scholarly journals A DYNAMICAL EXPRESSION OF WAVES IN SHALLOW WATER

1984 ◽  
Vol 1 (19) ◽  
pp. 30
Author(s):  
Y. Tsuchiya ◽  
T. Yasuda
Keyword(s):  
Shallow Water ◽  
Kdv Equation ◽  
Dynamic Structure ◽  
Elementary Excitation ◽  
Theoretical Expression ◽  
Random Wave ◽  
Random Waves ◽  
Internal Properties ◽  
Particle Velocities ◽  
The Waves

Making the assumptions that solitons are one of the most elementary excitation in random nonlinear waves in shallow water and that the waves have a coherent dynamic structure of solitons, we attempt to describe the swell-like waves theoretically "by deriving the asymptotic multisoliton solution for the KdV equation. Formulations of the random wave profiles and internal properties are also made. We conclude from the comparisons between observed and theoretical results of the propagation characteristics of the swell-like random waves and their water particle velocities, that the waves in shallow water have a coherent dynamic structure of solitons and that the theoretical expression for the waves has practically sufficient accuracy in estimating their propagation.

Experimental Study of Slow-Drift Ship Motions in Shallow Water Random Waves

2011 ◽  
Author(s):  
Carl Trygve Stansberg ◽  
Trygve Kristiansen
Keyword(s):  
Spectral Analysis ◽  
Shallow Water ◽  
Transfer Functions ◽  
Second Order ◽  
Ship Motions ◽  
Random Wave ◽  
Random Waves ◽  
Low Frequencies ◽  
Wave Basin ◽  
Drift Forces

Slowly varying motions and drift forces of a large moored ship in random waves at 35m water depth are investigated by an experimental wave basin study in scale 1:50. A simple horizontal mooring set-up is used. A second-order wave correction is applied to minimize “parasitic” long waves. The effect on the ship motion from the correction is clearly seen, although less in random wave spectra than in pure bi-chromatic waves. Empirical quadratic transfer functions (QTFs) of the surge drift force are found by use of cross-bi-spectral analysis, in two different spectra have been obtained. The QTF levels increase significantly with lower wave frequencies (except at the diagonal), which is special for finite and shallow water. Furthermore, the QTF levels frequencies at low frequencies increase significantly out from the QTF diagonal. Thus Newman’s approximation should preferrably not be used in these cases. Using the LF waves as a direct excitation in a “linear” ship force analysis gives random records that compare reasonably well with those from the cross-bi-spectral analysis. This confirms the idea that the drift forces in shallow water are closely correlated to the second-order potential, and thereby by the second-order LF waves.

scholarly journals Random wave-driven drag forces on near-bed vegetation in shallow water based on deepwater wind conditions

2019 ◽  
Vol 233 (4) ◽  
pp. 1287-1290
Author(s):  
Dag Myrhaug
Keyword(s):  
Shallow Water ◽  
Drag Force ◽  
Wind Waves ◽  
Wave Spectrum ◽  
Random Wave ◽  
Random Waves ◽  
Coastal Zones ◽  
Drag Forces ◽  
Mean Wind Speed ◽  
Wave Induced

This article provides a simple analytical method for giving estimates of random wave-driven drag forces on near-bed vegetation in shallow water from deepwater wind conditions. Results are exemplified using a Pierson–Moskowitz model wave spectrum for wind waves with the mean wind speed at the 10 m elevation above the sea surface as the parameter. The significant value of the drag force within a sea state of random waves is given, and an example typical for field conditions is presented. This method should serve as a useful tool for assessing random wave-induced drag force on vegetation in coastal zones and estuaries based on input from deepwater wind conditions.

scholarly journals ON THE RELATION BETWEEN CHANGES IN INTEGRAL QUANTITIES OF SHOALING WAVES AND BREAKING INCEPTION

1982 ◽  
Vol 1 (18) ◽  
pp. 2
Author(s):  
Takeshi Yasuda ◽  
Shintaro Goto ◽  
Yoshito Ysuchiya
Keyword(s):  
Conservation Laws ◽  
Stream Function ◽  
Function Method ◽  
Breaking Waves ◽  
Variable Coefficients ◽  
Shoaling Waves ◽  
Wave Profiles ◽  
Internal Properties ◽  
Particle Velocities ◽  
The Waves

