Cnoidal Wave Theory for Application To Offshore Structural Design

1972 ◽  
Author(s):  
Gerald O. Mallery ◽  
George C. Clark
Keyword(s):  
Structural Design ◽  
Wave Theory ◽  
Cnoidal Wave

Effects of Cnoidal Wave-Induced Seepage on Vertical Breakwater Resting on Permeable Elastic Seabed

2014 ◽  
Vol 716-717 ◽  
pp. 284-288
Author(s):  
Jian Kang Yang ◽  
Hua Huang ◽  
Lin Guo ◽  
Jing Rong Lin ◽  
Qing Yong Zhu ◽  
...  
Keyword(s):  
Shallow Water ◽  
Wave Theory ◽  
Cnoidal Wave ◽  
Load Prediction ◽  
Wave Load ◽  
Seepage Pressure ◽  
Theoretical Investigations ◽  
Nonlinearity Effect ◽  
Wave Nonlinearity ◽  
Wave Induced

Theoretical investigations on cnoidal waves interacting with breakwater resting on permeable elastic seabed are presented in this paper. Based on the shallow water reflected wave theory and Biot consolidation theory on wave-induced seepage pressure, the analytical solutions to first order cnoidal wave reflection and wave-induced seepage pressure are obtained by the eigenfunction expansion approach. Numerical results are presented to show the effects of depth of water, breakwater geometry on cnoidal wave-induced seepage uplift force and overturning moment. Compared with Airy wave theory, in certain shallow water conditions, the shallow water wave theory can more effectively illustrate wave nonlinearity effect in wave load prediction.

scholarly journals SHOALING OF CNOIDAL WAVES

1972 ◽  
Vol 1 (13) ◽  
pp. 18 ◽  
Author(s):  
I.A. Svendson ◽  
O. Brink-Kjaer
Keyword(s):  
Wave Train ◽  
Wave Theory ◽  
Cnoidal Wave ◽  
Sinusoidal Wave ◽  
Cnoidal Waves ◽  
Numerical Examples ◽  
Sloping Bottom

An equation is derived which governs the propagation of a cnoidal wave train over a gently sloping bottom. The equation is solved numerically, the solution being tabulated in terms of fH (Eq. 47) as a function of Ei = (Etr/pg) 1/3/gT2 and hi = h/gT2. Results are compared with sinusoidal wave theory. Two numerical examples are included.

scholarly journals EFFECT OF BEACH SLOPE AND SHOALING ON WAVE ASYMMETRY

1968 ◽  
Vol 1 (11) ◽  
pp. 10 ◽  
Author(s):  
M.D. Adeyemo
Keyword(s):  
Shallow Water ◽  
Quantitative Study ◽  
Experimental Work ◽  
Theoretical Study ◽  
Wave Theory ◽  
Cnoidal Wave ◽  
Quantitative Correlation ◽  
Wave Slope ◽  
Oscillatory Waves ◽  
Good Agreement

This paper is concerned with the quantitative study of the geometrical asymmetry associated with shallow water oscillatory waves in the breaker zone. Three descriptions of wave asymmetry are defined and examined : (l) Wave vertical asymmetry i2^ Wave slope asymmetry and (3) Wave horizontal asymmetry The effects of shoaling, produced by beaches of different slope, on the wave asymmetry are examined. Six beach slopes in the range 1:4 to 1:18 were employed, and a quantitative correlation was found to exist between the wave slope asymmetry, wave horizontal asymmetry and the wave vertical asymmetry. An expression is given for the wave horizontal asymmetry based on the expression for the wave vertical asymmetry from the cnoidal wave theory. The theoretical study of wave slope asymmetry made by Biesel (1) and the results of the experimental work on the wave slope asymmetry in the present work are compared and gave a good agreement*

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.

