DEVELOPMENT OF A VIRTUAL NUMERICAL LABORATORY FOR EARTH-PLANETARY FLUID DYNAMICS USING SPECTRAL METHODS

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The research was accomplished aiming to construct a virtual "numerical laboratory" of earth planetary fluid in the Internet.As for the development of necessary spectral methods, a new spectral method was developed for shallow water equations on a disk, the details of which are published as two original papers. This method uses Jacobi polynomials as a basis of expansion to avoid the singularity at the origin which often appears when the polar coordinate is adopted. The novelty of the method is in expanding vector fields directly.In addition, new spectral methods for 1d/2d infinite domains are developed, and the paper is being prepared now. By using this technique, numerical experiments of gravity wave radiation from an unstable jet in a shallow water system are conducted. The parameter dependency of the gravity waves are examined, and it is contributing as a submitted paper. The developed numerical library is distributed freely as http://www.gfd-dennou.org/arch/ispack/ispack-0.62beta.tar.gz. Furthermore, the first textbook for spectral methods in Japanese is published based on the experiences in the development of the numerical library.To provide the virtual laboratory environment, a firm web server is newly started up, which maintains not only the source code of a series of developed spectral models for the earth planetary fluid calculation and the explanation, but also the execution result of a typical exercise. The contents are distributed freely as http://www.gfd-dennou.org/arch/spmodel/.