Small amplitude ocean wave derivations (re1vised) (original) (raw)
Finite amplitude ocean wave derivations with exercises (re1vised)
Finite amplitude ocean wave derivations with exercises (re1vised), 2022
Finite amplitude ocean wave derivations with exercises in detail are provided for the graduate students of oceanography, meteorology, ocean engineering, earth atmospheric and ocean science students. some exercises also have been worked-out. The SPM tables were appended for working out the exercises.
Waves in Oceanic and Coastal Waters
The summary is not intended to include all information in the chapter; thus, the readers are strongly encouraged to read the original text to gain a broad perspective on the topic. Notwithstanding some minor changes and adjustments in the text, most sentences, figures, tables, and all equations are directly gotten from the book to keep the originality. * Some basic points needed for correct interpretation of the rest of the text are pointed out in a different color.
Deterministic wave model for short-crested ocean waves: Part I. Theory and numerical scheme
Applied Ocean Research, 1999
A directional hybrid wave model (DHWM) has been developed for deterministic prediction of short-crested irregular ocean waves. In using the DHWM, a measured wave field is first decomposed into its free-wave components based on as few as three point measurements. Then the wave properties are predicted in the vicinity of the measurements based on the decomposed free-wave components. Effects of nonlinear interactions among the free-wave components up to second order in wave steepness are considered in both decomposition and prediction. While the prediction scheme is straightforward, the decomposition scheme is innovative and accomplished through an iterative process involving three major steps. The extended maximum likelihood method is employed to determine the directional wave spreading; the initial phases of directional free-wave components are determined using a least-square fitting scheme; and nonlinear effects are computed using both conventional and phase modulation methods to achieve fast convergence. The free-wave components are obtained after the nonlinear effects being decoupled from the measurements. Variety of numerical tests have been conducted, indicating that the DHWM is convergent and reliable.
Directional wavenumber characteristics of short sea waves
2000
Interest in short waves on the ocean surface has been growing over the last three decades because they play an important role in surface electromagnetic (e.m.) scattering. Currently radars and scatterometers which use e.m. scattering to remotely examine the ocean can produce estimates of the surface wind field, surface currents, and other scientifically important ocean processes. These estimates are based on models which depend on a thorough understanding of electromagnetic scattering mechanisms, and of the three-dimensional surface wave field. Electromagnetic scattering theory is well developed, but the short wavelength portion of the surface wave field has only recently been experimentally explored. A single, consistent, and accurate model of the energy distribution on the ocean surface, also known as the wave height spectrum, has yet to be developed. A new instrument was developed to measure the height of waves with 2-30 cm wavelengths at an array of locations which can be post-processed to generate an estimate of the two-dimensional wave height spectrum. This instrument (a circular wire wave gage buoy) was deployed in an experiment which gathered not only in situ measurements of the two-dimensional wave height spectrum, but also coincident scatterometer measurements, allowing the comparison of current e.m. scattering and surface wave height spectrum models with at sea data. The experiment was conducted at the Buzzards Bay Tower located at the mouth of Buzzards Bay in Massachusetts. A rotating X-band scatterometer, a sonic anemometer, and a capacitive wire wave gage were mounted on the tower. The wave gage buoy was deployed nearby. The resulting data supports a narrowing trend in the two-dimensional spectral width as a function of wavenumber. Two current spectral models support this to some extent, while other models do not. The data also shows a similar azimuthal width for the scatterometer return and the width of the short wavelength portion of the wave height spectrum after it has been averaged and extrapolated out to the appropriate Bragg wavelength. This appears to support current e.m. composite surface (two-scale) theories which suggest that the scattered return from the ocean at intermediate incidence angles is dominated by Bragg scattering which depends principally on the magnitude and shape of the two-dimensional wave height spectrum. However, the mean wind direction (which corresponds well with the peak of the scatterometer energy distribution) and the peak of 20 minute averages of the azimuthal energy distribution were out of alignment in two out of three data sets, once was by nearly 900. There are a number of tenable explanations for this including instrument physical limitations and the possibility of significant surface currents, but none that would explain such a significant variation. Given that there are so few measurements of short wave directional spectra, however, these results should be considered preliminary in the field and more extensive measurements are required to fully understand the angular distribution of short wave energy and the parameters upon which it depends.