This paper describes a mechanism of breaking waves over sloping bottoms in terms of changes in integral quantities of the waves. Systematic computations are made of wave profiles of shoaling waves up to the numerical unstable points by using the K-dV equation with variable coefficients and internal properties such as horizontal and vertical water particle velocities by a stream function method satisfying the conservation laws of mass and energy. Applicability of the numerical results is examined and a relation between numerical unstable points and actual breaker points is found. Characteristics of the integral quantities of shoaling waves are investigated in relation to the existence of the extremum of the energy of the shoaling waves and their breaking inception.

Second-Order Random Wave Kinematics and Resulting Loads on a Bottom-Fixed Slender Monopile

2013 ◽  
Author(s):  
Carl Trygve Stansberg ◽  
Andreas Amundsen ◽  
Sebastien Fouques ◽  
Ole David Økland
Keyword(s):  
Second Order ◽  
Offshore Wind ◽  
Random Wave ◽  
Wave Loads ◽  
Random Waves ◽  
Shear Forces ◽  
Traditional Use ◽  
Wave Kinematics ◽  
Drag Forces ◽  
Particle Velocities

The importance of including second-order nonlinear random wave kinematics in the numerical prediction of drag-induced shear forces and moments, at various levels on a bottom-fixed slender monopile in 40m water depth, is investigated. A vertical circular cylinder of diameter 0.5m is considered, representing typical dimensions of members in jacket type foundations of offshore wind turbines. The focus is here on the wave loads only, and wind and a propeller are therefore not included in this study. In particular, the main focus is on the effects from second-order random wave kinematics on the structural quasi-static time-varying loads due to drag forces in heavy storm wave conditions. Comparisons are made to the traditional use of Airy waves with various ways of stretching. An in-house numerical FEM code developed for structural analysis, NIRWANA, is used for this study. Thus one purpose of the present work is also to verify the implementation of the second-order random waves in the code. The results show significant effects, especially in the wave zone. Extreme crests are around 15%–20% increased, free-surface extreme particle velocities increase by around 30%–40%, while the velocities at levels below MWL are, on the other hand, somewhat reduced. The resulting peak shear forces, and in particular the moments, are thereby increased by typically 50%–100% in the upper parts of the column. At the base the peak shear forces are comparable to the traditional methods, while moments are still somewhat higher. Another effect is the generation of more high-frequency load contributions, which may be important to address further with respect to natural frequencies of such towers.

scholarly journals NUMERICAL SIMULATION OF IRREGULAR BIMODAL WAVE SYSTEM DYNAMICS WITHIN THE FRAMEWORK OF KORTEWEG-DE VRIES EQUATION

2019 ◽  
Vol 47 (1) ◽  
pp. 38-40
Author(s):  
E.G. Didenkulova ◽  
A.V. Slunyaev ◽  
E.N. Pelinovsky
Keyword(s):  
Numerical Simulation ◽  
Shallow Water ◽  
Vries Equation ◽  
Kdv Equation ◽  
Wave Spectrum ◽  
Wave System ◽  
Quasi Equilibrium ◽  
Long Wave ◽  
De Vries ◽  
The Waves

