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Issue
Korean Journal of Chemical Engineering,
Vol.13, No.2, 136-143, 1996
LOW DIMENSIONAL MODELING OF TURBULENT THERMAL CONVECTION
Park HM
The Karhunen-Loeve decomposition is used to obtain a low dimensional model describing the dynamics of turbulent thermal convection in a finite box. The Karhunen-Loeve decomposition is a procedure for decomposing a stochastic field in an optimal way such that the stochastic field can be represented with a minimum number of degree of freedom. Numerical data for the turbulent thermal convection, generated by a pseudo-spectral method for the case of Pr=0.72 and aspect ratio=2, are processed by means of Karhunen-Loeve decomposition to yield a set of empirical eigenfunctions. A Galerkin procedure employing this set of empirical eigenfunctions reduces the Boussinesq equation to a small number of ordinary differential equations. this low dimensional model obtained from numerical data at the reference Rayleigh number of 70 times the critical Rayleigh number is found to predict turbulent convection reasonably well over a range of Rayleigh numbers around the reference value.
Keywords: Turbulence; Thermal Convection; Karhunen-Loeve Decomposition; Direct Spectral Simulation; Low Dimensional Dynamics
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