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.

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.