scholarly journals NATURAL WAVE TRAINS: DESCRIPTION AND REPRODUCTION

1978 ◽  
Vol 1 (16) ◽  
pp. 16 ◽  
Author(s):  
H. Lundgren ◽  
S.E. Sand
Keyword(s):  
Numerical Models ◽  
Wave Train ◽  
Three Dimensional ◽  
Correct Description ◽  
Linear Superposition ◽  
Natural Wave ◽  
Wave Trains ◽  
Steep Waves ◽  
Deterministic Description ◽  
The Waves

In many applications there is a great need for a correct description of the natural, irregular three-dimensional sea and its reproduction in physical and numerical models. Because of the tremendous difficulties inherent in the nonlinearities, the science of coastal engineering is still very far from this ultimate goal. Indeed, the scope of this paper is comparatively very modest: To describe and reproduce natural, irregular two-dimensional waves, i.e. waves propagating in one direction in a flume. In addition, this scope is fulfilled only by assuming linear superposition of Fourier terms. As opposed to the usual spectral description, the deterministic description presented here does not eliminate the phase information in the wave train recorded. Because of the nonlinearities, however, the linear deterministic description invariably degenerates with the distance travelled by the waves. It appears though from the present paper that the degeneration is fairly slow even for rather steep waves.

Periodic waves in shallow water

1973 ◽  
Vol 59 (4) ◽  
pp. 625-644 ◽  
Author(s):  
P. J. Bryant
Keyword(s):  
Wave Train ◽  
Surface Displacement ◽  
Finite Amplitude ◽  
Periodic Waves ◽  
Linear Superposition ◽  
Initial Wave ◽  
Regularized Long Wave Equation ◽  
Spatially Periodic ◽  
Uniform Channel ◽  
Wave Trains

An investigation is made into the evolution, from a sinusoidal initial wave train, of long periodic waves of small but finite amplitude propagating in one direction over water in a uniform channel. The spatially periodic surface displacement is expanded in a Fourier series with time-dependent coefficients. Equations for the Fourier coefficients are derived from three sources, namely the Korteweg–de Vries equation, the regularized long-wave equation proposed by Benjamin, Bona & Mahony (1972) and the relevant nonlinear boundary-value problem for Laplace's equation. Solutions are found by analytical and by numerical methods, and the three models of the system are compared. The surface displacement is found to take the form of an almost linear superposition of wave trains of the same wavelength as the initial wave train.

Modulational Instability in Directional Wave Fields, and Extreme Wave Events

2011 ◽  
Author(s):  
Alexander V. Babanin ◽  
Takuji Waseda ◽  
Igor Shugan ◽  
Hwung-Hweng Hwung
Keyword(s):  
Modulational Instability ◽  
Wave Train ◽  
Three Dimensional ◽  
Breaking Waves ◽  
Two Dimensional ◽  
Wave Fields ◽  
Linear Evolution ◽  
Individual Wave ◽  
Wave Trains ◽  
Directional Wave

The paper is based on review of research articles by the authors, with the purpose to demonstrate that the modulational-instability mechanism is active in typical directional wave fields. If so, possible limits for the wave height due to such mechanism can be outlined. The modulational instability can lead to occurrence of very high waves, which either proceed to the breaking or appear as rogue events, but it was derived for and is usually associated with two-dimensional wave trains. There exists argument, both analytical and experimental, that this kind of instability is impaired or even suppressed in three-dimensional (directional) wave systems. The first part of the paper demonstrates indirect experimental evidences which relate the wave breaking in oceanic conditions to features of two-dimensional breaking waves due to modulational instability. The second section is dedicated to direct measurements of such instability-caused breaking in a directional wave tank with directional spread and mean steepness typical of those in the field. The last section provides conclusions on what is maximal height of an individual wave, depending on the mean wave steepness in a wave train/field, that can be achieved due to such non-linear evolution of wave trains.