Integral properties of periodic gravity waves of finite amplitude

1975 ◽  
Vol 342 (1629) ◽  
pp. 157-174 ◽  
Keyword(s):  
Solitary Wave ◽  
Gravity Waves ◽  
Deep Water ◽  
Water Waves ◽  
Wave Theory ◽  
Finite Amplitude ◽  
Cnoidal Wave ◽  
The Mean ◽  
Exact Relations ◽  
Kinetic And Potential Energies

A number of exact relations are proved for periodic water waves of finite amplitude in water of uniform depth. Thus in deep water the mean fluxes of mass, momentum and energy are shown to be equal to 2T(4T—3F) and (3T—2V) crespectively, where T and V denote the kinetic and potential energies and c is the phase velocity. Some parametric properties of the solitary wave are here generalized, and some particularly simple relations are proved for variations of the Lagrangian The integral properties of the wave are related to the constants Q, R and S which occur in cnoidal wave theory. The speed, momentum and energy of deep-water waves are calculated numerically by a method employing a new expansion parameter. With the aid of Padé approximants, convergence is obtained for waves having amplitudes up to and including the highest. For the highest wave, the computed speed and amplitude are in agreement with independent calculations by Yamada and Schwartz. At the same time the computations suggest that the speed and energy, for waves of a given length, are greatest when the height is less than the maximum. In this respect the present results tend to confirm previous computations on solitary waves.

scholarly journals Structural Design of a Jacket Platform to the Colombian Caribbean Sea

2016 ◽  
Vol 10 (19) ◽  
pp. 61
Author(s):  
Jairo H. Cabrera ◽  
Jair Macía Ávilar
Keyword(s):  
Numerical Model ◽  
Structural Design ◽  
Theoretical Foundation ◽  
Caribbean Sea ◽  
Wave Theory ◽  
Type Structure ◽  
Analysis Model ◽  
Offshore Structure ◽  
New Type

This research paper summarizes the study of the requirements and basic theoretical foundation for the development of structural design of fixed platform type Jacket, resulting in the proposal for a analysis model for this type of offshore structure. Aspects related with cinematics evaluation, selecting of wave theory and hydrodynamic proper formula are also considered in the calculation of acting forces and the need for local metocean data in the analysis. A case study of application of the model for a new type structure jacket RC-5 Block of the Colombian Caribbean is also presented including its geometry proposed and some results of the numerical model procedures.

scholarly journals HYPERBOLIC WAVES AND THEIR SHOALING

1968 ◽  
Vol 1 (11) ◽  
pp. 9 ◽  
Author(s):  
Yuichi Iwagaki
Keyword(s):  
Wave Height ◽  
Elliptic Functions ◽  
Wave Theory ◽  
Wave Crest ◽  
Cnoidal Wave ◽  
Practical Application ◽  
Jacobian Elliptic Functions ◽  
Complete Elliptic Integrals ◽  
Hyperbolic Waves ◽  
The Waves

Is is very difficult for engineers to deal with the cnoidal wave theory for practical application, since this theory contains the Jacobian elliptic functions, their modulus k, and the complete elliptic integrals of the first and second kinds, K and E respectively. This paper firstly proposes formulae for various wave characteristics of new waves named "hyperbolic waves", which are derived from the cnoidal wave theory under the condition that k = 1 and E = 1 but K is not infinite and are a function of T/g/h and H/h, so that cnoidal waves can be approximately expressed as hyperbolic waves by primary functions only, in which T is the wave period, h the water depth and H the wave height. Secondly, as an application of the hyperbolic wave theory, the present paper deals with wave shoaling, that is, changes in the wave height, the wave crest height above still water level, and the wave velocity, when the waves proceed into shallow water from deep water.

A presentation of cnoidal wave theory for practical application

1960 ◽  
Vol 7 (2) ◽  
pp. 273-286 ◽  
Author(s):  
R. L. Wiegel
Keyword(s):  
Particle Velocity ◽  
Wave Theory ◽  
Periodic Waves ◽  
Cnoidal Wave ◽  
Laboratory Measurements ◽  
Practical Application ◽  
Water Particle ◽  
Wave Celerity

Cnoidal wave theory is appropriate to periodic waves progressing in water whose depth is less than about one-tenth the wavelength. The leading results of existing theories are modified and given in a more practical form, and the graphs necessary to their use by engineers are presented. As well as results for the wave celerity and shape, expressions and graphs for the water particle velocity and local acceleration fields are given. A few comparisons between theory and laboratory measurements are included.

Sign in / Sign up

Export Citation Format

Share Document