Simulation of ocean waves in coastal areas using the shallow-water equation
Journal of Physics: Conference Series, 2019
This study simulates shallow water waves using the Navier-Stokes equation. This simulation uses the MatLab application, especially Quickersim with 2-dimensional output. Mesh in simulation is made using Gmsh. Research about shallow water has an essential role in studying the characteristics of ocean waves. The depth of the sea influences this characteristic. Data obtained from this simulation is in the wave height and velocity positions at any time. The limitations in the data collected are not comparable with the experimental results because there are no experimental Navier-Stokes simulations, but these simulation results have shown the phenomenon of seawater movement. In future work, the results of this study can be used to analyse its application in tsunami waves.
Short-crested waves: a theoretical and experimental investigation
Analytical and experimental investigations were conducted on short-crested wave fields generated by a sea-wall reflection of an incident plane wave. A perturbation method was used to compute analytically the solution of the basic equations up to the sixth order for capillary-gravity waves in finite depth, and up to the ninth order for gravity waves in deep water. For the experiments, we developed a new video-optical tool to measure the full three dimensional wave field η(x, y, t). A good agreement was found between theory and experiments. The spatio-temporal bi-orthogonal decomposition technique was used to exhibit the periodic and progressive properties of the short-crested wave field.
Dynamics and modelling of ocean waves
Dynamics of Atmospheres and Oceans, 1997
The last and longest chapter is entitled "Chaotic Dynamics" and leads the reader through the most modern developments in the field. Starting with the method of Poincar6 sections and a discussion of nonlinear maps, the chapter proceeds to the various ways in which chaotic dynamics can be characterized and evaluated. The connections with random processes are clearly delineated and an outlook on problems of spatio-temporal chaos is given. The subject of fluid turbulence by and large remains outside the scope of the book since applications of the tools of nonlinear dynamics to this subject are still in their infancy. I only hope that the cover picture of the book showing the building of the tower of Babylon as painted by P. Bruegel the elder will not be interpreted as a prophecy for the ultimate futility of human endeavors to understand complex nonlinear systems.
Physical Modeling of Extreme Waves Propagating from the Open Sea to the Coastal Zone
Estuaries and Coastal Zones in Times of Global Change, 2020
The propagation of solitary waves above an horizontal bottom and a sloping bottom is considered in this paper. Experiments are carried out in a wave flume above smooth beds. The solitary waves are generated with a piston-type wave maker, using an impulsive mechanism (Marin, F et al. (2005)). Close to the generation zone, the profile contains elevation and depression components. These depressions are attached to the main solitary wave during the propagation along the flume. The energy damping along the horizontal and sloping bottoms (Zhang, C et al. (2010)), the wave height variation in the shoaling zone, the breaking modes and the runup height are investigated. It is shown that spatiotemporal diagrams are adapted for tracking the evolution of solitary waves propagating from a horizontal bed to a sloping bed (Chang, L et al. (2014)). The breaking parameters are obtained using high resolution cameras. Present results are in good agreement with earlier studies (Hsiao, S et al 2008). A new formula is proposed for the estimation of runup height.
On short-crested waves: experimental and analytical investigations
European Journal of Mechanics B-fluids, 1999
Analytical and experimental investigations were conducted on short-crested wave fields generated by a sea-wall reflection of an incident plane wave. A perturbation method was used to compute analytically the solution of the basic equations up to the sixth order for capillary-gravity waves in finite depth, and up to the ninth order for gravity waves in deep water. For the experiments, we developed a new video-optical tool to measure the full three dimensional wave field η(x, y, t). A good agreement was found between theory and experiments. The spatio-temporal bi-orthogonal decomposition technique was used to exhibit the periodic and progressive properties of the short-crested wave field. © 1999 Éditions scientifiques et médicales Elsevier SAS O. Kimmoun et al.
