A PSEUDOSPECTRAL CODE FOR CONVECTION WITH AN ANALYTICAL/NUMERICAL IMPLEMENTATION OF HORIZONTAL BOUNDARY CONDITIONS
✍ Scribed by S. M. Cox; P. C. Matthews
- Publisher
- John Wiley and Sons
- Year
- 1997
- Tongue
- English
- Weight
- 367 KB
- Volume
- 25
- Category
- Article
- ISSN
- 0271-2091
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✦ Synopsis
A new code for simulating convection in a horizontal layer of ¯uid is described. The code can be used to study the usual Rayleigh±Be Ânard convection problem but can also incorporate internal heating, rotation and the vortex force responsible for Langmuir circulation. Boundary conditions in the horizontal directions are periodic, but a wide range of conditions may be imposed on the upper and lower boundaries.
A novel feature of the method is the way in which these boundary conditions are implemented through the following analyticalanumerical technique. The governing partial differential equations are reduced to a number of inhomogeneous second-order ODEs for the horizontal Fourier modes. The solutions to these are then written as the sum of a particular integral and a complementary function. The former is easily computed (numerically) without regard to the boundary conditions and the latter is then selected (analyticallyanumerically) to ensure that the boundary conditions are met.
We apply our code to the problem of highly supercritical thermal convection in a shear ¯ow. We compare our results with simulations in the literature and, by integrating over a longer time interval, ®nd ¯ow features not observed in the previous simulations, including stable time-dependent states, multiple stable equilibria and chaos.