Providing an illustration of sound propagation in the Hormoz Strait ,this paper is about acoustic wave propagation in shallow water for a harmonic point source with low frequency, less than 1000 and solution of a homogenous Helmholtz equation using parabolic equation. C++ programming is used to solve Helmholtz equation [9] and MATLAB software is used to illustrate figures and animate them [6], ...

HF radar systems are widely and routinely used for the measurement of ocean surface currents and waves. Analysis methods presently in use are based on the assumption of infinite water depth, and may therefore be inadequate close to shore where the radar echo is strongest. In this paper, we treat the situation when the radar echo is returned from ocean waves that interact with the ocean floor. S...

It is now well known that the focussing nonlinear Schrödinger equation allows plane waves to be modulationally unstable, and at the same time supports breather solutions which are often invoked as models for rogue waves. This suggests a direct connection between modulation instability and the existence of rogue waves. In this chapter we review this connection for a suite of long wave models, su...

The paper presents an iterative algorithm for studying a nonlinear shallow-water wave equation. The equation is written as an evolution equation, involving only first-order spatial derivatives, coupled with the Helmholtz equation. We propose a two-step iterative method that first solves the evolution equation by the implicit midpoint rule and then solves the Helmholtz equation using a three-poi...

[1] The tidal flow field in a basin of small dimensions with respect to the tidal wavelength is calculated. Under these conditions, the tide becomes a standing wave oscillating synchronously (with a flat water surface) over the whole basin. The shallow water equations can thus be strongly simplified, expressing the discharge vector field in terms of a potential function and a stream function. T...

We describe a boundary integral method for computing time-dependent, doubly periodic, three-dimensional water waves. This method has been proved to converge to the exact solution. We discuss several analytical issues, including the quadrature of singular integrals, such as single and double layer potentials on surfaces, and stability estimates for discrete versions of operators such as the laye...

Impacts to the built environment from hazards such tsunami or flash floods are critical in understanding the economic and social effects on our communities. In order to simulate the behaviour of water flow from such hazards within the built environment, Geoscience Australia and the Australian National University are developing a software modelling tool for hydrodynamic simulations. The tool is ...