Conformal mapping of the Gulf of Gdañsk onto a canonical domain

Oceanologia

关键词: Shoreline;    Conformal mapping;    Domain of solution;    Computational domain;    Inversion;    Schwarz-Christoffel function;    Inverse of a function;   

DOI  :  

来源: DOAJ

【 摘 要 】

Thepaper deals with the conformal mapping of a plane, finite, simply connecteddomain, representing the southern segment of the Gulf of Gdansk, enclosedfrom the North by a parallel, tangential to Cape Rozewie. The segment containsthe Hel Peninsula.
The method of double decomposition, presented in Prosnak & Czesnik (2001), is applied to the transformation of such an original domain onto a canonical one, which consists of two separate unit discs.
The first decomposition concerns the domain which is split into two adjacent subdomains by means of a segment of a straight line.
The second decomposition involves two holomorphic functions,each one mapping a subdomain onto a separate disc. The decomposition consistsin replacing the function by a sequence of simple ones, so that the mappingis performed step-wise. Each sequence starts with the Schwarz-Christoffel function, the last step consisting in an inversion that transforms aninfinite circular domain onto a disc.
The data for the problem is contained in the Annex, and is representedby two sets of rectangular coordinates defining consecutive discrete pointsof the contours bounding the subdomains.
The solution to the problem consists of:
- two sets of functions, consecutively transforming each of the subdomains;
- the numerical values of the parameters of these functions;
- a set of figures illustrating the consecutive transformations.
The accuracy of the first, and of the penultimate transformation aregiven, because only in the case of these two functions do the unknown coefficientshave to be determined by means of a suitable iterative process. The coefficientsof all the remaining functions are evaluated from exact formulae.
It should be recalled that the depth of the Gulf of Gdansk variesconsiderably -from a few to 110 metres - the gradients of the bottom beingrather large. Therefore, the domain of the solution for any mathematicalproblem describing the hydrodynamical phenomena occurring in the Gulf isusually taken to be three-dimensional. Nevertheless, the paper deals with thetransformation of the free surface of the Gulf, assumed as plane. It should be emphasized that this assumption does not mean that the whole domain of the solution has to be regarded as plane.

【 授权许可】

Unknown