Extreme Forces in Short-Crested Seas

1980 ◽  
Vol 20 (06) ◽  
pp. 567-578
Author(s):  
S.W. Huntington ◽  
G. Gilbert
Keyword(s):  
Transfer Functions ◽  
Extreme Values ◽  
Numerical Models ◽  
Wave Spectrum ◽  
Standard Theory ◽  
Total Force ◽  
Random Waves ◽  
Linear Superposition ◽  
Incident Waves ◽  
The Waves

Abstract The overall wave force on a large structure in a real multidirectional sea does not occur in a single direction but is a vector randomly varying in magnitude and direction. Although existing theories enable us to calculate the extremes of the orthogonal components of force, the designer needs the extreme resultant or total force. A theory is presented for estimating the extremes of the resultant and is confirmed by experimental measurement. Introduction Recent development of offshore resources in deep water and severe environmental conditions has led to the use of monolithic concrete structures. These structures have members large enough to modify the wave field, and are regarded as being in the diffraction regime of wave loading. Thus, the induced forces and moments are considered linear responses to the incident waves. Estimation of the forces and moments on such structures is based on the linear diffraction theory of Havelock. Several numerical models are used to compute the transfer functions between the incident waves and resuring forces and moments on large structures of arbitrary shape. In general, such models give the magnitude and phase of the transfer function between the waves and the loading at a range of discrete frequencies and angles of wave incidence. In parallel with the numerical approach, analytical methods have been developed to give directly the transfer functions for force and moment on a vertical cylinder in long-crested random waves. This analytical approach has also been extended to real seas that are multidirectional (short crested). In such seas, forces and moments are induced on structures both in line with and at right angles to the principal wave direction. The method gives the transfer functions between the components of force and moment and the total wave spectrum for any particular angular distribution of wave energy. The validity of this direct approach in short-crested seas has been confirmed by laboratory model tests in multidirectional random waves. These two approaches are complementary in that the numerical method allows estimation for regular waves on arbitrarily-shaped real structures; the analytical and laboratory studies allows the extension of results to real multidirectional random seas using the principle of superposition. By using this method, it is possible to compute the spectra of force and moment in two horizontal component directions on a real structure in a real short-crested sea. Since linear superposition is used both in the frequency and angular domains, the calculated component forces and moments also are linear with respect to the waves. However, the spectra of force and moment on a structure are of little direct value to designers concerned with primary failure. They are interested in the possible extremes and will want to set design limits on the forces and moments that are unlikely to be exceeded during the lift of the structure. Since the component forces and moments are linear responses to the waves, the statistical technique used to describe extreme wave elevations can be used to describe the extremes of the components of the loading. This method requires only the gross parameters of the spectra. Since the total (vector) force or moment combines the components and their probabilities in a nonlinear manner, the vital extreme values cannot be derived from the standard theory. This paper presents an analytical solution to this vector problem. SPEJ P. 567＾

Quasi-wave trains in a cold collisionless plasma

1971 ◽  
Vol 6 (3) ◽  
pp. 513-526 ◽  
Author(s):  
Yoshinori Inoue
Keyword(s):  
Wave Train ◽  
Geometric Mean ◽  
Collisionless Plasma ◽  
Periodic Wave ◽  
Larmor Radius ◽  
Special Cases ◽  
Computer Calculations ◽  
Wave Trains ◽  
Hydromagnetic Waves ◽  
The Waves

Non-linear hydromagnetic waves in a cold collisionless plasma are investigated by numerical and analytic methods. For this problem, Saffman has already implied that there may exist a non-periodic wave different from the well-known solitary wave (or wave train). His analysis is based on the assumption that the quasi-ergodic theorem can be applied to the present problem. However, the propriety of the assumption has not been discussed.It is seen from the computer calculations that in general the waves do not have periodicity, as Saffman pointed out. Furthermore, some concrete examples show the behaviour of these ergodic waves more clearly. The width of the waves is of the order of ion Larmor radius. These waves are here called quasi-wave trains. In some special cases, the waves reduce to wave trains (with periodicity). Some of them have a length scale of the geometric mean between the Larmor radii of the electron and of the ion.

scholarly journals A Computational Approach to Solve a System of Transcendental Equations with Multi-Functions and Multi-Variables

