Long Wave Modification by Linear Transitions

by Robert G. Dean,

Serial Information: Journal of the Waterways and Harbors Division, 1964, Vol. 90, Issue 1, Pg. 1-30

Document Type: Journal Paper

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The interactions of long wave systems with three types of linearly varying (with distance) channel transitions are investigated analytically, and the results are shown to be bounded by approximate asymptotic formulas. In particular, the reflection and transmission coefficients are determined for the following three types of transitions: (1) uniform breadth, linearly varying depth, (2) uniform depth, linearly varying breadth, and (3) linearly varying breadth and depth. The method used, which would be valid for some other transition geometrics, is to consider the general analytic form of the long wave systems in the upstream uniform channel section, in the channel transition section, and in the downstream uniform channel section. The expressions for the water surface displacements and slopes valid for adjacent sections then are matched at the two extremities of the transition section. This results in a system of equations that is solved for the reflection and transmission coefficients. The reflection and transmission coefficients can be shown to satisfy the energy conservation requirement. Transitions investigated approximate configurations occurring in nature.

Subject Headings: Linear functions | Long waves | Power transmission | Rivers and streams | Linear analysis | Water surface | Geometrics | Displacement (mechanics)

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