination. References Craya, A. ''Theoretical research on the flow of nonhomogeneous fluids''. La Houille Blanche, (1):22–55, 1949. doi:10.1051/lhb/1949017 Dun, C. R. and Hocking, G. C. ''Withdrawal of fluid through a line sink beneath a free surface above a sloping boundary''. J. Eng. Math. 29:1–10, 1995. doi:10.1007/bf00046379 Hocking, G. ''Cusp-like free-surface flows due to a submerged source or sink in the presence of a flat or sloping bottom''. ANZIAM J. 26:470–486, 1985. doi:10.1017/s0334270000004665 Hocking, G. C. and Forbes, L. K. ''Subcritical free-surface flow caused by a line source in a fluid of finite depth''. J. Eng. Math. 26:455-466, 1992. doi:10.1007/bf00042763 Hocking, G. C. ''Supercritical withdrawal from a two-layer fluid through a line sink", J. Fluid Mech. 297:37–47, 1995. doi:10.1017/s0022112095002990 Hocking, G. C., Nguyen, H. H. N., Forbes, L. K. and Stokes,T. E. ''The effect of surface tension on free surface flow induced by a point sink''. ANZIAM J., 57:417–428, 2016. doi:10.1017/S1446181116000018 Landrini, M. and Tyvand, P. A. ''Generation of water waves and bores by impulsive bottom flux'', J. Eng. Math. 39(1–4):131-170, 2001. doi:10.1023/A:1004857624937 Lustri, C. J., McCue, S. W. and Chapman, S. J. ''Exponential asymptotics of free surface flow due to a line source''. IMA J. Appl. Math., 78(4):697–713, 2013. doi:10.1093/imamat/hxt016 Stokes, T. E., Hocking, G. C. and Forbes, L.K. ''Unsteady free surface flow induced by a line sink in a fluid of finite depth'', Comp. Fluids, 37(3):236–249, 2008. doi:10.1016/j.compfluid.2007.06.002 Tuck, E. O. and Vanden-Broeck, J.-M. ''A cusp-like free-surface flow due to a submerged source or sink''. ANZIAM J. 25:443–450, 1984. doi:10.1017/s0334270000004197 Vanden-Broeck, J.-M., Schwartz, L. W. and Tuck, E. O. ''Divergent low-Froude-number series expansion of nonlinear free-surface flow problems". Proc. Roy. Soc. A., 361(1705):207–224, 1978. doi:10.1098/rspa.1978.0099 Vanden-Broeck, J.-M. and Keller, J. B. ''Free surface flow due to a sink'', J. Fluid Mech, 175:109–117, 1987. doi:10.1017/s0022112087000314 Yih, C.-S. Stratified flows. Academic Press, New York, 1980. doi:10.1016/B978-0-12-771050-1.X5001-3

scholarly journals Hydrodynamic Forces on a Submerged Circular Cylinder in Two-layer Fluid with an Ice-cover

2021 ◽  
Vol 23 (08) ◽  
pp. 282-294
Author(s):  
Manomita Sahu ◽  
◽  
Dilip Das ◽  
Keyword(s):  
Free Surface ◽  
Circular Cylinder ◽  
Flexural Rigidity ◽  
Lower Layer ◽  
Wave Theory ◽  
Finite Depth ◽  
Ice Cover ◽  
Hydrodynamic Forces ◽  
Wave Number ◽  
Infinite Layer

We consider problems based on linear water wave theory concerning the interaction of wave with horizontal circular cylinder submerged in two-layer ocean consisting of a upper layer of finite depth bounded above by an ice-cover and below by an infinite layer of fluid of greater density, the ice-cover being modelled as an elastic plate of very small thickness. Using the method of multipoles, we formulate the problems of hydrodynamic forces on a submerged cylinder in either the upper or the lower layer. The vertical and horizontal forces on the circular cylinder are obtained and depicted graphically against the wave number for various values of flexural rigidity of ice-cover to show the effect of the presence of ice-cover on these quantities. Also when the flexural rigidity and surface density of the ice-cover are taken to be zero, the ice-cover tends to a free-surface. Then all the forces are the same as in the case of two-layer fluid with free surface.

Water Waves Over a Channel of Finite Depth With a Submerged Plane Barrier

1950 ◽  
Vol 2 ◽  
pp. 210-222 ◽  
Author(s):  
Albert E. Heins
Keyword(s):  
Surface Waves ◽  
Water Waves ◽  
Finite Depth ◽  
The Third ◽  
Plane Barrier

This is the third in a series of problems in the study of surface waves which have been disturbed by the presence of a plane barrier and to which a solution may be provided. We assume as in part I, that the fluid is incompressible and non-viscous, and that motion is irrotational.

Nonlinear water waves generated by an accelerated circular cylinder

1979 ◽  
Vol 92 (4) ◽  
pp. 767-781 ◽  
Author(s):  
H. J. Haussling ◽  
R. M. Coleman
Keyword(s):  
Free Surface ◽  
Circular Cylinder ◽  
Water Waves ◽  
Numerical Solutions ◽  
Nonlinear Effects ◽  
Surface Boundary ◽  
Nonlinear Water Waves ◽  
Pressure Distributions ◽  
Surface Boundary Conditions ◽  
Surface Profiles

Numerical solutions for the irrotational flow of an incompressible fluid about a circular cylinder accelerated from rest below a free surface are presented. The usual restriction to linearized free-surface boundary conditions has been avoided. The transient period from the start to a local steady state or to the development of a very steep wave slope is investigated in terms of free-surface profiles and body-surface pressure distributions. Linear and nonlinear results are used to illustrate the transition from deep submergence when nonlinear effects are small to shallow submergence when linearized analysis is inaccurate.