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 920
Author(s):  
Chukwuma Ogbonnaya ◽  
Chamil Abeykoon ◽  
Adel Nasser ◽  
Ali Turan
Keyword(s):  
Numerical Models ◽  
Problem Formulation ◽  
Science And Engineering ◽  
Physical Systems ◽  
Engineering Problems ◽  
Parametric Studies ◽  
Independent Variable ◽  
Transcendental Equations ◽  
The Waves ◽  
Modelling Approach

A system of transcendental equations (SoTE) is a set of simultaneous equations containing at least a transcendental function. Solutions involving transcendental equations are often problematic, particularly in the form of a system of equations. This challenge has limited the number of equations, with inter-related multi-functions and multi-variables, often included in the mathematical modelling of physical systems during problem formulation. Here, we presented detailed steps for using a code-based modelling approach for solving SoTEs that may be encountered in science and engineering problems. A SoTE comprising six functions, including Sine-Gordon wave functions, was used to illustrate the steps. Parametric studies were performed to visualize how a change in the variables affected the superposition of the waves as the independent variable varies from x1 = 1:0.0005:100 to x1 = 1:5:100. The application of the proposed approach in modelling and simulation of photovoltaic and thermophotovoltaic systems were also highlighted. Overall, solutions to SoTEs present new opportunities for including more functions and variables in numerical models of systems, which will ultimately lead to a more robust representation of physical systems.

scholarly journals Experimental and Numerical Investigation of 3D Dam-Break Wave Propagation in an Enclosed Domain with Dry and Wet Bottom

2021 ◽  
Vol 11 (12) ◽  
pp. 5638
Author(s):  
Selahattin Kocaman ◽  
Stefania Evangelista ◽  
Hasan Guzel ◽  
Kaan Dal ◽  
Ada Yilmaz ◽  
...  
Keyword(s):  
Wave Propagation ◽  
Numerical Models ◽  
Three Dimensional ◽  
Dam Break ◽  
Dam Failure ◽  
Navier Stokes ◽  
Negative Wave ◽  
Through Flow ◽  
Instantaneous Removal ◽  
Surface Patterns

Dam-break flood waves represent a severe threat to people and properties located in downstream regions. Although dam failure has been among the main subjects investigated in academia, little effort has been made toward investigating wave propagation under the influence of tailwater depth. This work presents three-dimensional (3D) numerical simulations of laboratory experiments of dam-breaks with tailwater performed at the Laboratory of Hydraulics of Iskenderun Technical University, Turkey. The dam-break wave was generated by the instantaneous removal of a sluice gate positioned at the center of a transversal wall forming the reservoir. Specifically, in order to understand the influence of tailwater level on wave propagation, three tests were conducted under the conditions of dry and wet downstream bottom with two different tailwater depths, respectively. The present research analyzes the propagation of the positive and negative wave originated by the dam-break, as well as the wave reflection against the channel’s downstream closed boundary. Digital image processing was used to track water surface patterns, and ultrasonic sensors were positioned at five different locations along the channel in order to obtain water stage hydrographs. Laboratory measurements were compared against the numerical results obtained through FLOW-3D commercial software, solving the 3D Reynolds-Averaged Navier–Stokes (RANS) with the k-ε turbulence model for closure, and Shallow Water Equations (SWEs). The comparison achieved a reasonable agreement with both numerical models, although the RANS showed in general, as expected, a better performance.

Ice-Phase Precipitation

2017 ◽  
Vol 58 ◽  
pp. 6.1-6.36 ◽  
Author(s):  
I. Gultepe ◽  
A. J. Heymsfield ◽  
P. R. Field ◽  
D. Axisa
Keyword(s):  
Collection Efficiency ◽  
Numerical Models ◽  
Mass Density ◽  
Three Dimensional ◽  
Phase Precipitation ◽  
Microphysical Parameters ◽  
Mass Size ◽  
Ice Water ◽  
Ice Phase

