Ermakov, Andrei
(2021)
DEVELOPMENT OF RIGOROUS METHODS IN FLUID MECHANICS AND THEORY OF WATER WAVES.
Bulletin of the Australian Mathematical Society, 103 (2).
pp. 350-352.
ISSN 0004-9727
Abstract
The transformation of surface waves over varying obstacles is far from a new problem, but it has become an increasing challenge in our world due to growing environmental,
societal and technological needs. Many stakeholders, from scientists and engineers through to governments and private companies, are searching for superior models to
describe the influences of changes in depth of the ocean or cross-section of canals, and how the speed of the current affects the wave transformation. This research can
have many impacts, from protecting coastlines or natural treasures like the Great Barrier Reef and bringing greater safety to marine vessels and offshore structures,
to answering complex new theories and concepts, including the application of the Hawking effect in relation to black holes. Whenever a wave passes over a surface, the
size of the transmitted wave may be significantly increased compared to the amplitude and speed of the incident wave. The impact of a transmitted wave on offshore or
coastal structures is impossible to calculate without closely calculating the transmitted waves. It is also impossible to trust the numerical results without deep analytical modelling of these problems due to the complex nature of the effects. This research looks at four important considerations: the transformation of long linear waves in an ocean with a variable depth, long-wave scattering in a canal with a rapidly varying cross-section, long linear surface waves on stationary currents in a canal of constant
depth and variable width, and the re-estimation of the forced Korteweg–de Vries equation to describe a resonant interaction of a solitary wave with external pulse-type
perturbations.
| Item Type: |
Article
|
| Additional Information: |
Cite as: ERMAKOV, A. (2021). DEVELOPMENT OF RIGOROUS METHODS IN FLUID MECHANICS AND THEORY OF WATER WAVES. Bulletin of the Australian Mathematical Society, 103(2), 350-352. doi:10.1017/S0004972720000660 |
| Keywords: |
Abstracts of Australasian PhD Theses;
Fluid mechanics;
Water waves; |
| Academic Unit: |
Faculty of Science and Engineering > Electronic Engineering |
| Item ID: |
17367 |
| Identification Number: |
https://doi.org/10.1017/S0004972720000660 |
| Depositing User: |
Dr Andrei Ermakov
|
| Date Deposited: |
29 Jun 2023 09:13 |
| Journal or Publication Title: |
Bulletin of the Australian Mathematical Society |
| Publisher: |
Cambridge Core |
| Refereed: |
Yes |
| URI: |
|
| Use Licence: |
This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available
here |
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