TR(BR)-11/98-99 : Modelling of flow in the canal due to breach of bank Part-I

Abstract

Canal breach modelling is of great significance in open channel hydraulics. A limited amount of literature parallel to dam break analysis is available. In this report, a methodology is suggested based on wavelet element method, a recent breakthrough.

Wavelet element method and Wavelet transforms is a new field (The concepts were developed by mathematicians in the last 10 years). The subject is expanding at a tremendous rate in varied directions. It is now that the concepts are being used in engineering. The initial applications are in signal processing and in data compression. The solution offered by wavelet transforms to the FBI data storage problem of storing fingerprints has dramatically shown the usefulness of wavelet analysis. The theoretical basis of dual and hi-orthogonal systems is presented.

Wavelet analysis is a method to separate the data into different frequencies and systematically study each component with a resolution matched to scale. They have distinct advantages over the Fourier methods. Wavelet method of analysis arose to remedy the shortcomings of Fourier analysis.

Wavelet element method combines the spectral methods with wavelet transforms. A bi-orthogonal wavelet system is obtained. Equations of motion and the boundary conditions require to be adapted to the multi-resolution paradigm. In this report, the wavelet element method is developed for hydrological applications purposes, in general, and modelling a canal breach in particular. To this end the fundamental concepts available elsewhere are reviewed, synthesised and discussed comprehensively and canal breach method is described in steps for future pragmatic application. The major finding of the complex mathematical development is that it can prove to be vital in hydraulic and hydrological applications in future.