Initial Wave Height and Total Energy of Landslide-Generated Tsunamis from Translatory Wave Theory

2017 ◽  
pp. 159-174
Author(s):  
Jonas Elíasson
Keyword(s):  
Total Energy ◽  
Wave Height ◽  
Wave Theory ◽  
Initial Wave

Contributions to the theory of stokes waves

1955 ◽  
Vol 51 (4) ◽  
pp. 713-736 ◽  
Author(s):  
S. C. De
Keyword(s):  
Wave Height ◽  
Flow Rate ◽  
Volume Flow Rate ◽  
Wave Theory ◽  
Finite Depth ◽  
Volume Flow ◽  
Steady Flows ◽  
Total Head ◽  
Stokes Waves ◽  
Fifth Order

ABSTRACTThe well-known Stokes theory (9, 10) of waves of permanent form in water of finite depth has been extended to the fifth order of approximation. The solutions have been first obtained in the form of equations for the space coordinates x and y as functions of the velocity potential Φ and stream function ψ. Expressions for the complex potential W in terms of the complex variable z ( = x + iy), the form of the wave profile, and the square of the wave velocity have been obtained to the fifth order.Expressions for the three physical quantities Q, R and S, where Q is the volume flow rate per unit span, R is the energy per unit mass (i.e. g times the total head, measuring heights from the bottom and pressures from atmospheric) and S is the momentum flow rate per unit spaa, corrected for pressure forces and divided by density, have been obtained to the fifth order. The values for the dimensionless quantities r = R/Rc and s = S/Sc, where Rc and Sc refer to the values of R and S for a critical stream of volume flow Q, are tabulated for certain values of the ratios mean depth to wavelength and amplitude to wavelength. The values of r and s thus obtained have been used to calculate the ratios of mean depth to wavelength and of wave height to wavelength according to the cnoidal wave theory as recently presented by Benjamin and Light-hill(1), and the results are found to be in satisfactory agreement with that from Stokes's theory for waves longer than six times the depth.The (r, s) diagram introduced in the recent work of Benjamin and Lighthill(1) has been further considered, and the unshaded part of the diagram referred to in that paper has been mapped with a network of curves for constant values of the ratios of mean depth to wavelength and of wave height to wavelength (Fig. 2). The third barrier to the existence of steady flows, corresponding to ‘waves of greatest height’ referred to in that paper, has also been indicated in Fig. 2.

scholarly journals MEASUREMENT OF INCIDENT WAVE HEIGHT IN COMPOSITE WAVE TRAINS

1974 ◽  
Vol 1 (14) ◽  
pp. 21
Author(s):  
Ake Sandstrom
Keyword(s):  
Wave Height ◽  
Incident Wave ◽  
Wave Train ◽  
Wave Length ◽  
Wave Theory ◽  
Arithmetic Mean ◽  
Reflected Waves ◽  
Wave Heights ◽  
Wave Trains ◽  
Composite Wave

A method is proposed for measurement of the incident wave height in a composite wave train. The composite wave train is assumed to consist of a superposition of regular incident and reflected waves with the same wave period. An approximate value of the incident wave height is obtained as the arithmetic mean of the wave heights measured "by two gauges separated a quarter of a wave length. The accuracy of the method in relation to the location of the gauges and the wave parameters is investigated using linear and second order wave theory. Results of the calculations are presented in diagrams.

scholarly journals DIRECTIONAL WAVE SPECTRA AND WAVE KINEMATICS IN HURRICANES CARMEN AND ELOISE

1980 ◽  
Vol 1 (17) ◽  
pp. 34
Author(s):  
G.Z. Forristall ◽  
E.G. Ward ◽  
V.J. Cardone
Keyword(s):  
Wave Height ◽  
Local Equilibrium ◽  
Wave Theory ◽  
Electromagnetic Current ◽  
Linear Wave ◽  
Directional Spectrum ◽  
Wave Kinematics ◽  
Storm Waves ◽  
Velocity Probability ◽  
Realistic Description

A realistic description of the kinematics of hurricane waves requires that the directional spectrum of the sea be known. Models for hindcasting the directional spectrum have existed for some time, but there has been a dearth of data available for checking the directional characteristics of the hindcasts. Hurricane Carmen in 1974 and hurricane Eloise in 1975 passed reasonably close to platforms in the Gulf of Mexico which were instrumented with wave staffs and electromagnetic current meters. The maximum recorded significant wave height was 29 feet. The simultaneous measurements of wave height and water particle velocity permitted estimates of the directional spectra to be made. The estimated directional spectra are complicated and often bimodal in frequency and direction. Swell from the center of the storm can propagate in directions over 90 degrees away from the direction of the shorter waves which are in local equilibrium with the wind. The hindcast model reproduces these directional features remarkably well. The measurements of wave kinematics also permitted tests of the accuracy of wave theories in high and confused storm waves. All of the unidirectional theories tested showed a bias toward overpredicting the velocity under the highest waves. However, the kinetic energy in the velocity components and the velocity probability distribution could be found to within a ten percent scatter using directional spectral concepts and linear wave theory.

