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1 2004

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The transformational analytical solution for nonlinear convection in the presence of two-way rotation

El-Kholy S. A., Ismail I. A.

Mechanics and Mechanical Engineering

2004

Vol. 7, nr 1

119-130

Steady two-dimensional finite amplitude solutions are obtained for the problem of convection in a horizontal fluid layer heated from below and rotated about its vertical axis. The flow is assumed to be laminar and two-dimensional. The density variation is taken into account by the Boussinesq approximation. Different boundaries with prescribed constant temperature are assumed and the solutions are obtained. The transform for summing the variables, which reduce the nonlinear partial differential equation into ordinary differential equation of the high order, is used. The existence of steady subcritical finite amplitude solutions is demonstrated for different Prandtl numbers. A strong reduction in the domain of stable rolls that occurs as the rotation rate is increasing. Convection driven by thermal buoyancy in the presence of the Coriolis force occurs in planetary atmospheres and interiors. Asymptotic expressions for the onset of convection in a horizontal fluid layer of finite extent heated from below and rotating about a vertical axis are derived in the limit of large rotation rates in the case of stress-free upper and lower boundaries. In the presence of the vertical sidewalls the critical Rayleigh number R is much lower than the classical value of the infinity extended layer.