AbstractIce-phase precipitation occurs at Earth’s surface and may include various types of pristine crystals, rimed crystals, freezing droplets, secondary crystals, aggregates, graupel, hail, or combinations of any of these. Formation of ice-phase precipitation is directly related to environmental and cloud meteorological parameters that include available moisture, temperature, and three-dimensional wind speed and turbulence, as well as processes related to nucleation, cooling rate, and microphysics. Cloud microphysical parameters in the numerical models are resolved based on various processes such as nucleation, mixing, collision and coalescence, accretion, riming, secondary ice particle generation, turbulence, and cooling processes. These processes are usually parameterized based on assumed particle size distributions and ice crystal microphysical parameters such as mass, size, and number and mass density. Microphysical algorithms in the numerical models are developed based on their need for applications. Observations of ice-phase precipitation are performed using in situ and remote sensing platforms, including radars and satellite-based systems. Because of the low density of snow particles with small ice water content, their measurements and predictions at the surface can include large uncertainties. Wind and turbulence affecting collection efficiency of the sensors, calibration issues, and sensitivity of ground-based in situ observations of snow are important challenges to assessing the snow precipitation. This chapter’s goals are to provide an overview for accurately measuring and predicting ice-phase precipitation. The processes within and below cloud that affect falling snow, as well as the known sources of error that affect understanding and prediction of these processes, are discussed.

scholarly journals The Formation of a Cavity in a 3D Flux Rope

2013 ◽  
Vol 8 (S300) ◽  
pp. 147-150 ◽  
Author(s):  
Donald Schmit ◽  
Sarah Gibson
Keyword(s):  
Ad Hoc ◽  
Numerical Models ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Flux Rope ◽  
Multiple Structures ◽  
Field Lines ◽  
Hydrostatic Balance ◽  
Distinct Field ◽  
Three Dimensional Space

AbstractThere are currently no three dimensional numerical models which describe the magnetic and energetic formation of prominences self-consistently. Consequently, there has not been significant progress made in understanding the connection between the dense prominence plasma and the coronal cavity. We have taken an ad-hoc approach to understanding the energetic implications of the magnetic models of prominence structure. We extract one dimensional magnetic field lines from a 3D MHD model of a flux rope and solve for hydrostatic balance along these field lines incorporating field-aligned thermal conduction, uniform heating, and radiative losses. The 1D hydrostatic solutions for density and temperature are then mapped back into three dimensional space, which allows us to consider the projection of multiple structures. We find that the 3D flux rope is composed of several distinct field line types. A majority of the flux rope interior field lines are twisted but not dipped. These field lines are density-reduced relative to unsheared arcade field lines. We suggest the cavity may form along these short interior field lines which are surrounded by a sheath of dipped field lines. This geometric arrangement would create a cavity on top of a prominence, but the two structures would not share field lines or plasma.

Long-term thermal two- and three-dimensional analysis of roller compacted concrete dams supported by monitoring verification

2010 ◽  
Vol 37 (4) ◽  
pp. 600-610 ◽  
Author(s):  
Vladan Kuzmanovic ◽  
Ljubodrag Savic ◽  
John Stefanakos
Keyword(s):  
Thermal Analysis ◽  
Boundary Conditions ◽  
Thermal Field ◽  
Numerical Models ◽  
Three Dimensional ◽  
Roller Compacted Concrete ◽  
Rcc Dam ◽  
Field Investigations ◽  
Good Agreement

This paper presents two-dimensional (2D) and three-dimensional (3D) numerical models for unsteady phased thermal analysis of RCC dams. The time evolution of a thermal field has been modeled using the actual dam shape, RCC technology and the adequate description of material properties. Model calibration and verification has been done based on the field investigations of the Platanovryssi dam, the highest RCC dam in Europe. The results of a long-term thermal analysis, with actual initial and boundary conditions, have shown a good agreement with the observed temperatures. The influence of relevant parameters on the thermal field of RCC dams has been analyzed. It is concluded that the 2D model is appropriate for the thermal phased analysis, and that the boundary conditions and the mixture properties are the most influential on the RCC dam thermal behavior.

Sign in / Sign up

Export Citation Format

Share Document