scholarly journals EFFECT OF WAVE-CURRENT INTERACTION ON THE WAVE PARAMETER

1982 ◽  
Vol 1 (18) ◽  
pp. 28
Author(s):  
Yu-Cheng Li ◽  
John B. Herbich
Keyword(s):  
Wave Height ◽  
Wave Length ◽  
Wave Theory ◽  
Length Change ◽  
Numerical Calculations ◽  
Wave Parameter ◽  
Linear Wave ◽  
Linear Wave Theory ◽  
Wide Range ◽  
Non Linear

The interaction of a gravity wave with a steady uniform current is described in this paper. Numerical calculations of the wave length change by different non-linear wave theories show that errors in the results computed by the linear wave theory are less than 10 percent within the range of 0.15 < d/Ls s 0.40, 0.01 < Hs/Ls < 0.07 and -0.15 < U/Cs i 0.30. Numerical calculations of wave height change employing different wave theories show that errors in the results obtained by the linear wave theory in comparison with the non-linear theories are greater when the opposing relative current and wave steepness become larger. However, within range of the following currents such errors will not be significant. These results were verified by model tests. Nomograms for the modification of wave length and wave height by the linear wave theory and Stokes1 third order theory are presented for a wide range of d/Ls, Hs/Ls and U/C. These nomograms provide the design engineer with a practical guide for estimating wave lengths and heights affected by currents.

scholarly journals Numerical Study on Regular Wave Shoaling, De-Shoaling and Decomposition of Free/Bound Waves on Gentle and Steep Foreshores

2020 ◽  
Vol 8 (5) ◽  
pp. 334 ◽  
Author(s):  
Mads Røge Eldrup ◽  
Thomas Lykke Andersen
Keyword(s):  
Stream Function ◽  
Wave Height ◽  
Energy Flux ◽  
Nonlinear Waves ◽  
Numerical Study ◽  
Mechanical Energy ◽  
Normal Incidence ◽  
Wave Theory ◽  
Numerical Tests ◽  
Linear Waves

Numerical tests are performed to investigate wave transformations of nonlinear nonbreaking regular waves with normal incidence to the shore in decreasing and increasing water depth. The wave height transformation (shoaling) of nonlinear waves can, just as for linear waves, be described by conservation of the mechanical energy flux. The numerical tests show that the mechanical energy flux for nonlinear waves on sloping foreshores is well described by stream function wave theory for horizontal foreshore. Thus, this theory can be used to estimate the shoaled wave height. Furthermore, the amplitude and the celerity of the wave components of nonlinear waves on mildly sloping foreshores can also be predicted with the stream function wave theory. The tests also show that waves propagating to deeper water (de-shoaling) on a very gentle foreshore with a slope of cot(β) = 1200 can be described in the same way as shoaling waves. For de-shoaling on steeper foreshores, free waves are released leading to waves that are not of constant form and thus cannot be modelled by the proposed approach.

scholarly journals THE MEASURED PROPERTIES OF IRREGULAR WAVE BREAKING AND WAVE HEIGHT CHANGE AFTER BREAKING ON THE SLOPE

1988 ◽  
Vol 1 (21) ◽  
pp. 29 ◽  
Author(s):  
Akira Seyama ◽  
Akira Kimura
Keyword(s):  
Wave Height ◽  
Water Depth ◽  
Wave Theory ◽  
Irregular Waves ◽  
Linear Wave ◽  
Periodic Waves ◽  
Zero Crossing ◽  
Irregular Wave ◽  
Height Change ◽  
Cross Waves

Wave height change of the zero-down-cross waves on uniform slopes were examined experimentally. The properties of shoaling, breaking and decay after breaking for a total of about 4,000 irregular waves of the Pierson-Moskowitz type on 4 different slopes (1/10, 1/20, 1/30 and 1/50) were investigated. The shoaling property of the zero-down-cross waves can be approximated by the linear wave theory. However, the properties of breaking and decay after breaking differ considerably from those for periodic waves. The wave height water depth ratio (H/d) at the breaking point for the zero-down-cross waves is about 30% smaller than that for periodic waves on average despite the slopes. Wave height decay after breaking also differs from that for periodic waves and can be classified into three regions, i.e. shoaling, plunging and bore regions. Experimental equations for the breaking condition and wave height change after breaking are proposed in the study. A new definition of water depth for the zero-crossing wave analysis which can reduce the fluctuation in the plotted data is also proposed.

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.

Tight-Binding Initialization for Generating High-Quality Initial Wave Functions: Application to Defects and Impurities in GaN

1995 ◽  
Vol 408 ◽  
Author(s):  
Jörg Neugebauer ◽  
Chris G. Van De Walle
Keyword(s):  
Plane Wave ◽  
Total Energy ◽  
Tight Binding ◽  
Wave Functions ◽  
Basis Set ◽  
Energy Methods ◽  
High Quality ◽  
Initial Wave ◽  
Efficient Construction ◽  
Energy Convergence

AbstractWe describe a new method that allows an efficient construction of high-quality initial wavefunctions which are required as input for iterative total-energy methods. The key element of the method is the reduction of the parameter space (number of wavefunctions) by about two orders of magnitude by projecting the plane-wave basis onto an atomic basis. We show that the wave functions constructed within this basis set are very close to the exact plane-wave wavefunctions, resulting in a rapid total-energy convergence.

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).

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.

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