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 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.

scholarly journals THE INTERACTION OF WAVES AND CURRENTS OVER A LONGSHORE BAR

1986 ◽  
Vol 1 (20) ◽  
pp. 116 ◽  
Author(s):  
I.A. Svendsen ◽  
J. Buhr Hansen
Keyword(s):  
Wave Height ◽  
Wave Motion ◽  
Surf Zone ◽  
Wave Theory ◽  
Runge Kutta Method ◽  
Waves And Currents ◽  
Set Up ◽  
The Waves ◽  
Wave Properties ◽  
A Current

A two-dimensional model for waves and steady currents in the surf zone is developed. It is based on a depth integrated and time averaged version of the equations for the conservation of mass, momentum, and wave energy. A numerical solution is described based on a fourth order Runge-Kutta method. The solution yields the variation of wave height, set-up, and current in the surf zone, taking into account the mass flux in the waves. In its general form any wave theory can be used for the wave properties. Specific results are given using the description for surf zone waves suggested by Svendsen (1984a), and in this form the model is used for the wave motion with a current on a beach with a longshore bar. Results for wave height and set-up are compared with measurements by Hansen & Svendsen (1986).

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.

scholarly journals CNOIDAL WAVES IN SHALLOW WATER

1964 ◽  
Vol 1 (9) ◽  
pp. 1
Author(s):  
Frank D. Masch
Keyword(s):  
Shallow Water ◽  
Power Transmission ◽  
Wave Train ◽  
Wave Theory ◽  
Finite Amplitude ◽  
Long Waves ◽  
Practical Application ◽  
Cnoidal Waves ◽  
Water Power ◽  
The Waves

The propagation of long waves of finite amplitude in water with depth to wavelength ratios less than about one-tenth and greater than about one-fiftieth can be described by cnoidal wave theory. To date little use has been made of the theory because of the difficulties involved in practical application. This paper presents the theory necessary for predicting the transforming characteristics of long waves based on cnoidal theory. Basically the method involves calculating the power transmission for a wave train m shallow water from cnoidal theory and equating this to the deep water power transmission assuming no reflections or loss of energy as the waves move into shoaling water. The equations for wave power have been programmed for the range of cnoidal waves, and the results are plotted in non-dimensional form.

How We Determine the Design Environmental Conditions and How They Impact the Structural Reliabilities?

2014 ◽  
Author(s):  
Linbin Li ◽  
Ping Li ◽  
Yuan Liu
Keyword(s):  
Wave Height ◽  
Environmental Conditions ◽  
Extreme Values ◽  
Grid Point ◽  
Steel Structures ◽  
Wave Theory ◽  
Wave Crest ◽  
Storm Event ◽  
Design Standards ◽  
Design Wave Height

This paper is based on the JIP study for the oceanographic hindcast and environmental load statistics of fixed steel structures at South China Sea under tropical cyclone conditions. It focuses on the sensitivity and comparison studies by exploring the degrees and reasons of variability that may occur in determination of design environmental conditions resulting from the selection of the design standards and approaches. The bias and efficiency in extreme values prediction are examined with respect to modeling uncertainty and statistical uncertainty. The long term distributions of maximum wave height as well as the associated wave period conditional on the design wave height are derived following the storm event based method. The approaches for combing wave, current and wind to define the design conditions and the associated biases on design load are investigated. Second order random and spreading wave theory is adopted to estimate the extreme wave crest height distributions. The extreme water level issue is addressed and recommendations are given for setting the deck elevation to achieve the explicit wave-in-deck probabilities. The studies are carried out by applying a dataset of a grid point containing 182 typhoons spanning 40 continuous years to demonstrate the analytical procedures in an understandable fashion. The results of this paper should lead to improvements in prediction of the environmental conditions for design of new-built structures to attain their target safety levels, as well as for assessment of existing structures to demonstrate their fitness-for-purpose.

scholarly journals Resonant Soliton and Soliton-Cnoidal Wave Solutions for a (3+1)-Dimensional Korteweg-de Vries-Like Equation

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Zheng-Yi Ma ◽  
Jin-Xi Fei ◽  
Jun-Chao Chen ◽  
Quan-Yong Zhu
Keyword(s):  
Wave Interaction ◽  
Elliptic Functions ◽  
Cnoidal Wave ◽  
Linear Superposition ◽  
Jacobian Elliptic Functions ◽  
Multiple Wave ◽  
Residual Symmetry ◽  
Wave Solutions ◽  
De Vries ◽  
Truncated Painlevé Expansion

The residual symmetry of a (3+1)-dimensional Korteweg-de Vries (KdV)-like equation is constructed using the truncated Painlevé expansion. Such residual symmetry can be localized and the (3+1)-dimensional KdV-like equation is extended into an enlarged system by introducing some new variables. By using Lie’s first theorem, the finite transformation is obtained for this localized residual symmetry. Further, the linear superposition of multiple residual symmetries is localized and the n-th Bäcklund transformation in the form of the determinants is constructed for this equation. For illustration more detail, the first three multiple wave solutions-the collisions of resonant solitons are depicted. Finally, with the aid of the link between the consistent tanh expansion (CTE) method and the truncated Painlevé expansion, the explicit soliton-cnoidal wave interaction solution containing three kinds of Jacobian elliptic functions for this equation is derived.

Jacobian elliptic functions and a family of bivariate peak polynomials

2021 ◽  
Vol 97 ◽  
pp. 103371
Author(s):  
Shi-Mei Ma ◽  
Jun Ma ◽  
Yeong-Nan Yeh ◽  
Roberta R. Zhou
Keyword(s):  
Elliptic Functions ◽  
Jacobian Elliptic Functions
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