# On the radiation of short surface waves by a heaving circular cylinder

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17 citations

5 citations

### Cites methods from "On the radiation of short surface w..."

...The method of solution is the systematic method of matched asymptotic expansions developed by Van Dyke (1964) as applied t o problems involving short surface waves by Leppington (1972, 1973a, b ) , Ayad & Leppington (1977) and Alker (1974, 1975)....

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4 citations

### Cites methods from "On the radiation of short surface w..."

...T he h e a v i n g s e m i c i r c u l a r c y l i n d e r As an example of the method, consider the geometry studied by Ursell (1953), Alker (1975) and Rhodes-Robinson (1982); later the generalization to other bodies will be described....

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...For the heaving semicircular cylinder this was first derived by Ursell (1953) using rigorous arguments, and later by Rhodes-Robinson (1970a, b), Hermans (1972) and Alker (1975) using simpler, but non-rigorous, methods....

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...(11.4) The result (11.1), given here for the first time, was derived by integrating the matched asymptotic solution of Alker (1975); this is therefore not a possible technique for other two-dimensional geometries without an amount of work at least as great as his....

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1 citations

##### References

2,966 citations

### "On the radiation of short surface w..." refers methods in this paper

...This method was intuitively similar to Van Dyke's [ 3 ] method of matched asymptotic expansions in that the solution was approximated by different asymptotic expansions in different regions....

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83 citations

### "On the radiation of short surface w..." refers methods in this paper

...The matching principle to be used is a modified version of that proposed by Van Dyke [-3] : the modification due to Crighton and Leppington [ 9 ] stipulates that all terms of the form e~ log e, e~ log log e must be grouped with e~ for matching purposes....

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69 citations

### "On the radiation of short surface w..." refers methods in this paper

...A rigorous treatment of this problem has been given by Ursell [ 1 ], who obtained a first order estimate of the amplitude of the generated surface waves and the virtual mass of the cylinder....

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30 citations

### "On the radiation of short surface w..." refers methods in this paper

...by Van Dyke [-3] as applied to short surface wave problems by Leppington [ 4 , 5, 6], Ayad [7] and Alker [8]....

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17 citations

### "On the radiation of short surface w..." refers background or methods in this paper

...As Leppington [ 5 ] has already given a formulation of this problem to first order, details will be kept to a minimum....

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...by Van Dyke [-3] as applied to short surface wave problems by Leppington [4, 5 , 6], Ayad [7] and Alker [8]....

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