Nonlinear Oscillations: Exact Solutions and their Approximations

Kumaraswamy [Generalized probability density-function for double-bounded random-processes, J. Hydrol. 462 (1980), pp. 79–88] introduced a distribution for double-bounded random processes with hydrological applications. For the first time, based on this distribution, we describe a new family of generalized distributions (denoted with the prefix ‘Kw’) to extend the normal, Weibull, gamma, Gumbel, inverse Gaussian distributions, among several well-known distributions. Some special distributions in the new family such as the Kw-normal, Kw-Weibull, Kw-gamma, Kw-Gumbel and Kw-inverse Gaussian distribution are discussed. We express the ordinary moments of any Kw generalized distribution as linear functions of probability weighted moments (PWMs) of the parent distribution. We also obtain the ordinary moments of order statistics as functions of PWMs of the baseline distribution. We use the method of maximum likelihood to fit the distributions in the new class and illustrate the potentiality of the new model with a...

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A new family of generalized distributions

Wind speeds over the world’s oceans have increased over the past two decades, as have wave heights. Studies of climate change typically consider measurements or predictions of temperature over extended periods of time. Climate, however, is much more than temperature. Over the oceans, changes in wind speed and the surface gravity waves generated by such winds play an important role. We used a 23-year database of calibrated and validated satellite altimeter measurements to investigate global changes in oceanic wind speed and wave height over this period. We find a general global trend of increasing values of wind speed and, to a lesser degree, wave height, over this period. The rate of increase is greater for extreme events as compared to the mean condition.

https://researchbank.swinburne.edu.au/file/bca43746-6f16-4ad2-a4b7-27f8d8d60fed/1/PDF (Published version).pdf

Global trends in wind speed and wave height over the past 25 years

Evolution of Design Method Against Random Waves Statistical Properties and Spectral of Sea Waves Transformation and Deformation of Random Sea Waves Design of Breakwaters Design of Coastal Dikes and Seawalls Probabilistic Design of Harbor Facilities Harbor Tranquility and Vessel Mooring Hydraulic Model Tests with Random Waves Theoretical Description of Random Sea Waves Statistical Theory of Irregular Waves Techniques of Random Wave Analysis 2D Computation of Wave Transformation with Random Breaking and Nearshore Currents Statistical Analysis of Extreme Waves Prediction and Control of Beach Deformation Processes.

Random seas and design of maritime structures

The interaction of waves with obstacles is an everyday phenomenon in science and engineering, arising for example in acoustics, electromagnetism, seismology and hydrodynamics. The mathematical theory and technology needed to understand the phenomenon is known as multiple scattering, and this book is the first devoted to the subject. The author covers a variety of techniques, describing first the single-obstacle methods and then extending them to the multiple-obstacle case. A key ingredient in many of these extensions is an appropriate addition theorem: a coherent, thorough exposition of these theorems is given, and computational and numerical issues around them are explored. The application of these methods to different types of problems is also explained; in particular, sound waves, electromagnetic radiation, waves in solids and water waves. A comprehensive bibliography of some 1400 items rounds off the book, which will be an essential reference on the topic for applied mathematicians, physicists and engineers.

Multiple Scattering: Interaction of Time-Harmonic Waves with N Obstacles

Wave kinematics in a groin field-frequency domain analysis

Propagation of the Indian Ocean Tsunami has been simulated using Shallow Water Equations The three dimensional shallow water equations are reduced, by a process of vertical integration relating to the pertinent variables, to obtain equivalent equations in two dimensions An Unstructured Explicit Finite Element Model is adopted for solution of the governing equations The method of weighted residuals, in particular the Galerkin method, coupled with the finite element discretisation technique is then used to obtain a set of integral equations which can be assembled in a matrix form The domain is discretised with 9-noded lagrangian isoparametric elements Simpson’s 9-point integration rule, used to integrate over the 9-noded elements, leads to an explicit form of the assembled matrix (diagonal matrix) The above mentioned Unstructured Explicit Finite Element Method requires less computational resources and ensures higher order representation of the solution
A computational domain (Bay of Bengal and northern part of the Indian Ocean) has been considered for simulation with an initial disturbance which resembles the type and location of the 2004 Indian Ocean Tsunami The wave elevations and deformations as well as time of travel of tsunami are reproduced The computed runup heights along Tamil Nadu coast of India were compared with the signature data and the agreement was found to be reasonable

Explicit FE Modeling of Indian Ocean Tsunami Using Unstructured Mesh

An inter-comparison exercise has been carried out between altimeter derived significant wave height with buoy measurements and numerical prediction. Measurements during the year 2004 have been taken from the buoys located in the Arabian Sea and Bay of Bengal. The statistics of variation between these observations has been studied at each buoy locations with the special emphasis to explore the applicability of altimeter measurements and numerical model prediction.

http://nopr.niscair.res.in/bitstream/123456789/34452/1/IJMS%2043%287%29%201347-1351.pdf

Inter comparison of wave height observations from buoy and altimeter with numerical prediction

In order to have an understanding of the coastal processes along the southwest coast of India (8°4′ N, 77° 33′ E to 8°13′ N, 77°14′ E), a data set available for the changes in beach width for a period of 5 years (1993–1998) over a length of about 50 km was categorized and analysed in relation to the seasons. Since the study area is densely populated and was also affected partially by the great Indian Ocean tsunami, a fresh measurement campaign of beach profile changes up to a water depth of 6 m at four different locations along the coast was carried out. These measurements have been adopted to validate a finite difference–based numerical model that employs the empirical formulation of Larson and Kraus (1989) for the prediction of beach profile changes. We simulated the offshore wave climate from National Centre for Environmental Prediction wind data using the Wave Analysis Model (WAM), whereas the nearshore wave climate was derived by adopting the MIKE21 Parabolic Mild Slope module. Results compa...

https://bioone.org/journals/Journal-of-Coastal-Research/volume-27/issue-1/JCOASTRES-D-09-00039.1/Numerical-Modelling-and-Measurement-of-Sediment-Transport-and-Beach-Profile/10.2112/JCOASTRES-D-09-00039.1.pdf

Numerical Modelling and Measurement of Sediment Transport and Beach Profile Changes along Southwest Coast of India

Abstract Tsunamis pose a substantial threat to coastal communities around the globe. To counter their effects, several hard and soft mitigation measures are applied, the choice of which essentially depends on regional expectations, historical experiences and economic capabilities. These countermeasures encompass hard measures to physically prevent tsunami impacts such as different types of seawalls or offshore breakwaters, as well as soft measures such as long-term tsunami hazard assessment, tsunami education, evacuation plans, early-warning systems or coastal afforestation. Whist hard countermeasures generally aim at reducing the inundation level and distance, soft countermeasures focus mainly on enhanced resilience and decreased vulnerability or nature-based wave impact mitigation. In this paper, the efficacy of hard countermeasures is evaluated through a comprehensive literature review. The recent large-scale tsunami events facilitate the assessment of performance characteristics of countermeasures and related damaging processes by in-situ observations. An overview and comparison of such damages and dependencies are given and new approaches for mitigating tsunami impacts are presented. 

/pdf/a-comprehensive-review-on-structural-tsunami-countermeasures-2t39vphx.pdf

Vallam Sundar

Papers

Wave kinematics in a groin field-frequency domain analysis

Explicit FE Modeling of Indian Ocean Tsunami Using Unstructured Mesh

Inter comparison of wave height observations from buoy and altimeter with numerical prediction

Numerical Modelling and Measurement of Sediment Transport and Beach Profile Changes along Southwest Coast of India

A comprehensive review on structural tsunami countermeasures