Kelvin waves in a shoaling shallow sea

Jesuthasan, Vasthiampillai Joseph (2009) Kelvin waves in a shoaling shallow sea. Doctoral thesis, London Metropolitan University.


We revisit Taylor's problem and discuss some model test problems both through Taylor's approach and other numerical methods such as a 'Finite approximation method' and 'Green's function technique'. The solutions generated by each method are compared for consistency. The objective lies in the fact that the more difficult generalization of Taylor's problem where the sea floor is in the form of a slope may be reduced to a sequence of problems, each of which may be approached by the techniques described above.
The Taylor's problem is effected with three mutually independent techniques in order to get insight of the problem and to obtain consistent solutions by these methods.
The problem of a propagation of a Kelvin wave over a step-bottom in a semi-infinite canal closed at one end is considered.
The solution obtained is compared with that generated by the long-time limit of a numerical solution for the time dependent initial value problem. A mean square error analysis indicate gOod agreement. Diagrams for co-range and co-tidal lines are displayed and it is found that the amphidromic points align along the central axes of the channel. This accounts for nondissipation of wave energy.
Two methods of solution are presented for the problem of a Kelvin wave propagation over a step in an infinite channel open at both ends.
One of the methods is the 'collocation method' which was first used by Defant (1960). The second method is a Fourier series method where the Kelvin wave system is first expanded as a half-range Fourier series. This idea was first used by Taylor (1921) in the analytical representation of the reflection of a Kelvin wave in a senii-infinite channel closed at one end.
Similar solutions are obtained and diagrams for 'co-range' and 'phase lines* are displayed. It is found that the amphidromic points are displaced from the central axis towards the east and this is attributed to a loss of reflected energy in that region.
Finally the problem of a Kelvin wave propagation over a step is generalized by assurning a sloping sea bed instead and treating the problem as two semi-infinite channels connected by a slope-like bottom topography. A technique is proposed to solve this system for the simplest configuration but in principle the technique should be extendable to deal with a more general situation.

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