The dynamics of wave ensembles in shallow water is studied within the framework of the nonlinear dispersive Korteweg – de Vries (KdV) equation by numerical simulation. Bimodal wave systems whose energy is distributed over two spectral domains are considered: the “additional” lobe which corresponds to the system of longer or shorter waves is added to the “main” spectral peak. The concerned problem describes, for example, the interaction between wind waves and swell in shallow water. The case of the unimodal waves (considered in (Pelinovsky, Sergeeva, 2006) is used as the reference. The limitations of the implied assumptions and the relationship of the idealized model to the realistic conditions in the ocean were discussed in the recent paper (Wang et al, 2018). Based on the detailed consideration of the 6 simulated cases, the following general conclusions may be formulated. The transition from the initial state to the quasi-equilibrium one is accompanied by strong variations of the wave characteristics, when the waves exhibit the most extreme features. In particular, the wave kurtosis grows suddenly and the abnormal heavy tails in the wave amplitude probability distributions appear. These processes are observed in all the cases of the bimodal spectra and are quite similar to the single-mode regime. The coexistence of a long-wave system smoothens the rapid oscillations of the wave extremes and kurtosis which take place during the transition stage. The presence of a short-wave system makes the waves on average more symmetric. Skewness attains the minimum value compared to the other cases. The co-existence of shorter waves practically does not change the wave kurtosis or the probability of the wave heights. In contrast, the presence of a long-wave system makes the waves more asymmetric and more extreme. The probability of large waves increases in the bimodal systems with a low-frequency component. The initial wave spectrum expands as a result of the wave interaction and tends to a quasistationary state. One may anticipate that the formulated conclusions are applicable beyond the limits of the Korteweg-de Vries equation to other kindred frameworks and corresponding phenomena. This work was supported by the Russian Science Foundation (project No. 18-77-00063).

scholarly journals On the Shoaling of Solitary Waves in the Presence of Short Random Waves

2015 ◽  
Vol 45 (3) ◽  
pp. 792-806 ◽  
Author(s):  
Miao Tian ◽  
Alex Sheremet ◽  
James M. Kaihatu ◽  
Gangfeng Ma
Keyword(s):  
Solitary Wave ◽  
Solitary Waves ◽  
Kdv Equation ◽  
Statistical Significance ◽  
Laboratory Data ◽  
Systematic Research ◽  
Random Wave ◽  
Random Waves ◽  
Tsunami Forecasting ◽  
Wave Basin

AbstractOverhead video from a small number of laboratory tests conducted by Kaihatu et al. at the Tsunami Wave Basin at Oregon State University shows that the breaking point of a shoaling solitary wave shifts to deeper water if random waves are present. The analysis of the laboratory data collected confirms that solitary waves indeed tend to break earlier in the presence of random wave field, and suggests that the effect is the result of the radiation stresses gradient induced by the random wave fields. A theoretical approach based on the forced KdV equation is shown to successfully predict the shoaling process of the solitary wave. An ensemble of tests simulated using a state-of-the-art nonhydrostatic model is used to test the statistical significance of the process. The results of this study point to a potentially significant oceanographic process that has so far been ignored and suggest that systematic research into the interaction between tsunami waves and the swell background could increase the accuracy of tsunami forecasting.

scholarly journals Time Scale for Scour Beneath Pipelines Due to Long-Crested and Short-Crested Nonlinear Random Waves Plus Current

2021 ◽  
Vol 9 (2) ◽  
pp. 114
Author(s):  
Dag Myrhaug ◽  
Muk Chen Ong
Keyword(s):  
Time Scale ◽  
Current Flow ◽  
Irregular Waves ◽  
Wave Crest ◽  
Random Wave ◽  
Random Waves ◽  
Flow Conditions ◽  
Regular Waves ◽  
Nonlinear Random Waves ◽  
2D And 3D

This article derives the time scale of pipeline scour caused by 2D (long-crested) and 3D (short-crested) nonlinear irregular waves and current for wave-dominant flow. The motivation is to provide a simple engineering tool suitable to use when assessing the time scale of equilibrium pipeline scour for these flow conditions. The method assumes the random wave process to be stationary and narrow banded adopting a distribution of the wave crest height representing 2D and 3D nonlinear irregular waves and a time scale formula for regular waves plus current. The presented results cover a range of random waves plus current flow conditions for which the method is valid. Results for typical field conditions are also presented. A possible application of the outcome of this study is that, e.g., consulting engineers can use it as part of assessing the on-bottom stability of seabed pipelines.

