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El. knyga: Linearised Dam-break Problem, The

(Univ Of Birmingham, Uk), (Univ Of Birmingham, Uk), (Univ Of Birmingham, Uk)
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Linearised Dam-break Problem, TheDidesnis paveikslėlis
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The monograph addresses a canonical problem in linear water wave theory, through the development-detailed, asymptotic analysis of contour integrals in the complex plane. It is anticipated that the methodology developed in the monograph will have applications to many associated linear wave evolution problems, to which the reader may adapt the approach developed in the monograph. The approach adopted in the monograph is novel, and there are no existing publications for comparison.
1 Introduction
1(8)
2 Formulation of the Dam-Break Problem
9(4)
3 The Linearised Dam-Break Problem
13(8)
3.1 Formulation of the Linearised Problem
13(2)
3.2 Exact Solution to the Linearised Problem
15(6)
4 Coordinate Expansions for η(x,t) as t → 0
21(22)
4.1 Outer Region Coordinate Expansion for I(x,t) as t →? 0
21(7)
4.2 Inner Region Coordinate Expansion for I(x,t) as t →> 0
28(11)
4.3 Coordinate Expansion for η(x,t) as t → 0
39(4)
5 Coordinate Expansions for η(x,t) as |x|→ ∞
43(24)
5.1 Coordinate Expansion for/(x,t) as |x| → ∞
43(21)
5.1.1 Coordinate Expansion for I(x,t) with t = 0 (x-1/2) as |x| → ∞
55(5)
5.1.2 Coordinate Expansion for I(x,t) with t ≤ 0(1) as |x| → ∞
60(2)
5.1.3 Coordinate Expansion for η (x,t) as |x| → ∞
62(2)
5.2 Coordinate Expansion for η(x,t) as |x| → ∞
64(3)
6 Coordinate Expansions for η (x,t) as t → ∞
67(58)
6.1 Outer Region Coordinate Expansion for η (x,t) as t → ∞
67(2)
6.2 Outer Region Coordinate Expansions for7+(y,t) and J- (y,t) as t → ∞
69(20)
6.3 Outer Region Coordinate Expansions for F(y,t) as t → ∞
89(15)
6.4 Outer Region Coordinate Expansions for η (y,t) as t → ∞
104(5)
6.5 Inner Region Coordinate Expansions for J+ (y,t) and J-(y,t) as → ∞
109(3)
6.6 Inner Region Coordinate Expansions for F(y,t) as t → ∞
112(10)
6.7 Inner Region Coordinate Expansion for η(y,t) as t→ ∞
122(3)
7 Summary of the Asymptotic Structure of η(x,t) as t → 0 and t → ∞
125(12)
7.1 Exact Solution for η (x,t)
125(1)
7.2 Asymptotic Structure of η(x,t) as t → 0
125(4)
7.3 Asymptotic Structure of η(x,t) as t → ∞
129(8)
8 Numerical Evaluation of the Exact Form of → (x,t)
137(6)
9 Comparison with the Linearised Shallow Water Theory
143(10)
9.1 Linearised Shallow Water Theory
143(2)
9.2 Comparison of the Linearised Shallow Water Theory with the Full Linearised Theory
145(3)
9.3 Comparison of the Linearised Shallow Water Theory with the Numerical Approximation
148(2)
9.4 Conclusions
150(3)
Bibliography 153(2)
Index 155
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