On the heaving motion of a circular cylinder more or less than half immersed in the free surface of a fluid

1988 ◽  
Vol 419 (1856) ◽  
pp. 107-120
Keyword(s):  
Integral Equation ◽  
Free Surface ◽  
Circular Cylinder ◽  
Integral Equations ◽  
Water Waves ◽  
Singular Integral Equations ◽  
Two Dimensional ◽  
Existence Of A Solution ◽  
Linearized Theory ◽  
Explicit Proof

We consider a problem in the linearized theory of water waves. A smooth oscillating two-dimensional body meets the free surface at angles other than right-angles. In this paper we prove the existence of a solution for this problem by using integral equations. This problem has been considered by other authors; however, their attempts have resulted in singular integral equations. To show that Fredholm theory applies to these equations involves a great deal of generalized analysis. It is shown that it is possible to obtain a well-behaved integral equation by means of an explicit modification of the source potential used to derive this equation. To illustrate this method a circular cylinder that is more than or less than half immersed and undergoing a heaving motion is considered. This method is in terms of more elementary concepts than those used by previous authors. The explicit proof also indicates how the problem may be solved in practice, and it is hoped to report on the numerical solution later.

A note on the secondary load cycle for a monopile in irregular deep water waves

2018 ◽  
Vol 849 ◽  
Author(s):  
Bjørn Hervold Riise ◽  
John Grue ◽  
Atle Jensen ◽  
Thomas B. Johannessen
Keyword(s):  
Deep Water ◽  
High Frequency ◽  
Water Waves ◽  
Load Cycle ◽  
Total Load ◽  
High Frequency Peak ◽  
Strongly Nonlinear ◽  
Secondary Load ◽  
Frequency Peak ◽  
Two Peaks

Laboratory experiments with a bottom hinged surface-piercing cylinder, exposed to irregular deep water waves, are used to investigate high-frequency forcing. The focus is on the secondary load cycle, a strongly nonlinear phenomenon regarding the wave load on a vertical cylinder, first identified by Grue et al. (1993 Preprint Series. Mechanics and Applied Mathematics, pp. 1–30. University of Oslo, available at http://urn.nb.no/URN:NBN:no-52740; 1994 Ninth International Workshop on Water Waves and Floating Bodies (ed. M. Ohkusu), pp. 77–81, available at http://iwwwfb.org). For a total of 2166 single wave events, the force above $3\unicode[STIX]{x1D714}$ (where $\unicode[STIX]{x1D714}$ is the governing wave frequency) is used to identify and split the strongly nonlinear forces into two peaks: a high-frequency peak closely correlated in time with the wave crest when the total load is positive and a high-frequency peak defining the secondary load cycle which occurs close in time to the wave zero downcrossing when the total load is negative. The two peaks are studied by regression analysis as a function of either the Keulegan–Carpenter number ($KC$) or the Froude number ($Fr$). Regarding the secondary load cycle, the best correlation is found with $Fr$. The speed of the travelling edge of the undisturbed wave approximates the fluid velocity. A threshold value separating between small and large forces is found for $KC\sim 4$–5, indicating effects of flow separation. Alternatively, the threshold occurs for $Fr\sim 0.3$–0.4, indicating local wave effects at the scale of the cylinder diameter. The findings suggest that both effects are present and important.

scholarly journals WAVE-INDUCED SEEPAGE EFFECTS ON A VERTICAL CYLINDER

1980 ◽  
Vol 1 (17) ◽  
pp. 108
Author(s):  
Thomas J.P. Durand ◽  
Peter L. Monkmeyer
Keyword(s):  
Circular Cylinder ◽  
Water Waves ◽  
Theoretical Calculations ◽  
Vertical Cylinder ◽  
Finite Depth ◽  
Pressure Amplitude ◽  
Uplift Force ◽  
Overturning Moment ◽  
Wave Induced ◽  
Circular Base

This study deals with the seepage effects experienced by a large, vertical, circular cylinder resting on a submerged bed of sand when planar water waves interact with it. Potential theory is used to describe the seepage flow field. The sea bottom pressure condition is determined from the water field velocity potential derived by MacCamy and Fuchs (1954) in the case of planar waves diffracted by a large impervious cylinder. Consideration is also given to cylinders with a thin circular base whose diameter exceeds that of the cylinder itself. The problem formulation as well as the initiation of the analysis apply to the general case of a bed of sand with finite depth. For the case of infinite depth of the porous medium, theoretical solutions for the seepage pressure are obtained in the form of infinite integrals. Theoretical solutions for the pressure along the cylinder circular base are then derived, leading by integration to closed form expressions for the wave-induced seepage uplift force and overturning moment exerted on the cylinder. These expressions for the force and moment, which are presented in non-dimensional form are shown to be universal functions of a unique variable. Graphs are provided so that very few computations are required to determine the uplift force and overturning moment exerted on a cylinder. A comparison with various approximate theories reveals the present theory to be the only one which gives reliable results in general. The amplitude and phase angle of the oscillating wave-induced pressure along the cylinder base are determined numerically. Results for the pressure amplitude are presented as non-dimensional ratios to the amplitude of the pressure that would prevail if no cylinder were disturbing the wave field. Expressions for the exit gradient around the cylinder base are also determined. Contours of the ratio of the exit gradient to the one that would prevail in the absence of a cylinder are presented. Laboratory measurements of uplift pressure amplitudes on a circular cylinder show good agreement with theoretical calculations.

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