scholarly journals Wave Breaking in Undular Bores with Shear Flows

Water Waves ◽  
2021 ◽  
Author(s):  
Maria Bjørnestad ◽  
Henrik Kalisch ◽  
Malek Abid ◽  
Christian Kharif ◽  
Mats Brun
Keyword(s):  
Turbulent Flows ◽  
Wave Breaking ◽  
Vries Equation ◽  
Kdv Equation ◽  
Flow Depth ◽  
Present Contribution ◽  
Undular Bore ◽  
Wave Flume ◽  
The Kdv Equation ◽  
The Waves

AbstractIt is well known that weak hydraulic jumps and bores develop a growing number of surface oscillations behind the bore front. Defining the bore strength as the ratio of the head of the undular bore to the undisturbed depth, it was found in the classic work of Favre (Ondes de Translation. Dunod, Paris, 1935) that the regime of laminar flow is demarcated from the regime of partially turbulent flows by a sharply defined value 0.281. This critical bore strength is characterized by the eventual breaking of the leading wave of the bore front. Compared to the flow depth in the wave flume, the waves developing behind the bore front are long and of small amplitude, and it can be shown that the situation can be described approximately using the well known Kortweg–de Vries equation. In the present contribution, it is shown that if a shear flow is incorporated into the KdV equation, and a kinematic breaking criterion is used to test whether the waves are spilling, then the critical bore strength can be found theoretically within an error of less than ten percent.

scholarly journals ESTIMATION OF WATER PARTICLE VELOCITIES OF SHALLOW WATER WAVES BY A MODIFIED TRANSFER FUNCTION METHOD

1986 ◽  
Vol 1 (20) ◽  
pp. 33 ◽  
Author(s):  
Hirofumi Koyama ◽  
Koichiro Iwata
Keyword(s):  
Transfer Function ◽  
Shallow Water ◽  
Approximate Method ◽  
Stream Function ◽  
Water Waves ◽  
Function Method ◽  
Finite Amplitude ◽  
Water Particle ◽  
Irregular Wave ◽  
Particle Velocities

This paper Is intended to propose a simple, yet highly reliable approximate method which uses a modified transfer function in order to evaluate the water particle velocity of finite amplitude waves at shallow water depth in regular and irregular wave environments. Using Dean's stream function theory, the linear function is modified so as to include the nonlinear effect of finite amplitude wave. The approximate method proposed here employs the modified transfer function. Laboratory experiments have been carried out to examine the validity of the proposed method. The approximate method is shown to estimate well the experimental values, as accurately as Dean's stream function method, although its calculation procedure is much simpler than that of Dean's method.

The Offshore Wave Simulation Based on the Improved P-M Spectrum and Multiple Fractal Interpolation

2014 ◽  
Vol 1030-1032 ◽  
pp. 1832-1836
Author(s):  
Ying Li ◽  
Rui Zhou ◽  
Hao Kuan Li ◽  
Ming Wang
Keyword(s):  
Shallow Water ◽  
Interpolation Method ◽  
Fractal Interpolation ◽  
Fractal Method ◽  
Growth State ◽  
Water Factor ◽  
Proposed Model ◽  
Simulation Based ◽  
Offshore Wave ◽  
The Waves

The Pierson - Moskowitz model is only applicable to full growth state of the waves, and it has low authenticity and hopping phenomenon under the condition of offshore shallow water. This paper proposes a simulation model of offshore wave based on the improved P-M spectrum and multiple fractal interpolation methods. In order to calculate the sea wave with shallow water, a spectrum peak regulation factor and a depth of the water factor are introduced to the P - M spectrum model. Based on this model, the wavelength and wave speed are used as the initial values of wave height. Then, the amplitude and the number of iterations in diamond square fractal method are controlled to obtain the fractal static sea. In order to reduce the influence of the hopping phenomenon to the simulation authenticity, meanwhile, a multiple dynamic non-uniform interpolation method is proposed. The experimental results show that the proposed model can simulate offshore wave with better effect and in real time.

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