The local properties of ocean surface waves by the phase-Time method
Geophysical Research Letters, 1992
The aim of this workshop was to take advantage of the recent freedom available to scientists in the Soviet Union (now Commonwealth of Independent States) to travel to the West in order to develop both contacts and an awareness of current research between research workers from East and West, most of whom have formerly had little contact. We consider this aim was achieved and are grateful for the substantial financial support from the European Office of the U.S. Office of Naval Research and the European Research Office of the U.S. Army. In addition we thank the home institutions or other fund providers which supported the travel costs of participants and the subsistence of western participants. The support of Bristol University's Department of Mathematics in holding the meeting is greatly appreciated. Scientific Committee: T.B. Benjamin (Oxford) D.H. Peregrine (Vice-chairmanBristol) D.J. Benney (MIT) P.G. Saffman (Caltech) K. Hasselmann (Hamburg) V.I. Shrira (Vice-chairman, Moscow) P.A.E.M. Janssen (KNMI) V.E. Zakharov (Chairman, Moscow) Local Committee: M.J. Cooker
2016
Modern day studies of wind-driven sea waves are usually focused on wind forcing rather than on the effect of resonant nonlinear wave interactions. The authors assume that these effects are dominating and propose a simple relationship between instant wave steepness and time or fetch of wave development expressed in wave periods or lengths. This law does not contain wind speed explicitly and relies upon this asymptotic theory. The validity of this law is illustrated by results of numerical simulations, in situ measurements of growing wind seas and wind wave tank experiments. The impact of the new vision of sea wave physics is discussed in the context of conventional approaches to wave modeling and forecasting.
Applicability of wave models in shallow coastal waters
Proc. of the 5th Int. Conf. on Coastal …, 1999
The wave propagation within coastal areas is strongly influenced by the coastal morphology with its islands, bars, shoals and channels. Predominant processes in this zone are shoaling, bottom friction, breaking, refraction, wind generation and to some extent diffraction of waves. The numerical formulation of these processes in standard wave models, like HISWA (HIndcast Shallow Water WAves, TU Delft), SWAN (Simulation WAves Nearshore, TU Delft) and MIKE 21 EMS (Elliptic Mild Slope, Danish Hydraulic Institute) were tested by comparing the simulation results with measurements in a wave tank and on site measurements at the North Frisian Coast of Germany. The numerical and experimental data measured in the wave flume are in very good agreement for all applied wave models proving the numerical formulation quality of bottom friction, shoaling and breaking. A comparison of numerical simulations results with SWAN and field data shows also a quite good agreement but revealed in some cases larger differences which may be contributed to the interaction of tidal currents and waves.
Com paring Nu mer i cal and Sat el lite Data on Wind Wave Fields in the In dian Ocean
Ab stract—The re sults of com pu ta tion of wind wave fields for two ver sions of the WAM model (the original ver sion of the Eu ro pean wind wave model WAM4 and its mod i fied ver sion WAM4-M) are com pared with sat el lite mea sure ments. The mapped data on the daily av er aged wave height ob tained from the data of com bined mea sure ments of sev eral sat el lite al tim e ters are used. Significant cor re la tion be tween wind wave se ries for both mod els and sat el lite data is dem on strated as well as the ad van tage of the WAM4-M model over its orig i nal ver sion in ac cu racy and some sta tis ti cal pa ram e ters of com par i-son with the al tim e ter. Ad van tages and short com ings of nu mer i cal and re mote sens ing meth ods of wind wave in ves ti ga tion at the ocean scales are noted., nu mer i cal mod el ing, sat el lite altimetric mea sure ments, com par i son IN TRO DUC TION The study of vari abil ity of wind wave fields in the World Ocean is of great sci en tific and prac ti cal in ter-est [1–4, 7, 12, 13]. The wave height is a ma jor char ac ter is tic of the sea sur face, while the in for ma tion on the lat ter is needed for pro vid ing nav i ga tion safety, for es ti mat ing the