| Author: | Zheng, Haojun |
| Title: | Corrections on Le Mehaute-Wang linear theory on explosion generated water waves |
| Advisors: | Chau, K. T. (CEE) |
| Degree: | M.Sc. |
| Year: | 2018 |
| Subject: | Hong Kong Polytechnic University -- Dissertations Water waves -- Mathematical models |
| Department: | Faculty of Construction and Environment |
| Pages: | 171 pages : color illustrations |
| Language: | English |
| Abstract: | After a review of Le Mehaute and Wang (1996a, 1996b), this thesis points out the differences between them and gives the omitted mathematical details among each step. In these progresses, this dissertation altogether finds ten typing mistakes shown in Section 4.1. For example, for the Laplace equation, Laplacian potential was not clearly declared that it should be equal to zero. Also, negative sign was missed in the result of using separation of variables and Equation (3.179). Except ten typing mistakes, four nondispersive solutions at or near GZ and three figures plotted by Le Mehaute-Wang solutions were found wrong. In four wrong formulas, formulas of case 2 for an initial free surface elevation and case 4 for an initial impulse missed a negative sign. Formula of case 3 for an initial velocity missed a sign of cube. Above three mistakes can be regarded as careless mistakes. But formula of case 5 for an initial impulse is wrong because the term 4R 1/2 should be 2τ. In three wrong figures, Figure 5-1 of case 4 for an initial impulse and Figure 5-2 of case 2 for an initial velocity indicate that Le Mehaute-Wang figures plotted by right formulas are not correct actually. Figure 5-2 of case 5 for an initial impulse indicates that Le Mehaute-Wang figure was plotted by their wrong formula totally. Above discoveries are proved by derivation and plotting in Chapter 5. Problems will appear when people use their results directly. This dissertation exhibits the derivation and revised results. |
| Rights: | All rights reserved |
| Access: | restricted access |
Files in This Item:
| File | Description | Size | Format | |
|---|---|---|---|---|
| 991022244147103411.pdf | For All Users (off-campus access for PolyU Staff & Students only) | 2.16 MB | Adobe PDF | View/Open |
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