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

The hydrodynamic behaviour of long floating structures in directional seas

Simulation of 2-D nonlinear waves using finite element method with cubic spline approximation

Two phase flows occur in different forms with liquid and gas in general, among which, the interaction of the flow of air and water is a common scenario However, modeling the two phase flow still remains a challenge due to the large density ratio between them and different space-time scales involved in the flow regimes In the present work, the lattice Boltzmann (LB) model capable of handling large density ratio (1000) and high Reynolds number (104) simultaneously is proposed The present model consists of two sets of LB equations, one for the flow field in terms of normalized pressure-velocity formulation and the other for the solution of the conservative Allen-Cahn equation to capture the interface The numerical tests such as stationary drop, bubble coalescence, and capillary wave decay have been performed, and the results exhibit excellent mass conservation property The capability of the present model to handle complex scenarios has been tested through test cases, for example, rise of an air bubble, splash of a water droplet on a wet bed, and Rayleigh-Taylor instability In all test cases, the simulation results agree well with the available reference data Finally, as an application of the present model, the breaking of a deep water wave with high Reynolds number (104) is simulated The plunging breaker with wave overturning and the generation of secondary jet and splashes are well described by the present LB model The evolution of wave energy dissipation during and after breaking is in agreement with the reference data

Phase field lattice Boltzmann model for air-water two phase flows

Current-induced scour around a vertical pile in cohesive soil

The significant wave height and wind speed derived for the period 1993–2010 from altimeter data sets over the Arabian Sea, Bay of Bengal, and the Indian Ocean categorized as six zones has been analyzed. The average variation of both significant wave height and wind speed is found to be almost stable for the period of study. The study reveals that the average wind speed increases by about 6cm/sec/year during monsoon and post monsoon in the southern Indian Ocean. The distribution of wind and waves was studied in the context of seasonal variations. In addition, the average inter-annual and intra-annual variations along with the statistical parameters such as standard deviation, and root mean square wave height for the six zones are also reported in this paper.

Vallam Sundar

Papers

The hydrodynamic behaviour of long floating structures in directional seas

Simulation of 2-D nonlinear waves using finite element method with cubic spline approximation

Phase field lattice Boltzmann model for air-water two phase flows

Current-induced scour around a vertical pile in cohesive soil

Wind-Wave Characteristics and Climate Variability in the Indian Ocean Region Using Altimeter Data