max i mum load on off shore and coastal tech ni cal struc tures, and for solv ing other ap plied prob lems [3, 12, 13]. Be sides, long-term trends in wave height can be used for as sess ing the Earth cli mate vari abil ity [5]. Two ap proaches are most widely used for study ing the large-scale fields of wind waves, namely, nu mer-i cal com pu ta tions of wind wave fields [13] and sat el lite mea sure ments [8, 11, 16, 17]. How ever, the stud ies on the de ter mi na tion of ad van tages and short com ings of both ap proaches have been car ried out un til now [8, 16, 17]. For the first time in Rus sian prac tice, the au thors of the pres ent pa per com pared the re sults of com pu ta-tions of wind wave fields based on two dif fer ent mod els, with sat el lite mea sure ment data. The ob tained results not only as sess a de gree of con sis tency of the ap proaches and re veal their ad van tages and short comings , but also give the com par a tive es ti mate of the ac cu racy of the mod els used. (Russian pa per [4] is note-wor thy, its au thors have al ready com pared the data of nu mer i cal com pu ta tions of wind waves with sat el lite ob ser va tions; how ever, they solved the merely prac ti cal prob lems of es ti mat ing the ac cu racy of wind wave fore cast which do not al low as sess ing the meth ods of the study of this phenomenon.) Usually the ver sions of the Eu ro pean model WAM [9] and Amer i can model WAVEWATCH (WW) [18] are used for the global com pu ta tion of sea wind wave pa ram e ters. There are mod i fied ver sions of these wind wave mod els [6, 7, 15] which were worked out in Rus sia and have higher ac cu racy char ac ter is tics than those of orig i nal ver sions WAM4 [9] and WW-III [18]. The o retically the ad van tage of mod i fied versions of the men tioned nu mer i cal mod els is caused by the es sen tial im prove ment of their phys i cal con tent [6, 14]. The ac tual cor rob o ra tion of the ad van tage of mod i fied ver sions of the men tioned mod els was presented in [7, 15] based on the com par i son of the re sults of nu mer i cal sim u la tion of wind waves with the data of con tact buoy mea sure ments. How ever, such com par i son is of lim ited (lo cal) na ture be cause the buoys were in stalled at very few points in the World Ocean.
Long waves generated by ships moving in shallow water
2019
Motivated by the relatively new phenomenon observed in Oslofjord where ships moving with subcritical speeds across substantial depth changes generated long waves with heights up to 1.4m, the linear generation mechanism for these upstream waves is investigated using the linear shallow water equations. The simulations are performed both with one and two horizontal dimensions where the average depth at the location where the bottom variation happens is twice the change in depth, ∆h/h̄ = 0.5. Analytical calculations on the amplitude of the generated free waves as the source moves over a step in bottom topography shows good agreement with the numerical results. For ships moving from deep to shallow water, the maximum elevation of the generated waves grow accroding to Fr, where n is in the range 3.6− 4.6. The simulations with two horizontal dimensions are compared to a dispersive model to give a measure of how well the linear shallow water model captures this phenomenon.
Numerical Study of Lee Waves Characteristics in the Ocean
2020
This study discusses the characteristics of lee waves in a vertical ocean slice model. To analyse the characteristics, this study applies two different scenarios; the first scenario employs a vertical ocean slice model with a uniform depth of 100 m and a width of 500 m and the second scenario uses the same model but considering an undersea mountain having a width of 100 m and a height of 40 m. Simulations on motions of the waves are generated by using a numerical method. Both scenarios implement the same force, which is the sea level gradient force that is maintained until the end of simulation time. In order to observe the significance of Courant-Friedrichs-Lewy (CFL) condition, numerical experiments are conducted using two values of time step sizes, ∆t = 0.1 second, which is obtained based on the CFL and ∆t = 1 second, which is chosen outside the interval of CFL criterion. The results of the experiments show that applying different values of the time step sizes do not significantl...